% Encoding: UTF-8
@Article{dovidio08,
author = {{d'Ovidio}, F. and J. Isern-Fontanet and C. Lopez and E. Hernandez-Garcia and E. Garcia-Ladona},
title = {Comparison between {Eulerian} diagnostics and finite-size {Lyapunov} exponents computed from altimetry in the {Algerian} basin},
journal = {Deep-Sea Res. Pt. I},
year = {2009},
volume = {56},
pages = {15--31},
doi = {10.1016/j.dsr.2008.07.014},
}
@Book{Sniatycki13,
Title = {Differential Geometry of Singular Spaces and Reduction of Symmetry},
Author = {{\'S}niatycki, J.},
Publisher = {Cambridge Univ. Press},
Year = {2013},
Address = {Cambridge},
DOI = {10.1017/cbo9781139136990}
}
@Article{ABBR12,
Title = {Algorithm 924: {TIDES}, a {Taylor} series integrator for differential equations},
Author = {Abad, A. and Barrio, R. and Blesa, F. and Rodr{\'i}guez, M.},
Journal = {ACM Trans. Math. Softw.},
Year = {2012},
Pages = {5:1--5:28},
Volume = {39},
DOI = {10.1145/2382585.2382590}
}
@Article{AbBrKe91,
author = {H. D. I. Abarbanel and R. Brown and M. B. Kennel},
title = {{Lyapunov} exponents in chaotic systems: their importance and their evaluation using observed data},
journal = {Int. J. Mod. Phys. B},
year = {1991},
volume = {5},
pages = {1347--1375},
doi = {10.1142/s021797929100064x},
}
@Article{AbBrKe91a,
author = {H. D. I. Abarbanel and R. Brown and M. B. Kennel},
title = {Variation of {Lyapunov} exponents on a strange attractor},
journal = {J. Nonlin. Sci.},
year = {1991},
volume = {1},
pages = {175--199},
doi = {10.1007/bf01209065},
}
@Article{ACFK09,
author = {H. D. I. Abarbanel and D. R. Creveling and R. Farsian and M. Kostuk},
title = {Dynamical state and parameter estimation},
journal = {SIAM J. Appl. Math.},
year = {2009},
volume = {8},
pages = {1341--1381},
doi = {10.1137/090749761},
}
@Article{AABHM99,
Title = {Rational dynamical zeta functions for birational transformations},
Author = {Abarenkova, N. and Angl{\`e}s d'Auriac, J.-Ch. and Boukraa, S. and Hassani, S. and Maillard, J.-M.},
Journal = {Physica A},
Year = {1999},
Pages = {264--293},
Volume = {264},
DOI = {10.1016/S0378-4371(98)00452-X}
}
@Article{asNHAM07,
Title = {{Newton}-homotopy analysis method for nonlinear equations},
Author = {Abbasbandy, S. and Tan, Y. and Liao, S. J.},
Journal = {Appl. Math. Comput.},
Year = {2007},
Pages = {1794--1800},
Volume = {188},
DOI = {10.1016/j.amc.2006.11.136}
}
@Book{ablowbook,
Title = {Solitions, Nonlinear Evolution Equations and Inverse Scattering},
Author = {M. J. Ablowitz and P. A. Clarkson},
Publisher = {Cambridge Univ. Press},
Year = {1992},
Address = {Cambridge}
}
@Article{Abraham95,
author = {N. B. Abraham and U. A. Allen and E. Peterson and A. Vicens and R. Vilaseca and V. Espinosa and G. L. Lippi},
title = {Structural similarities and differences among attractors and their intensity maps in the laser-{Lorenz} model},
journal = {Optics Commun.},
year = {1995},
volume = {117},
pages = {367--384},
doi = {10.1016/0030-4018(95)00087-o},
}
@Book{AbrMars78,
title = {{Foundations of Mechanics}},
publisher = {Benjamin-Cummings},
year = {1978},
author = {R. Abraham and J. E. Marsden},
isbn = {9780821869505},
address = {Reading, MA},
doi = {10.1090/chel/364},
}
@Book{mta,
Title = {Manifolds, Tensor Analysis, and Applications},
Author = {R. Abraham and J. E. Marsden and T. S. Ratiu},
Publisher = {Springer},
Year = {1988},
Address = {New York},
Edition = {2\textsuperscript{nd}}
}
@Article{AbSm70,
author = {R. Abraham and S. Smale},
title = {Nongenericity of {$\Omega$}-stability},
journal = {Proc. Symp. Pure Math.},
year = {1970},
volume = {14},
pages = {5--8},
doi = {10.1090/pspum/014/0271986},
}
@Book{AbSh92,
Title = {Dynamics - The Geometry of Behavior},
Author = {R. H. Abraham and C. D. Shaw},
Publisher = {Wesley},
Year = {1992},
Address = {Reading, MA}
}
@Article{Abramov09,
Title = {Short-time linear response with reduced-rank tangent map},
Author = {R. V. Abramov},
Journal = {Chin. Ann. Math.},
Year = {2009},
Pages = {447--462},
Volume = {30},
DOI = {10.1007/s11401-009-0088-3}
}
@Article{Abramov10,
Title = {Approximate linear response for slow variables of dynamics with explicit time scale separation},
Author = {R. V. Abramov},
Journal = {J. Comput. Phys.},
Year = {2010},
Pages = {7739--7746},
Volume = {229},
DOI = {10.1016/j.jcp.2010.06.029}
}
@Article{Abramov12a,
Title = {A simple linear response closure approximation for slow dynamics of a multiscale system with linear coupling},
Author = {Abramov, R. V.},
Journal = {Multiscale Modeling \&\ Simulation},
Year = {2012},
Pages = {28--47},
Volume = {10},
DOI = {10.1137/110844696}
}
@Article{Abramov12,
Title = {Improved linear response for stochastically driven systems},
Author = {Abramov, R. V.},
Journal = {Front. Math. China},
Year = {2012},
Pages = {199--216},
Volume = {7},
DOI = {10.1007/s11464-012-0192-7}
}
@Article{Abramov14,
author = {Abramov, R. V.},
title = {Linear response of the {Lyapunov} exponent to small external perturbations},
journal = {Commun. Math. Sci.},
year = {2016},
volume = {14},
pages = {1155--1167},
doi = {10.4310/cms.2016.v14.n4.a14},
}
@Article{AbrKje13,
author = {{Abramov}, R. V. and {Kjerland}, M. P.},
title = {The response of reduced models of multiscale dynamics to small external perturbations},
journal = {Commun. Math. Sci.},
year = {2016},
volume = {14},
pages = {831--855},
doi = {10.4310/cms.2016.v14.n3.a10},
}
@Article{AbrMaj08,
Title = {New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems},
Author = {Abramov, R. V. and Majda, A. J.},
Journal = {J. Nonlinear Sci.},
Year = {2008},
Pages = {303--341},
Volume = {18},
DOI = {10.1007/s00332-007-9011-9}
}
@Article{AS87,
author = {M. S. Acarlar and C. R. Smith},
title = {A study of hairpin vortices in a laminar boundary layer: {Part 1. Hairpin} vortices generated by a hemisphere protuberance},
journal = {J. Fluid Mech.},
year = {1987},
volume = {175},
pages = {1--41},
doi = {10.1017/S0022112087000272},
}
@Article{ABDFHKK16,
Title = {Dynamical playground of a higher-order cubic {Ginzburg-Landau} equation: {From} orbital connections and limit cycles to invariant tori and the onset of chaos},
Author = {V. Achilleos and A. R. Bishop and S. Diamantidis and D. J. Frantzeskakis and T. P. Horikis and N. I. Karachalios and P. G. Kevrekidis},
Journal = {Phys. Rev. E},
Year = {2016},
Volume = {94},
DOI = {10.1103/physreve.94.012210}
}
@Book{Adams:2003wi,
title = {{Sobolev Spaces}},
publisher = {Academic},
year = {2003},
author = {Adams, R. A. and Fournier, J. J. F.},
address = {New York},
edition = {2},
isbn = {9780080541297},
}
@Article{AdChDj12,
Title = {Travelling wave solution of the {Kuramoto-Sivashinsky} equation: A computational study},
Author = {Aderogba, A. A. and Chapwanya, M. and Djoko, J. K.},
Journal = {AIP Conf. Proc.},
Year = {2012},
Pages = {777--780},
Volume = {1479},
DOI = {10.1063/1.4756252}
}
@Article{AdKoMc65,
Title = {Topological entropy},
Author = {R.C. Adler and A.C. Konheim and M.H. McAndrew},
Journal = {Trans. Amer. Math. Soc.},
Year = {1965},
Pages = {309--319},
Volume = {114},
DOI = {10.2307/1994177}
}
@Article{AdWei67,
Title = {Entropy, a complete metric invariant for automorphisms of the torus},
Author = {Adler, R. L. and Weiss, B.},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1967},
Pages = {1573--1576},
Volume = {57},
DOI = {10.1073/pnas.57.6.1573}
}
@Book{AdWei70,
Title = {Similarity of automorphisms of the torus},
Author = {Adler, R. L. and Weiss, B.},
Publisher = {Amer. Math. Soc.},
Year = {1970},
Address = {Providence RI},
DOI = {10.1090/memo/0098},
ISBN = {978-0-8218-1298-3},
Series = {Memoirs Amer. Math. Soc.},
Volume = {98}
}
@Article{AfAkSo96,
Title = {Three forms of localized solutions of the quintic complex {Ginzburg-Landau} equation},
Author = {Afanasjev, V. V. and Akhmediev, N. and Soto-Crespo, J. M.},
Journal = {Phys. Rev. E},
Year = {1996},
Pages = {1931},
Volume = {53},
DOI = {10.1103/PhysRevE.53.1931}
}
@Article{AfrPes90,
Title = {Hyperbolicity of infinite-dimensional drift systems},
Author = {V. S. Afraimovich and Ya. B. Pesin},
Journal = {Nonlinearity},
Year = {1990},
Pages = {1--19},
Volume = {3},
DOI = {10.1088/0951-7715/3/1/001}
}
@InProceedings{sunil_ahuja_template-based_2006,
Title = {Template-based stabilization of relative equilibria},
Author = {S. Ahuja and {I.G.} Kevrekidis and {C.W.} Rowley},
Booktitle = {2006 American Control Conference, 14-16 June 2006},
Year = {2006},
Address = {Piscataway, NJ},
Pages = {3606--3611},
Publisher = {{IEEE}},
DOI = {10.1109/ACC.2006.1657278}
}
@Article{ahuja_template-based_2007,
Title = {Template-based stabilization of relative equilibria in systems with continuous symmetry},
Author = {S. Ahuja and I. G. Kevrekidis and C. W. Rowley},
Journal = {J. Nonlin. Sci.},
Year = {2007},
Pages = {109--143},
Volume = {17},
DOI = {10.1007/s00332-005-0801-7}
}
@Book{Aitken39,
title = {{Determinants \&\ Matrices}},
publisher = {Oliver \&\ Boyd},
year = {1939},
author = {Aitken, A.C.},
address = {Edinburgh},
isbn = {9781473347106},
}
@Article{AiLVWa16,
author = {Aizenman, M. and La{\'i}nz Valc{\'a}zar, M. and Warzel, S.},
title = {Pfaffian correlation functions of planar dimer covers},
journal = {J. Stat. Phys.},
year = {2017},
volume = {166},
pages = {1078--1091},
doi = {10.1007/s10955-016-1684-8},
}
@Article{Akhmediev95,
Title = {Novel arbitrary-amplitude soliton solutions of the cubic-quintic complex {Ginzburg-Landau} Eequation},
Author = {Akhmediev, N. and Afanasjev, V. V.},
Journal = {Phys. Rev. Lett.},
Year = {1995},
Pages = {2320--2323},
Volume = {75},
DOI = {10.1103/PhysRevLett.75.2320}
}
@Book{Akhmediev05,
Title = {Dissipative Solitons},
Author = {Akhmediev, N. and Ankiewicz, A.},
Publisher = {Springer},
Year = {2005},
Address = {Berlin}
}
@Article{Akhmediev03,
Title = {Exploding solitons and {Shil'nikov's} theorem},
Author = {Akhmediev, N and Soto-Crespo, J. M.},
Journal = {Phys. Lett. A},
Year = {2003},
Pages = {287--292},
Volume = {317},
DOI = {10.1016/j.physleta.2003.08.060}
}
@Article{Akhmediev04,
Title = {Strongly asymmetric soliton explosions},
Author = {Akhmediev, N. and Soto-Crespo, J. M.},
Journal = {Phys. Rev. E},
Year = {2004},
Volume = {70},
DOI = {10.1103/PhysRevE.70.036613}
}
@Article{AkhSotTow01,
Title = {Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: {Complex Ginzburg-Landau} equation approach},
Author = {Akhmediev, N. and Soto-Crespo, J. M. and Town, G.},
Journal = {Phys. Rev. E},
Year = {2001},
Pages = {056602},
Volume = {63},
DOI = {10.1103/PhysRevE.63.056602}
}
@Article{Akhmediev95b,
Title = {Singularities and special soliton solutions of the cubic-quintic complex {Ginzburg-Landau} equation},
Author = {Akhmediev, N. N. and Afanasjev, V. V. and Soto-Crespo, J. M.},
Journal = {Phys. Rev. E.},
Year = {1996},
Pages = {1190},
Volume = {53},
DOI = {10.1103/PhysRevE.53.1190}
}
@Article{AWGBG16,
author = {Akila, M. and {Waltner}, D. and {Gutkin}, B. and {Braun}, P. and {Guhr}, T.},
title = {Semiclassical identification of periodic orbits in a quantum many-body system},
journal = {Phys. Rev. Lett.},
year = {2017},
volume = {118},
pages = {164101},
doi = {10.1103/physrevlett.118.164101},
}
@Article{AllgGeorg88,
Title = {Numerically stable homotopy methods without an extra dimension},
Author = {E. L. Allgower and K. Georg},
Journal = {Lect. Appl. Math.},
Year = {1990},
Pages = {1--13},
Volume = {26},
URL = {http://www.math.colostate.edu/emeriti/georg/homExtra.pdf}
}
@Article{Allroth83,
Title = {Ground state of one-dimensional systems and fixed points of 2n-dimensional map},
Author = {E. Allroth},
Journal = {J. Phys. A},
Year = {1983},
Pages = {L497},
Volume = {16},
DOI = {10.1088/0305-4470/16/14/002}
}
@Article{AltTel08,
author = {Altmann, E. G. and T\'el, T.},
title = {Poincar\'e recurrences and transient chaos in systems with leaks},
journal = {Phys. Rev. E},
year = {2009},
volume = {79},
pages = {016204},
doi = {10.1103/physreve.79.016204},
}
@Article{alvarez_monodromy_2005,
author = {M. Alvarez},
title = {Monodromy and stability for nilpotent critical points},
journal = {Int. J. Bifur. Chaos},
year = {2005},
volume = {15},
pages = {1253--1265},
doi = {10.1142/s0218127405012740},
}
@Misc{Alves06,
Title = {Chaotic dynamics: physical measures and statistical features},
Author = {Alves, J. F.},
Year = {2006},
URL = {http://cmup.fc.up.pt/cmup/jfalves/CIM.pdf}
}
@Incollection{AlvSou13,
Title = {Statistical stability in chaotic dynamics},
Author = {Alves, J. F. and Soufi, M.},
Booktitle = {Progress and Challenges in Dynamical Systems},
Publisher = {Springer},
Year = {2013},
Address = {New York},
Editor = {Ib\'a\~nez, S. and P\'erez del Río, J. S. and Pumari\~no, A. and Rodríguez, J. \'A.},
Pages = {7--24},
Volume = {54},
DOI = {10.1007/978-3-642-38830-9_2}
}
@Article{AmLeAg06,
Title = {Piecewise affine models of chaotic attractors: {The R\"ossler} and {Lorenz} systems},
Author = {G. F. V. Amaral and C. Letellier and L. A. Aguirre},
Journal = {Chaos},
Year = {2006},
Pages = {013115},
Volume = {16},
DOI = {10.1063/1.2149527}
}
@Article{AmZaSa10,
Title = {Permutation complexity of spatiotemporal dynamics},
Author = {J. M. Amig{\'o} and S. Zambrano and M. A. F. Sanju{\'a}n},
Journal = {Europhys. Lett.},
Year = {2010},
Pages = {10007},
Volume = {90},
DOI = {10.1209/0295-5075/90/10007}
}
@Article{NLA:NLA198,
Title = {Almost block diagonal linear systems: sequential and parallel solution techniques, and applications},
Author = {Amodio, P. and Cash, J. R. and Roussos, G. and Wright, R. W. and Fairweather, G. and Gladwell, I. and Kraut, G. L. and Paprzycki, M.},
Journal = {Numer. Linear Algebra Appl.},
Year = {2000},
Pages = {275--317},
Volume = {7},
DOI = {10.1002/1099-1506(200007/08)7:5<275::AID-NLA198>3.0.CO;2-G}
}
@Article{AGGN91,
Title = {Stability of periodic orbits of coupled-map lattices},
Author = {Amritkar, R. E. and Gade, P. M. and Gangal, A. D. and Nandkumaran, V. M.},
Journal = {Phys. Rev. A},
Year = {1991},
Pages = {R3407--R3410},
Volume = {44},
DOI = {10.1103/PhysRevA.44.R3407}
}
@Article{AnBoAi07,
author = {Ando, H. and Boccaletti, S. and Aihara, K.},
title = {Automatic control and tracking of periodic orbits in chaotic systems},
journal = {Phys. Rev. E},
year = {2007},
volume = {75},
pages = {066211},
doi = {10.1103/physreve.75.066211},
}
@Article{angen88,
author = {S. B. Angenent},
title = {The periodic orbits of an area preserving twist-map},
journal = {Commun. Math. Phys.},
year = {1988},
volume = {115},
pages = {353--374},
doi = {10.1007/bf01218016},
}
@Article{AnBoMa99,
Title = {Functional relations in lattice statistical mechanics, enumerative combinatorics, and discrete dynamical systems},
Author = {Angl{\`e}s d'Auriac, J.-Ch. and Boukraa, S. and Maillard, J.-M.},
Journal = {Ann. Comb.},
Year = {1999},
Pages = {131--158},
Volume = {3},
DOI = {10.1007/BF01608780}
}
@Article{anosov67,
author = {D. V. Anosov},
title = {Geodesic flows on compact {Riemannian} manifolds of negative curvature},
journal = {Proc. Steklov Inst. of Math.},
year = {1967},
volume = {90},
pages = {1–235},
annote = {His famous paper about Anosov systems?},
url = {http://mi.mathnet.ru/eng/tm2795},
}
@Book{AnAr88,
Title = {{Dynamical Systems {I}: {Ordinary} Differential Equations and Smooth Dynamical Systems}},
Author = {D. V. Anosov and V. I. Arnol'd},
Publisher = {Springer},
Year = {1988},
Address = {New York}
}
@Article{AokKus00a,
Title = {Bulk properties of anharmonic chains in strong thermal gradients: non-equilibrium {$\phi^4$} theory},
Author = {K. Aoki and D. Kusnezov},
Journal = {Phys. Lett. A},
Year = {2000},
Pages = {250--256},
Volume = {265},
DOI = {10.1016/S0375-9601(99)00899-3}
}
@Article{AokKus00b,
Title = {Non-equilibrium steady states and transport in the classical lattice {$\phi^4$} theory},
Author = {K. Aoki and D. Kusnezov},
Journal = {Phys. Lett. B},
Year = {2000},
Pages = {348--354},
Volume = {477},
DOI = {10.1016/S0370-2693(00)00189-1}
}
@Article{AokKus02,
Title = {Nonequilibrium statistical mechanics of classical lattice {$\phi^4$} field theory},
Author = {K. Aoki and D. Kusnezov},
Journal = {Ann. Phys.},
Year = {2002},
Pages = {50--80},
Volume = {295},
DOI = {10.1006/aphy.2001.6207}
}
@Article{AokKus03,
Title = {Violations of local equilibrium and linear response in classical lattice systems},
Author = {K. Aoki and D. Kusnezov},
Journal = {Phys. Lett. A},
Year = {2003},
Pages = {377--381},
Volume = {309},
DOI = {10.1016/S0375-9601(03)00293-7}
}
@Article{Arai07a,
Title = {On hyperbolic plateaus of the {H\'enon} map},
Author = {Arai, Z.},
Journal = {Experimental Math.},
Year = {2007},
Pages = {181--188},
Volume = {16},
DOI = {10.1080/10586458.2007.10128992}
}
@Article{Arai07b,
author = {Arai, Z.},
title = {On loops in the hyperbolic locus of the complex {H\'enon} map and their monodromies},
journal = {Physica D},
year = {2016},
volume = {334},
pages = {133--140},
doi = {10.1016/j.physd.2016.02.006},
}
@Article{ArMi06,
Title = {Rigorous computations of homoclinic tangencies},
Author = {Arai, Z. and Mischaikow, K.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2006},
Pages = {280--292},
Volume = {5},
DOI = {10.1137/050626429}
}
@Article{AGRS86,
Title = {Strange attractors and the spatial development of turbulence in flow systems},
Author = {Aranson, I. S. and {Gaponov-Grekhov}, A. V. and {Rabinovich}, M. I. and {Starobinets}, I. M.},
Journal = {Sov. Phys. JETP},
Year = {1986},
Pages = {1000},
Volume = {63},
URL = {http://jetp.ac.ru/cgi-bin/dn/e_063_05_1000.pdf}
}
@Article{AKcgl02,
Title = {The world of complex {Ginzburg-Landau} equation},
Author = {I. S. Aranson and L. Kramer},
Journal = {Rev. Mod. Phys.},
Year = {2002},
Pages = {99--143},
Volume = {74},
DOI = {10.1103/RevModPhys.74.99}
}
@Book{ArWe05,
title = {{Mathematical Methods for Physicists: A Comprehensive Guide}},
publisher = {Academic},
year = {2005},
author = {G. B. Arfken and H. J. Weber},
isbn = {9780120598762},
address = {New York},
edition = {6},
}
@Article{ArCho91,
Title = {Heteroclinic orbits in a spherically invariant system},
Author = {D. Armbruster and P. Chossat},
Journal = {Physica D},
Year = {1991},
Pages = {155--176},
Volume = {50},
DOI = {10.1016/0167-2789(91)90173-7}
}
@Article{AGHO288,
Title = {Heteroclinic cycles and modulated travelling waves in systems with {O}(2) symmetry},
Author = {D. Armbruster and J. Guckenheimer and P. Holmes},
Journal = {Physica D},
Year = {1988},
Pages = {257--282},
Volume = {29},
DOI = {10.1016/0167-2789(88)90032-2}
}
@Article{AGHks89,
Title = {{Kuramoto-Sivashinsky} dynamics on the center-unstable manifold},
Author = {D. Armbruster and J. Guckenheimer and P. Holmes},
Journal = {SIAM J. Appl. Math.},
Year = {1989},
Pages = {676--691},
Volume = {49},
DOI = {10.1137/0149039}
}
@Article{ABBBBB08,
Title = {Universal intermittent properties of particle trajectories in highly turbulent flows},
Author = {A. Arneodo and R. Benzi and J. Berg and L. Biferale and E. Bodenschatz and A. Busse and E. Calzavarini and B. Castaing and M. Cencini and L. Chevillard and R. Fisher and R. Grauer and H. Homann and D. Lamb and A.S. Lanotte and E. Leveque and B. Luethi and J. Mann and N. Mordant and W.-C. Mueller and S. Ott and N.T. Ouellette and J.-F. Pinton and S. B. Pope and S.G. Roux and F. Toschi and H. Xu and P.K. Yeung},
Journal = {Phys. Rev. Lett.},
Year = {2008},
Volume = {100},
DOI = {10.1103/physrevlett.100.254504}
}
@Book{arnold82,
Title = {{Geometrical Methods in the Theory of Ordinary Differential Equations}},
Author = {V. I. Arnol'd},
Publisher = {Springer},
Year = {1982},
Address = {Berlin},
ISBN = {9781461210375}
}
@Book{arnold89,
title = {{Mathematical Methods for Classical Mechanics}},
publisher = {Springer},
year = {1989},
author = {V. I. Arnol'd},
address = {New York},
isbn = {9781475720631},
doi = {10.1007/978-1-4757-2063-1},
}
@Article{arnold91k,
Title = {Kolmogorov's hydrodynamic attractors},
Author = {V. I. Arnol'd},
Journal = {Proc. R. Soc. Lond. A},
Year = {1991},
Pages = {429--432},
Volume = {434},
Booktitle = {Vladimir I. Arnold - Collected Works},
DOI = {10.1007/978-3-642-31031-7_41}
}
@Book{arnold92,
Title = {{Ordinary Differential Equations}},
Author = {V. I. Arnol'd},
Publisher = {Springer},
Year = {1992},
Address = {New York}
}
@Book{ArnAve,
Title = {{Ergodic Problems of Classical Mechanics}},
Author = {V. I. Arnol'd and A. Avez},
Publisher = {Addison-Wesley},
Year = {1989},
Address = {Redwood City},
ISBN = {0201094061}
}
@Book{ArKoNe88,
title = {{Mathematical Aspects of Classical and Celestial Mechanics}},
publisher = {Springer},
year = {1988},
author = {V. I. Arnol'd and V. V. Kozlov and A. I. Neishtadt},
address = {New York},
doi = {10.1007/978-3-642-61237-4},
}
@Article{Arnoldi51,
author = {W. E. Arnoldi},
title = {The principle of minimized iterations in the solution of the matrix eigenvalue problem},
journal = {Quart. Appl. Math.},
year = {1951},
volume = {9},
pages = {17--29},
doi = {10.1090/qam/42792},
}
@Article{ArtMaz65,
Title = {On periodic points},
Author = {Artin, M. and Mazur, B.},
Journal = {Ann. Math.},
Year = {1965},
Pages = {82--99},
Volume = {81},
URL = {http://www.jstor.org/stable/1970384}
}
@Article{Artuso88,
Title = {Logarithmic strange sets},
Author = {R. Artuso},
Journal = {J. Phys. A},
Year = {1988},
Number = {19},
Pages = {L923--L927},
Volume = {21},
DOI = {10.1088/0305-4470/21/19/001}
}
@Article{art91,
Title = {Diffusive dynamics and periodic orbits of dynamic systems},
Author = {R. Artuso},
Journal = {Phys. Lett. A},
Year = {1991},
Pages = {528--530},
Volume = {160},
DOI = {10.1016/0375-9601(91)91062-I}
}
@Article{Artuso94,
Title = {Recycling deterministic diffusion},
Author = {R. Artuso},
Journal = {Physica D},
Year = {1994},
Pages = {1--7},
Volume = {76},
DOI = {10.1016/0167-2789(94)90245-3}
}
@Article{AACI,
Title = {Recycling of strange sets: {I. Cycle} expansions},
Author = {Artuso, R. and Aurell, E. and Cvitanovi\'c, P.},
Journal = {Nonlinearity},
Year = {1990},
Pages = {325--359},
Volume = {3},
DOI = {10.1088/0951-7715/3/2/005}
}
@Article{AACII,
Title = {Recycling of strange sets: {II. Applications}},
Author = {Artuso, R. and Aurell, E. and Cvitanovi\'c, P.},
Journal = {Nonlinearity},
Year = {1990},
Pages = {361--386},
Volume = {3},
DOI = {10.1088/0951-7715/3/2/006}
}
@Incollection{CBdiffusion,
Title = {Deterministic diffusion},
Author = {R. Artuso and P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#diffusion}
}
@Article{art03int,
Title = {Cycle expansions for intermittent maps},
Author = {Artuso, R. and Cvitanovi{\'c}, P. and Tanner, G.},
Journal = {Proc. Theo. Phys. Supp.},
Year = {2003},
Pages = {1--21},
Volume = {150},
DOI = {10.1143/PTPS.150.1}
}
@Article{ACK89,
Title = {Phase transitions on strange irrational sets},
Author = {Artuso, R. and Cvitanovi\'{c}, P. and Kenny, B. G.},
Journal = {Phys. Rev. A},
Year = {1989},
Pages = {268--281},
Volume = {39},
DOI = {10.1103/PhysRevA.39.268}
}
@Incollection{CBconverg,
Title = {Why does it work?},
Author = {R. Artuso and H. H. Rugh and P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#converg}
}
@Incollection{eigendensity,
Title = {Why does it work?},
Author = {R. Artuso and H. H. Rugh and P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
Editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay},
URL = {http://ChaosBook.org/paper.shtml#converg}
}
@Article{ArtStr97,
Title = {Reycling diffusion in sawtooth and cat maps},
Author = {R. Artuso and R. Strepparava},
Journal = {Phys. Lett. A},
Year = {1997},
Pages = {469--475},
Volume = {236},
DOI = {10.1016/S0375-9601(97)00792-5}
}
@Article{ASTIK09,
Title = {A numerical method for nonlinear eigenvalue problems using contour integrals},
Author = {Asakura, J. and Sakurai, T. and Tadano, H. and Ikegami, T. and Kimura, K.},
Journal = {JSIAM Lett.},
Year = {2009},
Pages = {52--55},
Volume = {1},
DOI = {10.14495/jsiaml.1.52}
}
@Article{Asami06,
author = {Asamizuya, T.},
title = {Statistical properties of periodic orbits in a 4-disk billiard system ---{The} pruning-proof property---},
journal = {Progr. Theor. Phys.},
year = {2006},
volume = {116},
pages = {247--271},
doi = {10.1143/ptp.116.247},
}
@Article{AschKnauf97,
author = {Asch, J. and Knauf, A.},
title = {Motion in periodic potentials},
journal = {Nonlinearity},
year = {1998},
volume = {11},
pages = {175--200},
doi = {10.1088/0951-7715/11/1/011},
}
@Article{Ascher95,
author = {U. Ascher and S. Ruuth and B. Wetton},
title = {Implicit-explicit methods for time-dependent partial differential equations},
journal = {SIAM J. Numer. Anal.},
year = {1995},
volume = {32},
number = {3},
pages = {797--823},
month = jun,
doi = {10.1137/0732037},
}
@Article{AshBoMe96,
author = {Ashwin, P. and B\"ohmer, K. and Mei, Z.},
title = {Forced symmetry breaking of homoclinic cycles in a {PDE} with {O(2)} symmetry},
journal = {J. Comput. Appl. Math.},
year = {1996},
volume = {70},
pages = {297--310},
doi = {10.1016/0377-0427(95)00212-x},
url = {http://wrap.warwick.ac.uk/18622/},
}
@Article{AshDang05,
author = {Ashwin, P. and Dangelmayr, G.},
title = {Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators},
journal = {Dyn. Sys.},
year = {2005},
volume = {20},
pages = {333--367},
doi = {10.1080/14689360500151813},
}
@Article{AshMe97,
author = {P. Ashwin and I. Melbourne},
title = {Noncompact drift for relative equilibria and relative periodic orbits},
journal = {Nonlinearity},
year = {1997},
volume = {10},
pages = {595--616},
doi = {10.1088/0951-7715/10/3/002},
}
@Article{AshMeNi99,
author = {P. Ashwin and I. Melbourne and M. Nicol},
title = {Drift bifurcations of relative equilibria and transitions of spiral waves},
journal = {Nonlinearity},
year = {1999},
volume = {12},
pages = {741--755},
doi = {10.1088/0951-7715/12/4/301},
}
@Article{AstMelb06,
author = {P. Aston and I. Melbourne},
title = {{Lyapunov} exponents of symmetric attractors},
journal = {Nonlinearity},
year = {2006},
volume = {19},
pages = {2455--2466},
doi = {10.1088/0951-7715/19/10/010},
}
@Article{AstDel99,
Title = {The computation of {Lyapunov} exponents via spatial integration with application to blowout bifurcations},
Author = {P. J. Aston and M. Dellnitz},
Journal = {Computer Methods Appl. Mech. Engineering},
Year = {1999},
Pages = {223--237},
Volume = {170},
DOI = {10.1016/S0045-7825(98)00196-0}
}
@Article{AstLai99,
Title = {Symmetry and chaos in the complex {Ginzburg--Landau} equation. {I. Reflectional} symmetries},
Author = {Aston, P. J. and Laing, C. R.},
Journal = {Dyn. Stab. Syst.},
Year = {1999},
Pages = {233--253},
Volume = {14},
DOI = {10.1080/026811199281985}
}
@Article{AstLai00,
Title = {Symmetry and chaos in the complex {Ginzburg--Landau} equation. {II. Translational }symmetries},
Author = {Aston, P. J. and Laing, C. R.},
Journal = {Physica D},
Year = {2000},
Pages = {79--97},
Volume = {135},
DOI = {10.1016/S0167-2789(99)00046-9}
}
@Article{Astor10,
Title = {Kauffman knot invariant from {$\mathrm{SO}(N)$ or $\mathrm{Sp}(N)$ Chern-Simons} theory and the {Potts} model},
Author = {Astorino, M.},
Journal = {Phys. Rev. D},
Year = {2010},
Pages = {125026},
Volume = {81},
DOI = {10.1103/PhysRevD.81.125026}
}
@Article{AtJaJo10,
Title = {Symbolic dynamics and synchronization of coupled map networks with multiple delays},
Author = {F. M. Atay and S. Jalan and J. Jost},
Journal = {Phys. Lett. A },
Year = {2010},
Pages = {130--135},
Volume = {375},
DOI = {10.1016/j.physleta.2010.10.044}
}
@Article{Aubry88,
author = {N. Aubry and P. Holmes and J. L. Lumley and E. Stone},
title = {The dynamics of coherent structures in the wall region of a turbulent boundary layer},
journal = {J. Fluid Mech.},
year = {1988},
volume = {192},
pages = {115},
doi = {10.1017/s0022112088001818},
}
@Article{aub95ant,
author = {S. Aubry},
title = {Anti-integrability in dynamical and variational problems},
journal = {Physica D},
year = {1995},
volume = {86},
pages = {284--296},
doi = {10.1016/0167-2789(95)00109-h},
}
@Article{AuAb90,
author = {Aubry, S. and Abramovici, G.},
title = {Chaotic trajectories in the standard map. {The} concept of anti-integrability},
journal = {Physica D},
year = {1990},
volume = {43},
pages = {199--219},
doi = {10.1016/0167-2789(90)90133-A},
}
@Article{AuDae83,
Title = {The discrete {Frenkel-Kontorova} model and its extensions. {I}. {Exact} results for the ground-states},
Author = {Aubry, S. and Le Daeron, P. Y.},
Journal = {Physica D},
Year = {1983},
Pages = {381--422},
Volume = {8},
Annote = {Original paper about Aubry-Mather sets}
}
@Article{pchaot,
Title = {Exploring chaotic motion through periodic orbits},
Author = {D. Auerbach and P. Cvitanovi{\'c} and J.-P. Eckmann and G. Gunaratne and I. Procaccia},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {2387--2389},
Volume = {58},
DOI = {10.1103/PhysRevLett.58.2387}
}
@Book{ausloos_logistic_2005,
Title = {The Logistic Map and the Route to Chaos: From the Beginnings to Modern Applications},
Author = {M. Ausloos and M. Dirickx},
Publisher = {Springer},
Year = {2005},
Address = {New York}
}
@Unpublished{AuKrTr13,
Title = {Numerical algorithms based on analytic function values at roots of unity},
Author = {Austin, A. P and Kravanja, P. and Trefethen, L. N.},
Note = {SIAM J. Numer. Anal., to appear.},
Year = {2013}
}
@Article{Auzinger2014,
Title = {Local error structures and order conditions in terms of {Lie} elements for exponential splitting schemes},
Author = {Auzinger, W. and Herfort, W.},
Journal = {Opuscula Math.},
Year = {2014},
Pages = {43--255},
Volume = {34},
DOI = {10.7494/opmath.2014.34.2.243}
}
@Article{Auzinger2016_2,
author = {Auzinger, W. and Hofst{\"{a}}tter, H. and Ketcheson, D. and Koch, O.},
title = {Practical splitting methods for the adaptive integration of nonlinear evolution equations. {Part I:} Construction of optimized schemes and pairs of schemes},
journal = {{BIT} Numer. Math.},
year = {2016},
volume = {57},
pages = {55--74},
doi = {10.1007/s10543-016-0626-9},
}
@Article{Auzinger2016,
Title = {Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions},
Author = {Auzinger, W. and Koch, O. and and Quell, M.},
Journal = {Numer. Algorithms},
Year = {2016},
Pages = {1--23},
DOI = {10.1007/s11075-016-0206-8}
}
@Article{AvMeRoHo13,
Title = {Streamwise-localized solutions at the onset of turbulence in pipe flow},
Author = {M. Avila and F. Mellibovsky and N. Roland and B. Hof},
Journal = {Phys. Rev. Lett.},
Year = {2013},
Pages = {224502},
Volume = {110},
DOI = {10.1103/PhysRevLett.110.224502}
}
@Article{AEOGS10,
Title = {Observation of periodic orbits on curved two-dimensional geometries},
Author = {Avlund, M. and Ellegaard, C. and Oxborrow, M. and Guhr, T. and S\o{}ndergaard, N.},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {164101},
Volume = {104},
DOI = {10.1103/PhysRevLett.104.164101},
Issue = {16}
}
@Article{ABLM98,
Title = {Is the geometry of nature fractal?},
Author = {Avnir, D. and Biham, O. and Lidar, D. and Malcai, O.},
Journal = {Science},
Year = {1998},
Pages = {39--40},
Volume = {279},
DOI = {10.1126/science.279.5347.39}
}
@Incollection{Axen11,
author = {Axenides, M.},
title = {Non {Hamiltonian} chaos from {Nambu} dynamics of surfaces},
booktitle = {{Chaos Theory: Modeling, Simulation and Applications}},
publisher = {World Scientific},
year = {2011},
editor = {Skiadas, C. H. and Dimotikalis, I. and Skiadas, C.},
isbn = {9789814460477},
doi = {10.1142/9789814350341_0012},
}
@Article{AxFl08,
author = {Axenides, M. and Floratos, E.},
title = {{Nambu-Lie} 3-algebras on fuzzy 3\mbox{-}{m}anifolds},
journal = {JHEP},
year = {2009},
volume = {902},
pages = {39},
doi = {10.1088/1126-6708/2009/02/039},
}
@Article{AxFl09,
author = {Axenides, M. and Floratos, E.},
title = {Strange attractors in dissipative {Nambu} mechanics: {Classical} and quantum aspects},
journal = {JHEP},
year = {2010},
volume = {1004},
pages = {036},
doi = {10.1007/JHEP04(2010)036},
}
@Article{AxFlNi09,
author = {Axenides, M. and Floratos, E.G. and Nicolis, S.},
title = {{Nambu} quantum mechanics on discrete 3-tori},
journal = {J. Phys. A},
year = {2009},
volume = {42},
pages = {275201},
doi = {10.1088/1751-8113/42/27/275201},
}
@Article{EckHoPo89,
Title = {Quantum mechanics of a classically chaotic system: Observations on scars, periodic orbits, and vibrational adiabaticity},
Author = {B. Eckhardt, G. Hose and E. Pollak},
Journal = {Phys. Rev. A},
Year = {1989},
Pages = {3776--3793},
Volume = {39},
DOI = {10.1103/PhysRevA.39.3776}
}
@Misc{BerMan13,
Title = {Spatiotemporal two-dimensional solitons in the complex {Ginzburg--Landau} equation},
Author = {B{\'e}rard, F. and Mancas, S. C.},
Year = {2013},
URL = {http://arxiv.org/abs/1302.1831}
}
@Article{Berard2015,
Title = {Two-dimensional structures in the quintic {Ginzburg--Landau} equation},
Author = {B{\'e}rard, F. and Vandamme, C.-J. and Mancas, S. C.},
Journal = {Nonlinear Dyn.},
Year = {2015},
Pages = {1413--1433},
Volume = {81},
DOI = {10.1007/s11071-015-2077-2}
}
@Article{BaTo03,
Title = {Correlation decay in certain soft billiards},
Author = {B\'alint, P. and T{\'o}th, I. P.},
Journal = {Commun. Math. Phys.},
Year = {2003},
Pages = {55--91},
Volume = {243},
DOI = {10.1007/s00220-003-0954-x}
}
@Article{BaTo04,
Title = {Mixing and its rate in `soft' and `hard' billiards motivated by the {Lorentz} process},
Author = {B\'alint, P. and T{\'o}th, I. P.},
Journal = {Physica D},
Year = {2004},
Pages = {128--135},
Volume = {187},
DOI = {10.1016/j.physd.2003.09.004}
}
@Article{BaCseGaHa08,
Title = {A computer-assisted proof of {$\Sigma_3$}-chaos in the forced damped pendulum equation},
Author = {B. B\'anhelyi and T. Csendes and B. M. Garay and L. Hatvani},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2008},
Pages = {843--867},
Volume = {7},
DOI = {10.1137/070695599}
}
@Article{benisti2010-1,
Title = {Nonlinear group velocity of an electron plasma wave},
Author = {B\'enisti, D. and Morice, O. and Gremillet, L. and Siminos, E. and Strozzi, D. J.},
Journal = {Physics of Plasmas},
Year = {2010},
Pages = {082301},
Volume = {17},
DOI = {10.1063/1.3464467}
}
@Article{benisti2010-2,
Title = {Nonlinear kinetic description of {Raman} growth using an envelope code, and comparisons with {Vlasov} simulations},
Author = {B\'enisti, D. and Morice, O. and Gremillet, L. and Siminos, E. and Strozzi, D. J.},
Journal = {Physics of Plasmas},
Year = {2010},
Pages = {102311},
Volume = {17},
DOI = {10.1063/1.3494223}
}
@Article{benisti2010,
Title = {Self-Organization and Threshold of Stimulated {Raman} Scattering},
Author = {B\'enisti, D. and Morice, O. and Gremillet, L. and Siminos, E. and Strozzi, D. J.},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {015001},
Volume = {105},
DOI = {10.1103/PhysRevLett.105.015001}
}
@Article{BaaRob97,
Title = {Reversing symmetry group of {Gl(2,z) and PGl(2,z)} matrices with connections to cat maps and trace maps},
Author = {M. Baake and J. A. G. Roberts},
Journal = {J. Phys. A},
Year = {1997},
Pages = {1549},
Volume = {30},
DOI = {10.1088/0305-4470/30/5/020}
}
@Article{BaaRob01,
Title = {Symmetries and reversing symmetries of toral automorphisms},
Author = {M. Baake and J. A. G. Roberts},
Journal = {Nonlinearity},
Year = {2001},
Pages = {R1},
Volume = {14},
DOI = {10.1088/0951-7715/14/4/201}
}
@Article{BaaRob05,
Title = {Symmetries and reversing symmetries of polynomial automorphisms of the plane},
Author = {M. Baake and J. A. G. Roberts},
Journal = {Nonlinearity},
Year = {2004},
Pages = {791--816},
Volume = {18},
DOI = {10.1088/0951-7715/18/2/017}
}
@Article{BaRoWe08,
Title = {Periodic orbits of linear endomorphisms on the 2-torus and its lattices},
Author = {M. Baake and J. A. G. Roberts and A. Weiss},
Journal = {Nonlinearity},
Year = {2008},
Pages = {2427},
Volume = {21},
DOI = {10.1088/0951-7715/21/10/012}
}
@Article{vanBaal91,
Title = {More (thoughts on) {Gribov} copies},
Author = {van Baal, P.},
Journal = {Nucl. Phys.},
Year = {1992},
Pages = {259--275},
Volume = {B369},
DOI = {10.1016/0550-3213(92)90386-P}
}
@Incollection{vanBaal97,
author = {van Baal, P.},
title = {Gribov ambiguities and the fundamental domain},
booktitle = {Confinement, Duality, and Non-Perturbative Aspects of QCD},
publisher = {Springer},
year = {2002},
editor = {van Baal, P.},
volume = {368},
series = {NATO Science Series: B},
pages = {161--178},
address = {New York},
doi = {10.1007/0-306-47056-X_7},
}
@Article{BCFLR08,
Title = {Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems},
Author = {R. Bachelard and C. Chandre and D. Fanelli and X. Leoncini and S. Ruffo},
Journal = {Phys. Rev. Lett.},
Year = {2008},
Pages = {260603},
Volume = {101}
}
@Unpublished{Bagheri12,
Title = {Spectral analysis of nonlinear flows},
Author = {Bagheri, S.},
Note = {Early version of \refref{Bagheri13}.},
Year = {2012}
}
@Unpublished{Bagheri13,
Title = {Spectral analysis of nonlinear flows},
Author = {Bagheri, S.},
Note = {Submitted to J. Fluid Mech.},
Year = {2013}
}
@Inbook{BILMR89,
Title = {Periodic orbits in a coupled map lattice model},
Author = {Bagnoli, F. and Isola, S. and Livi, R. and Mart{\'i}nez-Mekler, G. and Ruffo, S.},
Editor = {Manneville, P. and Boccara, N. and Vichniac, G. Y. and Bidaux, R.},
Pages = {282--290},
Publisher = {Springer},
Year = {1989},
Address = {Berlin},
Booktitle = {{Cellular Automata and Modeling of Complex Physical Systems: Proceedings of the Winter School, Les Houches 1989}},
DOI = {10.1007/978-3-642-75259-9_25},
ISBN = {978-3-642-75259-9}
}
@Article{Bagrinovskii57,
Title = {Difference schemes for multi-dimensional problems},
Author = {K. A. Bagrinovskii and S. K. Godunov},
Journal = {Dokl. Acad. Nauk.},
Year = {1957},
Pages = {431--433},
Volume = {115}
}
@Article{Bai06,
Title = {Multifractal analysis of the spectral measure of the {Thue-Morse} sequence: a periodic orbit approach},
Author = {Bai, Z.-Q.},
Journal = {J. Phys. A},
Year = {2006},
Pages = {10959},
Volume = {39},
DOI = {10.1088/0305-4470/39/35/002}
}
@Article{Bai07,
Title = {On the cycle expansion for the {Lyapunov} exponent of a product of random matrices},
Author = {Bai, Z.-Q.},
Journal = {J. Phys. A},
Year = {2007},
Pages = {8315},
Volume = {40},
DOI = {10.1088/1751-8113/40/29/008}
}
@Article{Bai09,
Title = {An infinite transfer matrix approach to the product of random {$2\times2$} positive matrices},
Author = {Bai, Z.-Q.},
Journal = {J. Phys. A},
Year = {2009},
Pages = {015003},
Volume = {42},
DOI = {10.1088/1751-8113/42/1/015003}
}
@Article{Bai11,
Title = {A transfer operator approach to random {Fibonacci} sequences},
Author = {Bai, Z.-Q.},
Journal = {J. Phys. A},
Year = {2011},
Pages = {115002},
Volume = {44},
DOI = {10.1088/1751-8113/44/11/115002}
}
@Article{BaBaBo12,
Title = {High-precision computation: {Mathematical} physics and dynamics},
Author = {D.H. Bailey and R. Barrio and J.M. Borwein},
Journal = {Appl. Math. Computation },
Year = {2012},
Pages = {10106--10121},
Volume = {218},
DOI = {10.1016/j.amc.2012.03.087}
}
@Article{BakasovAbraham93,
author = {Bakasov, A. A. and Abraham, N. B.},
title = {Laser second threshold: {Its} exact analytical dependence on detuning and relaxation rates},
journal = {Phys. Rev. A},
year = {1993},
volume = {48},
pages = {1633--1660},
doi = {10.1103/physreva.48.1633},
}
@Article{BMS71,
Title = {Aperiodic behavior of a non-linear oscillator},
Author = {N. H. Baker and D. W. Moore and E. A. Spiegel},
Journal = {Quatr. J. Mech. and Appl. Math.},
Year = {1971},
Pages = {391--422},
Volume = {24},
DOI = {10.1093/qjmam/24.4.391}
}
@Article{Balac2013_2,
Title = {High order embedded {Runge-Kutta} scheme for adaptive step-size control in the interaction picture method},
Author = {Balac, S.},
Journal = {J. KSIAM},
Year = {2013},
Pages = {238--266},
Volume = {17},
DOI = {10.12941/jksiam.2013.17.238}
}
@Article{Balac2013,
Title = {Embedded {Runge-Kutta} scheme for step-size control in the interaction picture method},
Author = {Balac, S. and Mah\'e, F.},
Journal = {Comput. Phys. Commun.},
Year = {2013},
Pages = {1211--1219},
Volume = {184},
DOI = {10.1016/j.cpc.2012.12.020}
}
@Article{Baladi98,
Title = {Periodic orbits and dynamical spectra},
Author = {Baladi, V.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {1998},
Pages = {255--292},
Volume = {18}
}
@Book{Baladi00,
title = {Positive transfer operators and decay of correlations},
publisher = {World Scientific},
year = {2000},
author = {Baladi, V.},
address = {Singapore},
doi = {10.1142/9789812813633},
}
@Article{Baladi07,
Title = {On the susceptibility function of piecewise expanding interval maps},
Author = {Baladi, V.},
Journal = {Commun. Math. Phys.},
Year = {2007},
Pages = {839--859},
Volume = {275},
DOI = {10.1007/s00220-007-0320-5}
}
@Article{Baladi08,
Title = {Linear response despite critical points},
Author = {V. Baladi},
Journal = {Nonlinearity},
Year = {2008},
Pages = {81--90},
Volume = {21},
DOI = {10.1088/0951-7715/21/6/T01}
}
@InProceedings{Baladi14,
author = {V. Baladi},
title = {Linear response, or else},
booktitle = {{ICM Seoul Proceedings}},
year = {2014},
volume = {3},
pages = {525--545},
url = {https://webusers.imj-prg.fr/~viviane.baladi/icm.pdf},
}
@Article{BalSma08,
author = {V. Baladi and D. Smania},
title = {Linear response formula for piecewise expanding unimodal maps},
journal = {Nonlinearity},
year = {2008},
volume = {21},
pages = {677},
doi = {10.1088/0951-7715/21/4/003},
}
@Article{BalTod15,
author = {{Baladi}, V. and {Todd}, M.},
title = {Linear response for intermittent maps},
journal = {Commun. Math. Phys.},
year = {2016},
volume = {347},
pages = {857--874},
doi = {10.1007/s00220-016-2577-z},
}
@Article{BaVo86,
author = {N. L. Balasz and A. Voros},
title = {Chaos on the pseudosphere},
journal = {Phys. Rep.},
year = {1986},
volume = {143},
pages = {109--240},
doi = {10.1016/0370-1573(86)90159-6},
}
@Article{BaMaReSe11,
author = {{Balci}, N. and {Mazzucato}, A. L. and {Restrepo}, J. M. and {Sell}, G. R.},
title = {Ensemble dynamics and bred vectors},
journal = {Monthly Weather Review},
year = {2012},
volume = {140},
pages = {2308--2334},
doi = {10.1175/mwr-d-10-05054.1},
}
@Article{Baldwin88,
Title = {Soft billiard systems},
Author = {Baldwin, P. R.},
Journal = {Physica D},
Year = {1988},
Pages = {321--342},
Volume = {29},
DOI = {10.1016/0167-2789(88)90034-6}
}
@Article{Ballard16,
Title = {Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation},
Author = {Ballard, Christopher C. and Esty, C. Clark and Egolf, David A.},
Journal = {Chaos},
Year = {2016},
Number = {11},
Volume = {26},
DOI = {10.1063/1.4966538}
}
@Article{BCISV93,
Title = {Advection of vector fields by chaotic flows},
Author = {Balmforth, N. J. and Cvitanovi{\'c}, P. and Ierley, G. R. and Spiegel, E. A. and Vattay, G.},
Journal = {Ann. New York Acad. Sci.},
Year = {1993},
Pages = {148--160},
Volume = {706},
DOI = {10.1111/j.1749-6632.1993.tb24687.x}
}
@Book{BHLL13,
Title = {Zeta functions for two-dimensional shifts of finite type},
Author = {Ban, J.-C. and Hu, W.-G. and Lin, S.-S. and Lin, Y.-H.},
Publisher = {Amer. Math. Soc.},
Year = {2013},
Address = {Providence RI},
DOI = {10.1090/S0065-9266-2012-00653-8},
ISBN = {978-0-8218-9457-6},
Series = {Memoirs Amer. Math. Soc.},
Volume = {221}
}
@Misc{BHLL11,
Title = {Verification of mixing properties in two-dimensional shifts of finite type},
Author = {{Ban}, J.-C. and {Hu}, W.-G. and {Lin}, S.-S. and {Lin}, Y.-H.},
Year = {2015},
URL = {http://arxiv.org/abs/1112.2471}
}
@Article{BanLin05,
Title = {Patterns generation and transition matrices in multi-dimensional lattice models},
Author = {Ban, J.-C. and Lin, S.-S.},
Journal = {Discrete Continuous Dyn. Syst. Ser. A},
Year = {2005},
Pages = {637--658},
Volume = {13},
DOI = {10.3934/dcds.2005.13.637}
}
@Article{Bandelow1998,
author = {U. Bandelow and L. Recke and B. Sandstede},
title = {Frequency regions for forced locking of self-pulsating multi-section {DFB} lasers},
journal = {Opt. Commun.},
year = {1998},
volume = {147},
pages = {212--218},
doi = {10.1016/s0030-4018(97)00570-1},
}
@Inbook{BaJePo13,
Title = {Ergodic Theory, Open Dynamics, and Coherent Structures},
Author = {O. F. Bandtlow and O. Jenkinson and M. Pollicott},
Chapter = {Periodic points, escape rates and escape measures},
Editor = {Bahsoun, W. and Bose, C. and Froyland, G.},
Pages = {41--58},
Publisher = {Springer},
Year = {2014},
Addendum = {homepages.warwick.ac.uk/~masdbl/periodic-escape6.pdf},
Address = {New York},
DOI = {10.1007/978-1-4939-0419-8_3},
ISBN = {978-1-4939-0419-8}
}
@Article{BaoYan12,
Title = {Period of the discrete {Arnold} cat map and general cat map},
Author = {Bao, J. and Yang, Q.},
Journal = {Nonlinear Dyn.},
Year = {2012},
Pages = {1365--1375},
Volume = {70},
DOI = {10.1007/s11071-012-0539-3},
ISSN = {1573-269X}
}
@Article{baranger88,
Title = {The calculation of periodic trajectories},
Author = {M. Baranger and K. T. R. Davies and J. H. Mahoney},
Journal = {Ann. Phys.},
Year = {1988},
Pages = {95--110},
Volume = {186},
DOI = {10.1016/S0003-4916(88)80018-6}
}
@Article{BaEvCo93,
Title = {Field-dependent conductivity and diffusion in a two-dimensional {Lorentz} gas},
Author = {Baranyai, A. and Evans, D. J. and Cohen, E. G. D.},
Journal = {J. Stat. Phys.},
Year = {1993},
Pages = {1085--1098},
Volume = {70},
DOI = {10.1007/BF01049423}
}
@Article{BarShc06,
Title = {Periodic orbits of the ensemble of {Sinai-Arnold} cat maps and pseudorandom number generation},
Author = {Barash, L. and Shchur, L. N.},
Journal = {Phys. Rev. E},
Year = {2006},
Pages = {036701},
Volume = {73},
DOI = {10.1103/PhysRevE.73.036701}
}
@Article{BarKel06,
Title = {Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling},
Author = {J.-B. Bardet and G. Keller},
Journal = {Nonlinearity},
Year = {2006},
Pages = {2193},
Volume = {19},
DOI = {10.1088/0951-7715/19/9/012}
}
@Article{BarChor98,
author = {G. I. Barenblatt and A. J. Chorin},
title = {New perspectives in turbulence: {Scaling} laws, asymptotics, and intermittency},
journal = {SIAM Rev.},
year = {1998},
volume = {40},
pages = {265--291},
doi = {10.1137/s0036144597320047},
}
@Article{PhysWorld04,
author = {C. Barenghi},
title = {Turbulent transition for fluids},
journal = {Physics World},
year = {2004},
volume = {17},
pages = {17--18},
doi = {10.1088/2058-7058/17/12/25},
}
@Article{BJNRZ12,
Title = {Stability of periodic { Kuramoto-Sivashinsky} waves},
Author = {B. Barker and M. A. Johnson and P. Noble and L. M. Rodrigues and K. Zumbrun},
Journal = {Appl. Math. Lett.},
Year = {2012},
Pages = {824--829},
Volume = {25},
DOI = {10.1016/j.aml.2011.10.026}
}
@Article{Barkley92,
Title = {Linear stability analysis of rotating spiral waves in excitable media},
Author = {Barkley, D.},
Journal = {Phys. Rev. Lett.},
Year = {1992},
Month = mar,
Pages = {2090--2093},
Volume = {68},
DOI = {10.1103/PhysRevLett.68.2090}
}
@Article{Barkley94,
author = {Barkley, D.},
title = {{Euclid}ean symmetry and the dynamics of rotating spiral waves},
journal = {Phys. Rev. Lett.},
year = {1994},
volume = {72},
pages = {164--167},
doi = {10.1103/physrevlett.72.164},
}
@Techreport{EZRide,
Title = {{EZRide}: {A} code for simulating spiral waves in a comoving frame of reference},
Author = {D. Barkley and V. N. Biktashev and A. J. Foulkes},
Institution = {U. Liverpool},
Year = {2010},
URL = {http://www.maths.liv.ac.uk/~vadim/software/EZRide/}
}
@Article{BarKev94,
Title = {A dynamical systems approach to spiral wave dynamics},
Author = {Barkley, D. and Kevrekidis, I. G.},
Journal = {Chaos},
Year = {1994},
Pages = {453--460},
Volume = {4},
DOI = {10.1063/1.166023}
}
@Article{BaKnTu90,
author = {D. Barkley and M. Kness and L. S. Tuckerman},
title = {Spiral-wave dynamics in a simple model of excitable media: {The} transition from simple to compound rotation},
journal = {Phys. Rev. A},
year = {1990},
volume = {42},
pages = {2489--2492},
doi = {10.1103/PhysRevA.42.2489},
}
@Book{barnsley,
Title = {{Fractals Everywhere: New Edition}},
Author = {Barnsley, M.F.},
Publisher = {Dover},
Year = {2012},
Address = {New York},
ISBN = {9780486320342}
}
@Article{Barreira15,
Title = {Dimension theory of flows: {A} survey},
Author = {L. Barreira},
Journal = {Discrete Continuous Dyn. Syst. Ser. B},
Year = {2015},
Pages = {3345--3362},
Volume = {20},
DOI = {10.3934/dcdsb.2015.20.3345}
}
@Article{BarBle09,
Title = {Systematic search of symmetric periodic orbits in {2DOF Hamiltonian} systems},
Author = {R. Barrio and F. Blesa},
Journal = {Chaos Solit. Fract.},
Year = {2009},
Pages = {560--582},
Volume = {41},
DOI = {10.1016/j.chaos.2008.02.032}
}
@Article{BarRod14,
Title = {Systematic computer assisted proofs of periodic orbits of {Hamiltonian systems}},
Author = {R. Barrio and M. Rodr{\'i}guez},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2014},
DOI = {10.1016/j.cnsns.2013.12.025}
}
@Book{JBG97,
Title = {Poincar\'e and the Three Body Problem},
Author = {J. Barrow-Green},
Publisher = {Amer. Math. Soc.},
Year = {1997},
Address = {Providence RI}
}
@Article{Bartholdi14,
Title = {{Zeta} functions of graphs: a stroll through the garden, by {Audrey Terras}. Book review},
Author = {L. Bartholdi},
Journal = {Bull. Amer. Math. Soc.},
Year = {2014},
Pages = {177--185},
Volume = {51},
DOI = {10.1090/S0273-0979-2013-01426-5}
}
@Article{Bass92,
Title = {The {Ihara-Selberg} zeta function of a tree lattice},
Author = {H. Bass},
Journal = {Int. J. Math.},
Year = {1992},
Pages = {717--797},
Volume = {3},
DOI = {10.1142/S0129167X92000357}
}
@InCollection{Basu07,
author = {A. Basu},
title = {Construction of {Poincar\'e} return maps for {R\"ossler} flow},
booktitle = {{ChaosBook.org/projects}},
publisher = {Georgia Inst. of Technology},
year = {2007},
url = {http://ChaosBook.org/projects/index.shtml#Basu},
}
@Article{bauer2007,
Title = {Vacuum heating versus skin layer absorption of intense femtosecond laser pulses},
Author = {Bauer, D. and Mulser, P.},
Journal = {Phys. Plasmas},
Year = {2007},
Pages = {023301--023301-11},
Volume = {14},
DOI = {10.1063/1.2435326}
}
@Article{bauer1995,
Title = {Relativistic Ponderomotive Force, Uphill Acceleration, and Transition to Chaos},
Author = {Bauer, D. and Mulser, P. and Steeb, W. -H.},
Journal = {Phys. Rev. Lett.},
Year = {1995},
Pages = {4622--4625},
Volume = {75},
DOI = {10.1103/PhysRevLett.75.4622}
}
@Article{BayMor88,
Title = {Standard bases and geometric invariant theory {I. Initial} ideals and state polytopes},
Author = {D. Bayer and I. Morrison},
Journal = {J. Symbolic Comp.},
Year = {1988},
Pages = {209--217},
Volume = {6},
DOI = {10.1016/S0747-7171(88)80043-9}
}
@Article{BaySti92,
Title = {Computation of {Hilbert} functions},
Author = {D. Bayer and M. Stillman},
Journal = {J. Symbolic Comp.},
Year = {1992},
Pages = {31--50},
Volume = {14},
DOI = {10.1016/0747-7171(92)90024-X}
}
@InProceedings{BayOrt04,
Title = {Lie algebra template tracking},
Author = {E. Bayro-Corrochano and J. Ortegon-Aguilar},
Booktitle = {International Conf. on Pattern Recognition},
Year = {2004},
Pages = {56--59},
Volume = {2},
DOI = {10.1109/ICPR.2004.1334036}
}
@Article{tbohr,
Title = {The diversity of steady state solutions of the complex {Ginzburg-Landau} equation},
Author = {M. Bazhenov and T. Bohr and K. Gorshkov and M. Rabinovich},
Journal = {Phys. Lett. A},
Year = {1996},
Pages = {104--110},
Volume = {217},
DOI = {10.1016/0375-9601(96)00328-3}
}
@Article{BeBuRi95,
Title = {Periodic orbits of difference equations},
Author = {A. F. Beardon and S. R. Bullett and P. J. Rippon},
Journal = {Proc. Roy. Soc. Edinburgh Sect. A},
Year = {1995},
Pages = {657--674},
Volume = {125},
DOI = {10.1017/s0308210500030286}
}
@Article{BeKoSt03,
author = {Becker, L. E. and Koehler, S. A. and Stone, H. A.},
title = {On self-propulsion of micro-machines at low {Reynolds} number: {Purcell's} three-link swimmer},
journal = {J. Fluid Mech.},
year = {2003},
volume = {490},
pages = {15--35},
doi = {10.1017/s0022112003005184},
}
@Article{BedDil05,
Title = {Real and complex dynamics of a family of birational maps of the plane: {The} golden mean subshift},
Author = {E. Bedford and J. Diller},
Journal = {Amer. J. Math.},
Year = {2005},
Pages = {595--646},
Volume = {127},
DOI = {10.1353/ajm.2005.0015}
}
@Article{Behrends98,
Title = {The ghosts of the cat},
Author = {Behrends, E.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {1998},
Pages = {321--330},
Volume = {18},
URL = {http://journals.cambridge.org/article_S0143385798100378}
}
@Article{BehFie98,
Title = {Periods of discretized linear {Anosov} maps},
Author = {Behrends, E. and Fielder, B.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {1998},
Pages = {331--341},
Volume = {18},
URL = {http://journals.cambridge.org/article_S0143385798100366}
}
@Misc{GrPo12,
author = {{beim Graben}, P. and Potthast, R.},
title = {Implementing {Turing} machines in dynamic field architectures},
year = {2012},
url = {http://arXiv.org/abs/1204.5462},
}
@Article{bknk,
Title = {Formations of spatial patterns and holes in the generalized {Ginzburg-Landau} equation},
Author = {N. Bekki and K. Nozaki},
Journal = {Phys. Lett.},
Year = {1985},
Pages = {133--135},
Volume = {110},
DOI = {10.1016/0375-9601(85)90759-5}
}
@Article{Belot03,
Title = {Symmetry and gauge freedom},
Author = {G. Belot},
Journal = {Stud. History and Philosophy of Modern Physics},
Year = {2003},
Pages = {189--225},
Volume = {34},
DOI = {10.1016/S1355-2198(03)00004-2}
}
@Article{BelMos96,
Title = {One-dimensional map lattices: {Synchronization}, bifurcations, and chaotic structures},
Author = {Belykh, V. N. and Mosekilde, E.},
Journal = {Phys. Rev. E},
Year = {1996},
Pages = {3196--3203},
Volume = {54},
DOI = {10.1103/PhysRevE.54.3196}
}
@Article{bene80b,
author = {Benettin, G. and Galgani, L. and Giogilli, A. and Strelcyn, J. M.},
title = {{Lyapunov} characteristic exponents for smooth dynamical systems and for {Hamiltonian} systems; a method for computing all of them. {P}art 2: numerical application},
journal = {Meccanica},
year = {1980},
volume = {15},
pages = {21--30},
doi = {10.1007/bf02128237},
}
@Article{bene80a,
Title = {{Lyapunov} characteristic exponents for smooth dynamical systems and for {Hamiltonian} systems; a method for computing all of them. {P}art 1: theory},
Author = {Benettin, G. and Galgani, L. and Giorgilli, A. and Strelcyn, J. M.},
Journal = {Meccanica},
Year = {1980},
Pages = {9--20},
Volume = {15},
DOI = {10.1007/BF02128236}
}
@Article{Eben02,
author = {E. Ben-Naim and P. L. Krapivsky},
title = {Growth and structure of stochastic sequences},
journal = {J. Phys. A},
year = {2002},
volume = {35},
pages = {L557--L563},
doi = {10.1088/0305-4470/35/41/101},
}
@Article{BenKS66,
author = {Benney, D. J.},
title = {Long waves on liquid films},
journal = {J. Math. Phys.},
year = {1966},
volume = {45},
pages = {150--155},
doi = {10.1002/sapm1966451150},
}
@Article{B84,
author = {D. J. Benney},
title = {The evolution of disturbances in shear flows at high {Reynolds} numbers},
journal = {Stud. Appl. Math.},
year = {1984},
volume = {70},
pages = {1--19},
doi = {10.1002/sapm19847011},
}
@Article{BC89,
author = {D. J. Benney and K. A. Chow},
title = {A mean flow first harmonic theory for hydrodynamic instabilities},
journal = {Stud. Appl. Math.},
year = {1989},
volume = {80},
pages = {37--73},
doi = {10.1002/sapm198980137},
}
@Article{BG81,
author = {D. J. {Benney} and L. H. {Gustavsson}},
title = {A new mechanism for linear and nonlinear hydrodynamic instability},
journal = {Stud. Appl. Math.},
year = {1981},
volume = {64},
number = {3},
pages = {185--209},
month = {jun},
doi = {10.1002/sapm1981643185},
publisher = {Wiley-Blackwell},
}
@Article{BeCa80,
author = {V. G. Benza and V. Callegaro},
title = {Phase transitions on strange sets: the {Ising} quasicrystal},
journal = {J. Phys. A},
year = {1990},
volume = {23},
pages = {L841--L846},
doi = {10.1088/0305-4470/23/16/012},
}
@Article{BeBoRa13,
Title = {Decay properties of spectral projectors with applications to electronic structure},
Author = {Benzi, M. and Boito, P. and Razouk, N.},
Journal = {SIAM Rev.},
Year = {2013},
Pages = {3--64},
Volume = {55},
DOI = {10.1137/100814019}
}
@Article{Berkooz94,
author = {G. Berkooz and P. Holmes and J. L. Lumley and N. Aubry and E. Stone},
title = {Observations regarding ``{Coherence} and chaos in a model of turbulent boundary layer'' by {X. Zhou and L. Sirovich [Phys. Fluids A 4, 2855 (1992)]}},
journal = {Phys. Fluids},
year = {1994},
volume = {6},
pages = {1574--1578},
doi = {10.1063/1.868270},
}
@Article{Berland05,
Title = {B-series and order conditions for exponential integrators},
Author = {H. Berland and B. Owren and B. Skaflestad},
Journal = {SIAM J. Numer. Anal.},
Year = {2005},
Pages = {1715--1727},
Volume = {43},
DOI = {10.1137/040612683}
}
@Article{Bernoff88,
Title = {Slowly varying fully nonlinear wavetrains in the {Ginzburg-Landau} equation},
Author = {A. J. Bernoff},
Journal = {Physica D},
Year = {1988},
Pages = {363--381},
Volume = {30},
DOI = {10.1016/0167-2789(88)90026-7}
}
@Article{Berry12,
author = {M. V. Berry},
title = {{Martin Gutzwiller} and his periodic orbits},
journal = {Commun. Swiss Phys. Soc.},
year = {2012},
volume = {37},
number = {23--30},
pages = {4839--4849},
doi = {10.1142/9789813221215_0053},
}
@Article{BK90,
Title = {A rule for quantizing chaos},
Author = {M. V. Berry and J. P. Keating},
Journal = {J. Phys. A},
Year = {1990},
Pages = {4839--4849},
Volume = {23},
DOI = {10.1088/0305-4470/23/21/024}
}
@Article{BerTab76,
Title = {Closed orbits and the regular bound spectrum},
Author = {M. V. Berry and M. Tabor},
Journal = {Proc. Roy. Soc. Ser A},
Year = {1976},
Pages = {101--123},
Volume = {349},
DOI = {10.1098/rspa.1976.0062}
}
@Article{BerstelPocchiola94,
author = {J. Berstel and M. Pocchiola},
title = {Average cost of {D}uval's algorithm for generating {L}yndon words},
journal = {Theoret. Comput. Sci.},
year = {1994},
volume = {132},
pages = {415--425},
doi = {10.1016/0304-3975(94)00013-1},
}
@Article{Beyn12,
author = {W.-J. Beyn},
title = {An integral method for solving nonlinear eigenvalue problems},
journal = {Linear Algebra Appl.},
year = {2012},
volume = {436},
pages = {3839--3863},
doi = {10.1016/j.laa.2011.03.030},
}
@Article{BeyHuls14,
Title = {Continuation and collapse of homoclinic tangles},
Author = {W.-J. Beyn and T. H{\"u}ls},
Journal = {J. Comput. Dynamics},
Year = {2014},
Pages = {71--109},
DOI = {10.3934/jcd.2014.1.71}
}
@Article{BeyLus09,
Title = {A hybrid method for computing {Lyapunov} exponents},
Author = {Beyn, W.-J. and Lust, A.},
Journal = {Numer. Math.},
Year = {2009},
Pages = {357--375},
Volume = {113},
DOI = {10.1007/s00211-009-0236-4}
}
@Article{BeyLus13,
Title = {Error analysis of a hybrid method for computing {Lyapunov} exponents},
Author = {Beyn, W.-J. and Lust, A.},
Journal = {Numer. Math.},
Year = {2013},
Pages = {189--217},
Volume = {123},
DOI = {10.1007/s00211-012-0486-4}
}
@Article{BeyOtt16,
Title = {Spatial decay of rotating waves in reaction diffusion systems},
Author = {Beyn, W.-J. and Otten, D.},
Journal = {Dynami. Part. Differ. Eq.},
Year = {2016},
Pages = {191--240},
Volume = {13},
DOI = {10.4310/DPDE.2016.v13.n3.a2}
}
@Incollection{BeOtRo14,
Title = {Stability and computation of dynamic patterns in {PDEs}},
Author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.},
Booktitle = {Current Challenges in Stability Issues for Numerical Differential Equations},
Publisher = {Springer},
Year = {2014},
Pages = {89--172},
Series = {Lect. Notes Math.},
DOI = {10.1007/978-3-319-01300-8_3},
Editors = {Dieci, L. and Guglielmi, N.}
}
@Misc{BeOtRo16,
Title = {Computation and stability of traveling waves in second order evolution equations},
Author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.},
Year = {2016},
URL = {http://arxiv.org/abs/1606.08844}
}
@Article{beyn2008freezing,
Title = {Freezing multipulses and multifronts},
Author = {Beyn, W.-J. and Selle, S. and Th{\"u}mmler, V.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2008},
Pages = {577--608},
Volume = {7},
DOI = {10.1137/07070749X}
}
@Article{BeTh04,
Title = {Freezing solutions of equivariant evolution equations},
Author = {W.-J. Beyn and V. Th\"ummler},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2004},
Pages = {85--116},
Volume = {3},
DOI = {10.1137/030600515}
}
@Article{BiKoTi13,
Title = {Stalling chaos control accelerates convergence},
Author = {C. Bick and C. Kolodziejski and M. Timme},
Journal = {New J. Phys.},
Year = {2013},
Pages = {063038},
Volume = {15},
DOI = {10.1088/1367-2630/15/6/063038}
}
@Incollection{jones_dynamics_1992,
Title = {Topological approach to differential inclusions on closed subset of {$R^n$}},
Author = {Bielawski, R. and G{\'o}rniewicz, L. and Plaskacz, S.},
Booktitle = {Dynamics Reported},
Publisher = {Springer},
Year = {1992},
Address = {New York},
Editor = {Jones, C. K. R. T. and Kirchgraber, U. and Walther, H.-O.},
Pages = {225--250},
Volume = {1},
DOI = {10.1007/978-3-642-61243-5_6},
ISBN = {978-3-642-64758-1}
}
@Article{afind,
author = {O. Biham and W. Wenzel},
title = {Characterization of unstable periodic orbits in chaotic attractors and repellers},
journal = {Phys. Rev. Lett.},
year = {1989},
volume = {63},
pages = {819},
doi = {10.1103/physrevlett.63.819},
}
@Article{biham90c,
author = {O. Biham and W. Wenzel},
title = {Unstable periodic orbits and the symbolic dynamics of the complex {H\'enon} map},
journal = {Phys. Rev. E},
year = {1990},
volume = {42},
pages = {4639--4646},
doi = {10.1103/physreva.42.4639},
}
@Article{BiHo95,
Title = {Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities},
Author = {V. N. Biktashev and A. V. Holden},
Journal = {Chaos Solit. Fract.},
Year = {1995},
Pages = {575--622},
Volume = {5},
DOI = {10.1016/0960-0779(93)E0044-C}
}
@Article{BiHoNi96,
Title = {Spiral wave meander and symmetry of the plane},
Author = {V. N. Biktashev and A. V. Holden and E. V. Nikolaev},
Journal = {Int. J. Bifur. Chaos},
Year = {1996},
Pages = {2433--2440},
Volume = {6},
DOI = {10.1142/s0218127496001582}
}
@Article{biktasheva2003wave,
author = {Biktasheva, I. V. and Biktashev, V. N.},
title = {Wave-particle dualism of spiral waves dynamics},
journal = {Phys. Rev. E},
year = {2003},
volume = {67},
pages = {026221},
doi = {10.1103/physreve.67.026221},
}
@Article{BiBiFo10,
author = {I. V. Biktasheva and V. N. Biktashev and A. J. Foulkes},
title = {Computation of the drift velocity of spiral waves using response functions},
journal = {Phys. Rev. E},
year = {2010},
volume = {81},
doi = {10.1103/PhysRevE.81.066202},
}
@Book{gauge,
title = {Chaos and Gauge Field Theory},
publisher = {World Scientific},
year = {1994},
author = {T. S. Bir{\'o} and S. G. Matinyan and B. M{\"{u}}ller},
address = {Singapore},
doi = {10.1142/9789812798978},
}
@Article{BirViv,
Title = {Periodic orbits of the sawtooth maps},
Author = {N. Bird and F. Vivaldi},
Journal = {Physica D},
Year = {1988},
Pages = {164--176},
Volume = {30},
DOI = {10.1016/0167-2789(88)90104-2}
}
@Article{Birkhoff31,
Title = {Proof of the {Ergodic Theorem}},
Author = {Birkhoff, G. D.},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1931},
Pages = {656--660},
Volume = {17},
DOI = {10.1073/pnas.17.2.656}
}
@Article{BALL92,
Title = {Existence of stable periodic orbits in the {$x^2 y^2$} potential: a semiclassical approach},
Author = {D. Biswas and M. Azam and Q. V. Lawande and S. V Lawande},
Journal = {J. Phys. A},
Year = {1992},
Pages = {L297},
Volume = {25},
DOI = {10.1088/0305-4470/25/7/003}
}
@Phdthesis{BittihnThesis,
Title = {Complex Structure and Dynamics of the Heart},
Author = {Bittihn, P.},
School = {Georg-August Universit\"at},
Year = {2013},
Address = { G\"{o}ttingen}
}
@Article{BjoGol73,
Title = {Numerical methods for computing angles between linear subspaces},
Author = {Bj{\"o}rck, \AA. and Golub, G. H.},
Journal = {Math. Comput.},
Year = {1973},
Pages = {579--594},
Volume = {27},
DOI = {10.1090/S0025-5718-1973-0348991-3}
}
@Article{BlMaLo05,
Title = {Symmetry breaking of two-dimensional time-periodic wakes},
Author = {H. M. Blackburn and F. Marques and Lopez, J. M.},
Journal = {J. Fluid Mech.},
Year = {2005},
Pages = {395--411},
Volume = {522},
DOI = {10.1017/S0022112004002095}
}
@Article{Blanes2013,
Title = {New families of symplectic splitting methods for numerical integration in dynamical astronomy},
Author = {S. Blanes and F. Casas and A. Farr\'es and J. Laskar and J. Makazaga and A. Murua},
Journal = {Appl. Numer. Math.},
Year = {2013},
Pages = {58 -- 72},
Volume = {68},
DOI = {10.1016/j.apnum.2013.01.003}
}
@Book{Blank97,
Title = {{Discreteness and Continuity in Problems of Chaotic Dynamics}},
Author = {Blank, M .L.},
Publisher = {Amer. Math. Soc.},
Year = {1997},
Address = {Providence RI},
ISBN = {9780821897751}
}
@Article{BlaKel98,
Title = {Random perturbations of chaotic dynamical systems: stability of the spectrum},
Author = {M. Blank and G. Keller},
Journal = {Nonlinearity},
Year = {1998},
Pages = {1351--1364},
Volume = {11},
DOI = {10.1088/0951-7715/11/5/010}
}
@Article{BKL02,
Title = {{Ruelle-Perron-Frobenius} spectrum for {Anosov} maps},
Author = {M. Blank and G. Keller and C. Liverani},
Journal = {Nonlinearity},
Year = {2002},
Pages = {1905--1973},
Volume = {15},
DOI = {10.1088/0951-7715/15/6/309}
}
@Incollection{Bleher99,
Title = {Trace formula for quantum integrable systems, lattice-point problem, and small divisors},
Author = {Pavel Bleher},
Booktitle = {{Emerging Applications of Number Theory}},
Publisher = {Springer},
Year = {1999},
Editor = {D. A. Hejhal and J.Friedman and M. C. Gutzwiller and A. M. Odlyzko},
Pages = {1--38},
DOI = {10.1007/978-1-4612-1544-8_1}
}
@Article{BleDys94b,
Title = {Mean square limit for lattice points in a sphere},
Author = {P. M. Bleher and F. J. Dyson},
Journal = {Acta Arith.},
Year = {1994},
Pages = {383--393},
Volume = {68},
URL = {pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav68i4p383bwm}
}
@Article{BleDys94a,
Title = {Mean square value of exponential sums related to representation of integers as sum of two squares},
Author = {P. M. Bleher and F. J. Dyson},
Journal = {Acta Arith.},
Year = {1994},
Pages = {71--84},
Volume = {68},
URL = {pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav68i1p71bwm}
}
@Article{BleDys94,
Title = {The variance of the error function in the shifted circle problem is a wild function of the shift},
Author = {P. M. Bleher and F. J. Dyson},
Journal = {Commun. Math. Phys.},
Year = {1994},
Pages = {493--505},
Volume = {160},
DOI = {10.1007/bf02173426}
}
@Book{BH86,
Title = {Asymptotic Expansions of Integrals},
Author = {N. Bleistein and R. A. Handelsman},
Publisher = {Dover},
Year = {1986},
Address = {New York}
}
@Article{BlMaZe05,
Title = {Nonholonomic dynamics},
Author = {Bloch, A. M. and Marsden, J. E. and Zenkov, D. V.},
Journal = {Notices Amer. Math. Soc.},
Year = {2005},
Pages = {324--333},
Volume = {52}
}
@Article{BlGaPa05,
Title = {Hopping behavior in the {Kuramoto-Sivashinsky} equation},
Author = {Blomgren, P. and Gasner, S. and Palacios, A.},
Journal = {Chaos},
Year = {2005},
Pages = {013706},
Volume = {15},
DOI = {10.1063/1.1848311}
}
@Article{BloWan13,
author = {{Blonigan}, P. and {Wang}, Q.},
title = {Multigrid-in-time for sensitivity analysis of chaotic dynamical systems},
journal = {Numer. Linear Algebra Appl.},
year = {2014},
doi = {10.1002/nla.1946},
}
@Article{Bluman07,
author = {G. Bluman},
title = {Connections between symmetries and conservation laws},
journal = {SIGMA},
year = {2005},
volume = {1},
pages = {011},
month = {oct},
doi = {10.3842/sigma.2005.011},
}
@Book{BlumanAnco02,
Title = {Symmetry and Integration Methods for Differential Equations},
Author = {G. W. Bluman and S. C. Anco},
Publisher = {Springer},
Year = {2002},
Address = {New York}
}
@Book{BlumanSDE89,
title = {Symmetries and Differential Equations},
publisher = {Springer},
year = {1989},
author = {G. W. Bluman and S. Kumei},
address = {New York},
doi = {10.1007/978-1-4757-4307-4},
}
@Article{BoaKea95,
Title = {Semiclassical asymptotics of perturbed cat maps},
Author = {Boasman, P. A. and Keating, J. P.},
Journal = {Proc. Roy. Soc. Ser A},
Year = {1995},
Pages = {629--653},
Volume = {449},
DOI = {10.1098/rspa.1995.0063}
}
@Book{Boccotti00,
Title = {Wave Mechanics for Ocean Engineering},
Author = {P. Boccotti},
Publisher = {Elsevier},
Year = {2000},
Address = {New York},
DOI = {10.1016/S0422-9894(00)80024-0}
}
@Article{Boccotti11,
Title = {Field verification of quasi-determinism theory for wind waves in the space-time domain},
Author = {P. Boccotti},
Journal = {Ocean Eng.},
Year = {2011},
Pages = {1503--1507},
Volume = {38},
DOI = {10.1016/j.oceaneng.2011.07.015}
}
@Incollection{Bochi04,
Title = {How frequently are dynamical systems hyperbolic?},
Author = {Bochi, J. and Viana, M.},
Booktitle = {Modern Dynamical Systems and Applications},
Publisher = {Cambridge Univ. Press},
Year = {2004},
Address = {Cambridge},
Editor = {Brin, M. and Hasselblatt, B. and Pesin, Y.},
Pages = {271--297},
ISBN = {9780521840736}
}
@Article{Bochi05,
author = {Bochi, J. and Viana, M.},
title = {The {Lyapunov} exponents of generic volume-preserving and symplectic maps},
journal = {Ann. Math.},
year = {2005},
volume = {161},
pages = {1423--1485},
doi = {10.4007/annals.2005.161.1423},
}
@Article{BBLTFC11,
author = {Boghosian, B. M. and Brown, Aa. and L\"att, J. and Tang, H. and Fazendeiro, L. M. and Coveney, P. V.},
title = {Unstable periodic orbits in the {Lorenz} attractor},
journal = {Philos. Trans. Royal Soc. A},
year = {2011},
volume = {369},
pages = {2345--2353},
doi = {10.1098/rsta.2011.0067},
}
@Article{BFLTC11,
Title = {New variational principles for locating periodic orbits of differential equations},
Author = {Boghosian, B. M. and Fazendeiro, L. M. and L\"att, J. and Tang, H. and Coveney, P. V.},
Journal = {Philos. Trans. Royal Soc. A},
Year = {2011},
Pages = {2211--2218},
Volume = {369},
DOI = {10.1098/rsta.2011.0066}
}
@Book{BogMit61,
Title = {Asymptotic Methods in the Theory of Nonlinear Oscillations},
Author = {Bogoliubov, N. N. and Mitropolski, Y. A.},
Publisher = {Gordon and Breach},
Year = {1961},
Address = {New York}
}
@Article{BohHubOtt96,
author = {Bohr, T. and Huber, G. and Ott, E.},
title = {The structure of spiral domain patterns},
journal = {Europhys. Lett.},
year = {1996},
volume = {33},
pages = {589--594},
doi = {10.1209/epl/i1996-00383-8},
}
@Article{BohHubOtt97,
Title = {The structure of spiral-domain patterns and shocks in the {2D} complex {Ginzburg-Landau} equation},
Author = {Bohr, T. and Huber, G. and Ott, E.},
Journal = {Physica D},
Year = {1997},
Pages = {95--112},
Volume = {106},
DOI = {10.1016/s0167-2789(97)00025-0}
}
@Book{bohr98tur,
title = {Dynamical Systems Approach to Turbulence},
publisher = {Cambridge Univ. Press},
year = {1998},
author = {T. Bohr and M. H. Jensen and G. Paladin and A. Vulpiani},
address = {Cambridge},
isbn = {9780521017947},
doi = {10.1017/cbo9780511599972},
}
@InProceedings{Bojanczyk92theperiodic,
author = {A. Bojanczyk and G. H. Golub and P. Van Dooren},
title = {The periodic {Schur} decomposition. {Algorithm}s and applications},
booktitle = {{Proc. SPIE Conference}},
year = {1992},
pages = {31--42},
url = {http://hdl.handle.net/2078.1/81012},
}
@Article{bollt07,
author = {Bollt, E.},
title = {Attractor modeling and empirical nonlinear model reduction of dissipative dynamical systems},
journal = {Int. J. Bifur. Chaos},
year = {2007},
volume = {17},
pages = {1199--1219},
doi = {10.1142/s021812740701777x},
}
@Article{BoKuLe05,
Title = {Absolute continuity of projected {SRB} measures of coupled {Arnold} cat map lattices},
Author = {F. Bonetto and A. Kupiainen and J. L. Lebowitz},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {2005},
Pages = {59--88},
Volume = {25},
DOI = {10.1017/S0143385704000252}
}
@Article{Bor92,
author = {G. Bor},
title = {{Yang-Mills} fields which are not self-dual},
journal = {Commun. Math. Phys.},
year = {1992},
volume = {145},
pages = {393--410},
doi = {10.1007/bf02099144},
}
@Article{borghesi02,
author = {Borghesi, M. and Bulanov, S. and {Campbell et. al.}, D. H.},
title = {Macroscopic Evidence of Soliton Formation in Multiterawatt Laser-Plasma Interaction},
journal = {Phys. Rev. Lett.},
year = {2002},
volume = {88},
pages = {135002},
doi = {10.1103/physrevlett.88.135002},
}
@Article{borot12,
Title = {Attosecond control of collective electron motion in plasmas},
Author = {Borot, A. and Malvache, A. and Chen, X. and Jullien, A. and Geindre, J.-P. and Audebert, P. and Mourou, G. and Qu{\'e}r{\'e}, F. and Lopez-Martens, R.},
Journal = {Nature Phys.},
Year = {2012},
Number = {5},
Pages = {416--421},
Volume = {8},
DOI = {10.1038/nphys2269}
}
@Misc{BCS12,
Title = {2-dimensional {Landau} turbulence sliced},
Author = {Borrero-Echeverry, D. and Schatz, M. and Cvitanovi\'c, P.},
Note = {In preparation},
Year = {2012}
}
@Article{BoPo10,
Title = {Covariant {Lyapunov} vectors for rigid disk systems},
Author = {Bosetti, H. and Posch, H. A.},
Journal = {Chem. Phys.},
Year = {2010},
Pages = {296--308},
Volume = {375},
DOI = {10.1016/j.chemphys.2010.06.010}
}
@Article{BosPos14,
Title = {What does dynamical systems theory teach us about fluids?},
Author = {H. Bosetti and H. A. Posch},
Journal = {Commun. Theor. Phys.},
Year = {2014},
Pages = {451--468},
Volume = {62},
DOI = {10.1088/0253-6102/62/4/03}
}
@Article{Bosetti2010,
Title = {Time-reversal symmetry and covariant {Lyapunov} vectors for simple particle models in and out of thermal equilibrium},
Author = {Bosetti, H. and Posch, H. A. and Dellago, C. and Hoover, W. G.},
Journal = {Phys. Rev. E},
Year = {2010},
Pages = {1--10},
Volume = {82},
DOI = {10.1103/PhysRevE.82.046218}
}
@Article{BCOR11,
Title = {Bifurcations in the {Lozi} map},
Author = {Botella-Soler, V. and Castelo, J. M. and Oteo, J. A. and Ros, J.},
Journal = {J. Phys. A},
Year = {2011},
Pages = {305101},
Volume = {44},
DOI = {10.1088/1751-8113/44/30/305101}
}
@Article{BoSmWi36,
Title = {Theory of {Brillouin} zones and symmetry properties of wave functions in crystals},
Author = {Bouckaert, L. P. and Smoluchowski, R. and Wigner, E.},
Journal = {Phys. Rev.},
Year = {1936},
Pages = {58--67},
Volume = {50},
DOI = {10.1103/PhysRev.50.58}
}
@Article{Bount81,
Title = {On the stability of periodic orbits of two-dimensional mappings},
Author = {Bountis, T. and Helleman, R. H. G.},
Journal = {J. Math. Phys},
Year = {1981},
Pages = {1867--1877},
Volume = {22},
DOI = {10.1063/1.525159}
}
@Article{ksham95,
author = {S. Bouquet},
title = {Hamiltonian structure and integrability of the stationary {Kuramoto-Sivashinsky} equation},
journal = {J. Math. Phys.},
year = {1995},
volume = {36},
pages = {1242},
doi = {10.1063/1.531118},
}
@Article{BouCro92,
Title = {Coupled map models for chaos in extended systems},
Author = {Bourzutschky, M. S. and Cross, M. C.},
Journal = {Chaos},
Year = {1992},
Pages = {173--181},
Volume = {2},
DOI = {10.1063/1.165905}
}
@Article{Bowen71,
Title = {Periodic points and measures for {Axiom A} diffeomorphisms},
Author = {R. Bowen},
Journal = {Trans. Amer. Math. Soc.},
Year = {1971},
Pages = {377--397},
Volume = {154},
DOI = {10.2307/1995452}
}
@Book{bowen,
Title = {{Equilibrium States and the Ergodic Theory of {Anosov} Diffeomorphisms}},
Author = {R. Bowen},
Publisher = {Springer},
Year = {1975},
Address = {Berlin},
ISBN = {9783540776956}
}
@Book{boyd01,
title = {{Chebyshev and Fourier Spectral Methods}},
publisher = {Dover},
year = {2001},
author = {Boyd, J. P.},
address = {New York},
edition = {2},
isbn = {9780486411835},
}
@Article{BoyPavSch10,
Title = {Multidimensional sofic shifts without separation and their factors},
Author = {Boyle, M. and Pavlov, R. and Schraudner, M.},
Journal = {Trans. Amer. Math. Soc.},
Year = {2010},
Pages = {4617--4653},
Volume = {362},
DOI = {10.1090/S0002-9947-10-05003-8}
}
@Article{Bracco03,
author = {A. Bracco and J. Pedlosky},
title = {Vortex generation by topography in locally unstable baroclinic flows},
journal = {J. Phys. Oceanogr.},
year = {2003},
volume = {33},
pages = {207--219},
doi = {10.1175/1520-0485(2003)033<0207:vgbtil>2.0.co;2},
}
@Article{BrOgYuRe05,
Title = {Uniform semiclassical trace formula for {$U(3) \to SO(3)$} symmetry breaking},
Author = {M. Brack and M. \"Ogren and Y. Yu and S. M. Reimann},
Journal = {J. Phys. A},
Year = {2005},
Pages = {9941},
Volume = {38}
}
@Incollection{brand03,
Title = {Computational aspects of astrophysical {MHD} and turbulence},
Author = {A. Brandenburg},
Booktitle = {{Advances in Nonlinear Dynamos}},
Publisher = {Informa {UK} Limited},
Year = {2003},
Address = {London},
Editor = {A. Ferriz-Mas and M. N{\'{u}\~{n}ez}},
Pages = {269--344},
DOI = {10.1201/9780203493137.ch9}
}
@Book{Bredon72,
Title = {{Introduction to Compact Transformation Groups}},
Author = {G. Bredon},
Publisher = {Academic},
Year = {1972},
Address = {New York},
ISBN = {9780080873596}
}
@Article{Bredon61,
Title = {On the structure of orbit spaces of generalized manifolds},
Author = {G. E. Bredon},
Journal = {Trans. Amer. Math. Soc.},
Year = {1961},
Pages = {162--162},
Volume = {100},
DOI = {10.1090/S0002-9947-1961-0126503-5}
}
@Article{Bridges08,
author = {T. J. Bridges},
title = {Degenerate relative equilibria, curvature of the momentum map,and homoclinic bifurcation},
journal = {J. Diff. Eqn.},
year = {2008},
volume = {244},
number = {7},
pages = {1629--1674},
doi = {10.1016/j.jde.2008.01.019},
}
@Misc{Bridges_priv,
Author = {T. J. Bridges},
Note = {private communication}
}
@Article{Briggs1990,
author = {Briggs, K.},
title = {An improved method for estimating {Liapunov} exponents of chaotic time series},
journal = {Phys. Lett. A},
year = {1990},
volume = {151},
pages = {27--32},
doi = {10.1016/0375-9601(90)90841-b},
}
@Article{BSTV97,
Title = {Decay of correlations for the automorphism of the torus {$T^2$}},
Author = {F. Brini and S. Siboni and G. Turchetti and S. Vaienti},
Journal = {Nonlinearity},
Year = {1997},
Pages = {1257--1268},
Volume = {10},
DOI = {10.1088/0951-7715/10/5/012}
}
@Article{bro94sur,
author = {G. Brodin and J. Lundberg},
title = {Nonlinear surface waves in a plasma with a diffuse boundary},
journal = {Phys. Plasmas},
year = {1994},
volume = {1},
pages = {96--102},
doi = {10.1063/1.870465},
}
@Book{BroTak10,
Title = {{Dynamical Systems and Chaos}},
Author = {Broer, H. and Takens, F.},
Publisher = {Springer},
Year = {2010},
Address = {New York},
ISBN = {9781441968708}
}
@Article{broer_quasi-periodic_2007,
Title = {The quasi-periodic reversible {Hopf} bifurcation},
Author = {H. W. Broer and M. C. Ciocci and H. Hanssmann},
Journal = {Int. J. Bifur. Chaos},
Year = {2007},
Pages = {2605--2623},
Volume = {17}
}
@Book{BHLV03,
Title = {Bifurcations in {Hamiltonian} Systems: Computing Singularities by Gr\"obner Bases},
Author = {Broer, H. W. and Hoveijn, I. and Lunter, G. A. and Vegter, G.},
Publisher = {Springer},
Year = {2003},
Address = {New York}
}
@Article{Broer90,
Title = {Unfoldings and bifurcations of quasi-periodic tori},
Author = {Broer, H. W. and G. B. Huitema and F. Takens and B. L. J. Braaksma},
Journal = {Memoirs Amer. Math. Soc.},
Year = {1990},
Number = {421},
DOI = {10.1090/memo/0421},
ISBN = {9780821824832}
}
@Article{broer97,
author = {H. W. Broer and H. M. Osinga and G. Vegter},
title = {Algorithms for computing {Normally Hyperbolic Invariant Manifolds}},
journal = {Z. Angew. Math. Phys.},
year = {1997},
volume = {48},
pages = {480},
doi = {10.1007/s000330050044},
}
@Article{bronski2005,
Title = {Uncertainty estimates and {$L_2$} bounds for the {Kuramoto-Sivashinsky} equation},
Author = {J. C. Bronski and T. N. Gambill},
Journal = {Nonlinearity},
Year = {2006},
Pages = {2023--2039},
Volume = {19},
DOI = {10.1088/0951-7715/19/9/002}
}
@Article{Broucke75,
author = {R. Broucke},
title = {On relative periodic solutions of the planar general three-body problem},
journal = {Celest. Mech. Dynam. Astronom.},
year = {1975},
volume = {12},
pages = {439--462},
doi = {10.1007/bf01595390},
}
@Article{Brouwer1,
Title = {\"Uber Abbildung von Mannigfaltigkeiten},
Author = {Brouwer, L. E. J.},
Journal = {Math. Ann.},
Year = {1911},
Pages = {97--115},
Volume = {71},
DOI = {10.1007/BF01456931}
}
@Incollection{BrKevr96,
Title = {Modulated traveling waves for the {Kuramoto-Sivashinsky} equation},
Author = {Brown, H. S. and Kevrekidis, I. G.},
Booktitle = {Pattern Formation: Symmetry Methods and Applications},
Publisher = {AMS},
Year = {1996},
Address = {Providence, RI},
Editor = {D. Benest and C. Froeschl\'{e}},
Pages = {45--66}
}
@Article{Brunet07,
Title = {Stabilized {Kuramoto-Sivashinsky} equation: {A} useful model for secondary instabilities and related dynamics of experimental one-dimensional cellular flows},
Author = {Brunet, P.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {017204},
Volume = {76},
DOI = {10.1103/PhysRevE.76.017204}
}
@Article{BTBmaw03,
author = {L. Brusch and A. Torcini and M. B{\"{a}}r},
title = {Nonlinear analysis of the {Eckhaus} instability: {Modulated} amplitude waves and phase chaos with nonzero average phase gradient},
journal = {Physica D},
year = {2003},
volume = {174},
pages = {152--167},
doi = {10.1016/s0167-2789(02)00688-7},
}
@Article{BTHmaw01,
Title = {Modulated amplitude waves and defect formation in the one-dimensional complex {Ginzburg-Landau} equation},
Author = {L. Brusch and A. Torcini and M. van Hecke and M. G. Zimmermann and M. B{\"{a}}r},
Journal = {Physica D},
Year = {2001},
Pages = {127--148},
Volume = {160},
DOI = {10.1016/s0167-2789(01)00355-4}
}
@Article{BZMmaw00,
author = {L. Brusch and M. G. Zimmermann and M. van Hecke and M. B{\"{a}}r and A. Torcini},
title = {Modulated amplitude waves and the transition from phase to defect chaos},
journal = {Phys. Rev. Lett.},
year = {2000},
volume = {85},
pages = {86--89},
doi = {10.1103/physrevlett.85.86},
}
@Article{BrEllGBAHo10,
Title = {Un-reduction},
Author = {Bruveris, M. and Ellis, D. C. P. and Gay-Balmaz, F. and Holm, D. D.},
Journal = {J. Geom. Mech.},
Year = {2011},
Pages = {363--387},
Volume = {3},
DOI = {10.3934/jgm.2011.3.363}
}
@Phdthesis{Bsaisou14,
Title = {Electric Dipole Moments of Light Nuclei in Chiral Effective Field Theory},
Author = {J. Bsaisou},
School = {U. Bonn},
Year = {2014},
URL = {http://hss.ulb.uni-bonn.de/2014/3585/3585.pdf}
}
@Misc{ffmSliceGitHub,
Title = {{FFM Slice}},
Author = {Budanur, N. B.},
Note = {\HREF{https://github.com/burakbudanur/ffmSlice} {GitHub.com/\-burakbudanur/\-ffmSlice}},
Year = {2014},
Institution = {Georgia Inst.\ of Technology}
}
@Phdthesis{BudanurThesis,
author = {Budanur, N. B.},
title = {{Exact Coherent Structures in Spatiotemporal Chaos: From Qualitative Description to Quantitative Predictions}},
school = {School of Physics, Georgia Inst. of Technology},
year = {2015},
address = {Atlanta},
url = {http://hdl.handle.net/1853/54445},
}
@Unpublished{Bud15,
Title = {Invariant measurement of torsion within eigenframes of periodic orbits},
Author = {Budanur, N. B.},
Note = {In preparation},
Year = {2016}
}
@Article{BuBoCvSi14,
Title = {Periodic orbit analysis of a system with continuous symmetry - {A} tutorial},
Author = {Budanur, N. B. and Borrero-Echeverry, D. and Cvitanovi\'c, P.},
Journal = {Chaos},
Year = {2015},
Pages = {073112},
Volume = {25},
DOI = {10.1063/1.4923742}
}
@Article{BudCvi15,
author = {Budanur, N. B. and Cvitanovi\'c, P.},
title = {Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the {Kuramoto-Sivashinsky} system},
journal = {J. Stat. Phys.},
year = {2015},
volume = {167},
pages = {636--655},
doi = {10.1007/s10955-016-1672-z},
}
@Article{BudCvi14,
Title = {Reduction of the {SO(2)} symmetry for spatially extended dynamical systems},
Author = {Budanur, N. B. and Cvitanovi\'c, P. and Davidchack, R. L. and Siminos, E.},
Journal = {Phys. Rev. Lett.},
Year = {2015},
Pages = {084102},
Volume = {114},
DOI = {10.1103/PhysRevLett.114.084102}
}
@Misc{BuDiCv15,
Title = {Turbulent {Kuramoto-Sivashinsky} system recycled},
Author = {Budanur, N. B. and Ding, D. and Cvitanovi\'c, P.},
Note = {In preparation},
Year = {2015}
}
@Article{BudHof17,
title={Heteroclinic path to spatially localized chaos in pipe flow},
volume={827},
DOI={10.1017/jfm.2017.516},
journal={J. Fluid Mech.},
author={N. B. Budanur and B. Hof},
year={2017},
url = {https://arxiv.org/abs/1204.2050}
}
@Article{BuMoMe12,
author = {M. Budi\v{s}i\'c, M. and Mohr, R. M. and Mezi{\'c}, I.},
title = {{Applied Koopmanism}},
journal = {Chaos},
year = {2012},
volume = {22},
pages = {047510},
doi = {10.1063/1.4772195},
}
@Article{BudMez12,
author = {M. Budi\v{s}i\'c and I. Mezi\'c},
title = {Geometry of the ergodic quotient reveals coherent structures in flows},
journal = {Physica D},
year = {2012},
volume = {241},
pages = {1255--1269},
doi = {10.1016/j.physd.2012.04.006},
}
@Article{Bullett86,
Title = {Invariant circles for the piecewise linear standard map},
Author = {S. Bullett},
Journal = {Commun. Math. Phys.},
Year = {1986},
Pages = {241--262},
Volume = {107},
DOI = {10.1007/bf01209394}
}
@Article{Bunimovich85,
Title = {Decay of correlations in dynamical systems with chaotic behavior},
Author = {Bunimovich, L. A.},
Journal = {Sov. Phys. JETP},
Year = {1985},
Pages = {842--852},
Volume = {62},
URL = {http://jetp.ac.ru/cgi-bin/dn/e_062_04_0842.pdf}
}
@Article{BFGV97,
Title = {On stability of structures and patterns in extended systems},
Author = {L. A. Bunimovich and V. Franceschini and C. Giberti and C. Vernia},
Journal = {Physica D},
Year = {1997},
Pages = {412--418},
Volume = {103},
DOI = {10.1016/S0167-2789(96)00273-4}
}
@Article{BLMR92,
Title = {Coupled trivial maps},
Author = {Bunimovich, L. A. and Livi, R. and Mart{\'i}nez-Mekler, G. and Ruffo, S.},
Journal = {Chaos},
Year = {1992},
Pages = {283--291},
Volume = {2},
DOI = {10.1063/1.165870}
}
@Article{BunSin80,
Title = {{Markov} partitions for dispersed billiards},
Author = {Bunimovich, L. A. and Sinai, Ya. G.},
Journal = {Commun. Math. Phys.},
Year = {1980},
Note = {Erratum, ibid. {\bf 107}, 357 (1986)},
Pages = {247--280},
Volume = {78},
DOI = {10.1007/BF01942372}
}
@Article{BunSin88,
Title = {Spacetime chaos in coupled map lattices},
Author = {L. A. Bunimovich and Ya. G. Sinai},
Journal = {Nonlinearity},
Year = {1988},
Pages = {491},
Volume = {1},
DOI = {10.1088/0951-7715/1/4/001}
}
@Inproceedings{BuReSh11,
author = {S. Burden and S. Revzen and S. S. Sastry},
title = {Dimension reduction near periodic orbits of hybrid systems},
booktitle = {50th IEEE Conference on Decision and Control},
year = {2011},
pages = {6116-6121},
doi = {10.1109/CDC.2011.6160405},
}
@Article{Burgoyne63,
Title = {Remarks on the combinatorial approach to the {Ising} problem},
Author = {Burgoyne, P. N.},
Journal = {J. Math. Phys.},
Year = {1963},
Pages = {1320--1326},
Volume = {4},
DOI = {10.1063/1.1703907}
}
@Article{Busse04,
Title = {Visualizing the dynamics of the onset of turbulence},
Author = {F. H. Busse},
Journal = {Science},
Year = {2004},
Pages = {1574--1575},
Volume = {305}
}
@Book{ByFu92,
Title = {Mathematics of Classical and Quantum Physics},
Author = {F. W. Byron and R. W. Fuller},
Publisher = {Dover},
Year = {1992},
Address = {New York}
}
@Incollection{Calabi70,
Title = {On the group of automorphisms of a symplectic manifold},
Author = {Calabi, E.},
Booktitle = {{Problems in Analysis: A Symposium in Honor of Salomon Bochner}},
Publisher = {Princeton Univ. Press},
Year = {1970},
Address = {Princeton NJ},
Pages = {1--26},
DOI = {10.1515/9781400869312-002}
}
@Article{CaKno97,
Title = {Symmetry-breaking bifurcations on cubic lattices},
Author = {T. K. Callahan and E. Knobloch},
Journal = {Nonlinearity},
Year = {1997},
Pages = {1179--1216},
Volume = {10},
DOI = {10.1088/0951-7715/10/5/009}
}
@Article{CaKno99,
Title = {Pattern formation in three-dimensional reaction-diffusion systems},
Author = {T. K. Callahan and E. Knobloch},
Journal = {Physica D},
Year = {1999},
Pages = {339--362},
Volume = {132},
DOI = {10.1016/S0167-2789(99)00041-X}
}
@Article{Calvo2008,
Title = {Variable step implementation of {ETD} methods for semilinear problems},
Author = {Calvo, M. P. and Portillo, A. M.},
Journal = {Appl. Math. Comput.},
Year = {2008},
Pages = {627--637},
Volume = {196},
DOI = {10.1016/j.amc.2007.06.025}
}
@Article{camporeale06,
Title = {New approach for the study of linear {Vlasov} stability of inhomogeneous systems},
Author = {E. Camporeale and G. L. Delzanno and G. Lapenta and W. Daughton},
Journal = {Phys. Plasmas},
Year = {2006},
Pages = {092110},
Volume = {13}
}
@Article{Cantwell92,
Title = {Exact solution of a restricted {Euler} equation for the velocity gradient tensor},
Author = {B. J. Cantwell},
Journal = {Phys. Fluids A},
Year = {1992},
Pages = {782--793},
Volume = {4},
DOI = {10.1063/1.858295}
}
@Book{Canuto88,
Title = {Spectral Methods in Fluid Dynamics},
Author = {C. Canuto and M. Y. Hussaini and A. Quateroni and T. A. Zhang},
Publisher = {Springer},
Year = {1988},
Address = {New York},
ISBN = {9783642841088}
}
@InBook{CapTof11,
pages = {77--88},
title = {Can anything from {Noether's} theorem be salvaged for discrete dynamical systems?},
publisher = {Springer},
year = {2011},
author = {Capobianco, S. and Toffoli, T.},
editor = {Calude, C. S. and Kari, J. and Petre, I. and Rozenberg, G.},
address = {Berlin, Heidelberg},
isbn = {978-3-642-21341-0},
booktitle = {Unconventional Computation: 10th International Conference, UC 2011, Turku, Finland},
doi = {10.1007/978-3-642-21341-0_13},
}
@Phdthesis{Caradoc2000,
Title = {Vortex dynamics in {Bose-Einstein} condensates},
Author = {B. M. Caradoc-Davies},
School = {Univ. Otago},
Year = {2000},
Address = {Dunedin, New Zealand}
}
@Article{car88,
author = {F. Cariello and M. Tabor},
title = {{P}ainlev\'{e} expansions for nonintegrable evolution equations},
journal = {Physica D},
year = {1989},
volume = {39},
pages = {77},
doi = {10.1016/0167-2789(89)90040-7},
}
@Article{CFGT15,
Title = {Noose structure and bifurcations of periodic orbits in reversible three-dimensional piecewise linear differential systems},
Author = {Carmona, V. and Fern{\'a}ndez-S{\'a}nchez, F. and Garc{\'i}a-Medina, E. and Teruel, A. E.},
Journal = {J. Nonlin. Sci},
Year = {2015},
Pages = {1209--1224},
Volume = {25},
DOI = {10.1007/s00332-015-9251-z}
}
@Article{CaPe84,
Title = {Regular and chaotic motion in some quartic potentials},
Author = {A. Carnegie and I. C. Percival},
Journal = {J. Phys. A},
Year = {1984},
Pages = {801},
Volume = {17},
DOI = {10.1088/0305-4470/17/4/020}
}
@Incollection{Carr12,
Author = {K. M. Carroll},
Booktitle = {{ChaosBook.org/projects}},
Publisher = {Georgia Inst. of Technology},
Year = {2012},
Chapter = {A review of return maps for {R\"ossler} and the complex {Lorenz}},
URL = {http://ChaosBook.org/projects/index.shtml#Carroll}
}
@Book{CartanMF,
Title = {La m\'ethode du rep\`ere mobile, la th\'eorie des groupes continus, et les espaces g\'en\'eralis\'es},
Author = {Cartan, \'E.},
Publisher = {Hermann},
Year = {1935},
Address = {Paris},
Series = {{Expos\'es} de {G\'eom\'etrie}},
Volume = {5}
}
@Book{Cartan01,
Title = {Riemannian geometry in an orthogonal frame: {From} lectures delivered by \'Elie Cartan at the Sorbonne in 1926-1927},
Author = {Cartan, \'E.},
Publisher = {World Scientific},
Year = {2001},
Address = {River Edge, NJ},
ISBN = {9810247478}
}
@Article{CaCiDeBr12,
Title = {Model of a two-dimensional extended chaotic system: {Evidence} of diffusing dissipative solitons},
Author = {Cartes, C. and Cisternas, J. and Descalzi, O. and Brand, H. R.},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Pages = {178303},
Volume = {109},
DOI = {10.1103/PhysRevLett.109.178303}
}
@Article{Cartes14,
Title = {Exploding dissipative solitons in the cubic-quintic complex {Ginzburg-Landau} equation in one and two spatial dimensions},
Author = {C. Cartes and O. Descalzi and H. R. Brand},
Journal = {Eur. Phys. J. Spec. Top.},
Year = {2014},
Pages = {2145--2159},
Volume = {223},
DOI = {10.1140/epjst/e2014-02255-2}
}
@Article{CarLit45,
Title = {On non-linear differential equations of the second order},
Author = {M. L. Cartwright and J. E. Littlewood},
Journal = {J. London Math. Soc.},
Year = {1945},
Pages = {180--189},
Volume = {20},
DOI = {10.1112/jlms/s1-20.3.180}
}
@Article{Carvalho99,
Title = {Pruning fronts and the formation of horseshoes},
Author = {de Carvalho, A.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {1999},
Pages = {851--894},
Volume = {19},
DOI = {10.1017/S0143385799133972}
}
@Article{CaHa01a,
Title = {Pruning theory and {Thurston}'s classification of surface homeomorphisms},
Author = {de Carvalho, A. and Hall, T.},
Journal = {J. Eur. Math. Soc.},
Year = {2001},
Pages = {287--333},
Volume = {3}
}
@Article{CaHa02,
Title = {How to prune a horseshoe},
Author = {de Carvalho, A. and Hall, T.},
Journal = {Nonlinearity},
Year = {2002},
Pages = {R19--R68},
Volume = {15}
}
@Article{CaHa01b,
Title = {The forcing relation for horseshoe braid types},
Author = {de Carvalho, A. and Hall, T.},
Journal = {Experimental Math.},
Year = {2002},
Pages = {271--288},
Volume = {11}
}
@Article{CaHa03,
Title = {Conjugacies between horseshoe braids},
Author = {de Carvalho, A. and Hall, T.},
Journal = {Nonlinearity},
Year = {2003},
Pages = {1329--1338},
Volume = {16}
}
@Article{CaHa04a,
author = {de Carvalho, A. and Hall, T.},
title = {Braid forcing and star-shaped train tracks},
journal = {Topology},
year = {2004},
volume = {43},
pages = {247--287},
doi = {10.1016/s0040-9383(03)00042-9},
}
@Article{CaHa04b,
Title = {Unimodal generalized pseudo-{Anosov} maps},
Author = {de Carvalho, A. and Hall, T.},
Journal = {Geometry and Topology},
Year = {2004},
Pages = {1127--1188},
Volume = {8}
}
@Article{CarMei,
Title = {Rigorously diffusive deterministic map},
Author = {J. R. Cary and J. D. Meiss},
Journal = {Phys. Rev. A},
Year = {1981},
Pages = {2664--2668},
Volume = {24},
DOI = {10.1103/PhysRevA.24.2664}
}
@Book{GiBo,
Title = {Quantum chaos: Between order and disorder},
Author = {G. Casati and B. V. Chirikov},
Publisher = {Cambridge Univ. Press},
Year = {1995},
Address = {Cambridge}
}
@Misc{CaCaKi63,
Title = {{The Ring of Fire}},
Author = {Cash, J. and Carter Cash, J. and Kilgore, M.},
Year = {1963},
Address = {New York},
Publisher = {Columbia Records}
}
@Article{Cassanas05b,
author = {R. Cassanas},
title = {Reduced {Gutzwiller} formula with symmetry: {Case} of a {Lie} group},
journal = {J. Math. Pures et Appl.},
year = {2006},
volume = {85},
pages = {719--742},
doi = {10.1016/j.matpur.2005.11.003},
}
@Article{Cassanas05a,
Title = {Reduced {Gutzwiller} formula with symmetry: {Case} of a finite group},
Author = {R. Cassanas},
Journal = {J. Math. Phys.},
Year = {2006},
Pages = {042102},
Volume = {47},
DOI = {10.1063/1.2184890}
}
@Article{castel01,
Title = {Experimental study of chaotic advection regime in a twisted duct flow},
Author = {Castelain, C. and Mokrani, A. and Le Guer, Y. and Peerhossaini, H.},
Journal = {Eur. J. Mechanics B},
Year = {2001},
Pages = {205--232},
Volume = {20},
DOI = {10.1016/S0997-7546(00)01116-X}
}
@Article{Cattell2000,
author = {K. Cattell and F. Ruskey and J. Sawada and M. Serra and C. R. Miers},
title = {Fast algorithms to generate necklaces, unlabeled necklaces, and irreducible polynomials over {GF(2)}},
journal = {J. Algorithms},
year = {2000},
volume = {37},
pages = {267--282},
doi = {10.1006/jagm.2000.1108},
}
@Article{CeMaOw03,
Title = {Commutator-free {Lie} group methods},
Author = {E. Celledoni and A. Marthinsen and B. Owren},
Journal = {Future Generation Computer Systems },
Year = {2003},
Pages = {341--352},
Volume = {19},
DOI = {10.1016/S0167-739X(02)00161-9}
}
@Article{CenGin13,
Title = {{Lyapunov} analysis: from dynamical systems theory to applications},
Author = {M. Cencini and F. Ginelli},
Journal = {J. Phys. A},
Year = {2013},
Pages = {250301},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/250301}
}
@Article{CenVul13,
Title = {Finite size {Lyapunov} exponent: review on applications},
Author = {M. Cencini and A. Vulpiani},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254019},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254019}
}
@Article{CHHM98,
author = {Cendra, H. and Holm, D. D. and Hoyle, M. J. W. and Marsden, J. E.},
title = {The {Maxwell-Vlasov} equations in {Euler-Poincar\'e} form},
journal = {J. of Math. Phys.},
year = {1998},
volume = {39},
pages = {3138--3157},
doi = {10.1063/1.532244},
}
@Article{detect,
Title = {Numerical detection and continuation of codimension-two homoclinic bifurcations},
Author = {Champneys, A. R. and Kuznetsov, Y. A.},
Journal = {Int. J. Bifur. Chaos},
Year = {1994},
Pages = {785--822},
Volume = {4}
}
@Article{homcont,
Title = {A numerical toolbox for homoclinic bifurcation analysis},
Author = {Champneys, A. R. and Kuznetsov, Y. A. and Sandstede, B.},
Journal = {Int. J. Bifur. Chaos},
Year = {1996},
Pages = {867--887},
Volume = {6}
}
@Article{ChaKer12,
author = {Chandler, G. J. and Kerswell, R. R.},
title = {Invariant recurrent solutions embedded in a turbulent two-dimensional {Kolmogorov} flow},
journal = {J. Fluid Mech.},
year = {2013},
volume = {722},
pages = {554--595},
doi = {10.1017/jfm.2013.122},
}
@Incollection{ChaosBookChaDiaSch,
Title = {Discrete iteration relaxation method},
Author = {C. Chandre and F.K. Diakonos and P. Schmelcher},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Institute},
Year = {2012},
Edition = {14},
Editor = {P. Cvitanovi\'c and R. Artuso and R. Mainieri and G. Tanner and G. Vattay},
URL = {http://ChaosBook.org/paper.shtml#relax}
}
@Article{chand03tf,
author = {C. Chandre and S. Wiggins and T. Uzer},
title = {Time-frequency analysis of chaotic systems},
journal = {Physica D},
year = {2003},
volume = {181},
pages = {171--196},
doi = {10.1016/s0167-2789(03)00117-9},
}
@Article{kschang86,
Title = {Travelling waves on fluid interfaces: {Normal} form analysis of the {Kuramoto-Sivashinsky} equation},
Author = {H.-C. Chang},
Journal = {Phys. Fluids},
Year = {1986},
Pages = {3142},
Volume = {29},
DOI = {10.1063/1.865965}
}
@Article{chang94,
Title = {Wave evolution on a falling film},
Author = {H.-C. Chang},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1994},
Pages = {103--136},
Volume = {26},
DOI = {10.1146/annurev.fl.26.010194.000535}
}
@Article{Chang07,
Title = {Creeping solitons in dissipative systems and their bifurcations},
Author = {Chang, W. and Ankiewicz, A. and Akhmediev, N. and Soto-Crespo, J. M.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {016607},
Volume = {76},
DOI = {10.1103/PhysRevE.76.016607}
}
@Article{Chang2015b,
Title = {Extreme amplitude spikes in a laser model described by the complex {Ginzburg--Landau} equation},
Author = {Chang, W. and Soto-Crespo, J. M. and Vouzas, P. and Akhmediev, N.},
Journal = {Opt. Lett.},
Year = {2015},
Pages = {2949--2952},
Volume = {40},
DOI = {10.1364/OL.40.002949}
}
@Article{Change15,
Title = {Extreme soliton pulsations in dissipative systems},
Author = {Chang, W. and Soto-Crespo, J. M. and Vouzas, P. and Akhmediev, N.},
Journal = {Phys. Rev. E},
Year = {2015},
Pages = {022926},
Volume = {92},
DOI = {10.1103/PhysRevE.92.022926}
}
@Article{C02,
Title = {Subcritical transition in channel flows},
Author = {S. J. Chapman},
Journal = {J. Fluid Mech.},
Year = {2002},
Pages = {35--97},
Volume = {451}
}
@Article{ChaDeVore79,
Title = {Multiple flow equilibria in the atmosphere and blocking},
Author = {J. G. Charney and J. G. DeVore},
Journal = {J. Meteorology},
Year = {1979},
Pages = {1205--1216},
Volume = {36},
DOI = {10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2}
}
@Article{CLMM96,
author = {Chat{\'e}, H. and Lemaitre, A. and Marcq, P. and Manneville, P.},
title = {Non-trivial collective behavior in extensively-chaotic dynamical systems: an update},
journal = {Physica A},
year = {1996},
volume = {224},
pages = {447--457},
doi = {10.1016/0378-4371(95)00352-5},
}
@Article{chate94,
Title = {Spatiotemporal intermittency regimes of the one-dimensional complex {Ginzburg-Landau} equation},
Author = {H. Chat\'{e}},
Journal = {Nonlinearity},
Year = {1994},
Pages = {185--204},
Volume = {7},
DOI = {10.1088/0951-7715/7/1/007}
}
@Article{CM87tran,
author = {H. Chat\'{e} and Manneville, P.},
title = {Transition to Turbulence via spatiotemporal Intermittency},
journal = {Phys. Rev. Lett.},
year = {1987},
volume = {58},
pages = {112},
doi = {10.1007/978-3-642-74554-6_75},
}
@Article{ChaMann91,
Title = {Evidence of collective behaviour in cellular automata},
Author = {H. Chat\'{e} and P. Manneville},
Journal = {Europhys. Lett.},
Year = {1991},
Pages = {409},
Volume = {14},
Abstract = {A nontrivial collective behaviour occurring in cellular automata for
rather high space dimensions is presented and investigated numerically.
Evidence is given that this dynamical state is neither transient
nor due to the finite size of the lattice. Possible theoretical approaches
are discussed for this phenomenon showing many aspects of low-dimensional
dynamical systems and yet exhibited by many-body nonequilibrium models.},
DOI = {10.1209/0295-5075/14/5/004}
}
@Book{chat_mixing99,
Title = {Mixing - chaos and turbulence},
Author = {H. Chat\'{e} and E. Villermaux and J.-M. Chomaz},
Publisher = {Kluwer},
Year = {1999},
Address = {Dordrecht}
}
@Article{Cha74,
Title = {Formule de {Poisson} pour les vari\'et\'es riemanniennes},
Author = {Chazarain, J.},
Journal = {Inv. Math.},
Year = {1974},
Pages = {65--82},
Volume = {24},
DOI = {10.1007/BF01418788}
}
@Article{chemillier04,
author = {M. Chemillier},
title = {Periodic musical sequences and {Lyndon} words},
journal = {Soft Comput.},
year = {2004},
volume = {8},
pages = {611--616},
doi = {10.1007/s00500-004-0387-2},
}
@Book{ChPiWa89,
Title = {{Group Representation Theory for Physicists}},
Author = {Chen, J.-Q. and Ping, J. and Wang, F.},
Publisher = {World Scientific},
Year = {1989},
Address = {Singapore},
DOI = {10.1142/0262}
}
@Article{Chen90b,
Title = {Resonances and transport in the sawtooth map},
Author = {Q. Chen and I. Dana and Meiss, J. D. and N. W. Murray and I. C. Percival},
Journal = {Physica D},
Year = {1990},
Pages = {217--240},
Volume = {46},
DOI = {10.1016/0167-2789(90)90037-P}
}
@Article{Chen87,
author = {Q. Chen and Meiss, J. D., and I. C. Percival},
title = {Orbit extension methods for finding unstable orbits},
journal = {Physica D},
year = {1987},
volume = {29},
pages = {143--154},
doi = {10.1016/0167-2789(87)90051-0},
}
@Article{Chen08,
Title = {Theory of dissipative solitons in complex {Ginzburg-Landau} systems},
Author = {Chen, S.},
Journal = {Phys. Rev. E},
Year = {2008},
Pages = {025601},
Volume = {78},
DOI = {10.1103/PhysRevE.78.025601}
}
@Article{ChChYu14,
Title = {Topological horseshoes in travelling waves of discretized nonlinear wave equations},
Author = {Chen, Y.-C. and Chen, S.-S. and Yuan, J.-M.},
Journal = {J. Math. Phys.},
Year = {2014},
Pages = {042701},
Volume = {55},
DOI = {10.1063/1.4870618}
}
@Article{Chenc05,
author = {A. Chenciner},
title = {A note by {P}oincar{\'e}},
journal = {Regul. Chaotic Dyn.},
year = {2005},
volume = {10},
pages = {119--128},
url = {http://www.turpion.org/php/paper.phtml?journal_id=rd&paper_id=306},
}
@Article{ChencinerLink,
author = {A. Chenciner},
title = {Three body problem},
journal = {Scholarpedia},
year = {2007},
volume = {2},
pages = {2111},
doi = {10.4249/scholarpedia.2111},
}
@Incollection{CGMS02,
Title = {Simple choreographic motions of {$N$}-bodies: {A} preliminary study},
Author = {A. Chenciner and J. Gerver and R. Montgomery and Sim{\'o}, C.},
Booktitle = {Geometry, Mechanics and Dynamics},
Publisher = {Springer},
Year = {2002},
Address = {New York},
Editor = {P. Newton and P. Holmes and A. Weinstein},
Pages = {287--308},
DOI = {10.1007/0-387-21791-6_9},
ISBN = {978-0-387-95518-6}
}
@Article{CheMon00,
Title = {A remarkable solution of the 3\mbox{-}{b}ody problem in the case of equal masses},
Author = {A. Chenciner and R. Montgomery},
Journal = {Ann. Math.},
Year = {2000},
Pages = {881--901},
Volume = {152}
}
@Article{CheSu90,
Title = {Existence of invariant tori in three-dimensional measure-preserving mappings},
Author = {Cheng, C. Q. and Sun, Y. S.},
Journal = {Celest. Mech. Dynam. Astronom.},
Year = {1990},
Pages = {275--292},
Volume = {47},
DOI = {10.1007/BF00053456}
}
@Article{Cherry28,
Title = {On periodic solutions of {Hamiltonian} systems of differential equations},
Author = {Cherry, T. M.},
Journal = {Proc. Roy. Soc. Lond. Ser A},
Year = {1928},
Pages = {137--221},
Volume = {227}
}
@Article{CheChe06,
Title = {Loop calculus in statistical physics and information science},
Author = {M. Chertkov and V. Y. Chernyak},
Journal = {Phys. Rev. E},
Year = {2006},
Pages = {065102},
Volume = {73},
DOI = {10.1103/PhysRevE.73.065102}
}
@Article{CheChe06a,
Title = {Loop series for discrete statistical models on graphs},
Author = {M. Chertkov and V. Y. Chernyak},
Journal = {J. Stat. Mech.},
Year = {2006},
Pages = {P06009},
Volume = {2006},
DOI = {10.1088/1742-5468/2006/06/P06009}
}
@Article{ChChTe08,
Title = {Belief propagation and loop series on planar graphs},
Author = {M. Chertkov and V. Y. Chernyak and R. Teodorescu},
Journal = {J. Stat. Mech.},
Year = {2008},
Pages = {P05003},
Volume = {2008},
DOI = {10.1088/1742-5468/2008/05/P05003}
}
@Article{ChePuShr99,
author = {Chertkov, M. and Pumir, A. and Shraiman, B. I.},
title = {Lagrangian tetrad dynamics and the phenomenology of turbulence},
journal = {Phys. Fluids},
year = {1999},
volume = {11},
pages = {2394--2410},
doi = {10.1063/1.870101},
}
@Article{CRMRF02,
author = {A. {C.-L.} Chian and E. L. Rempel and E. E. Macau and R. R. Rosa and F. Christiansen},
title = {High-dimensional interior crisis in the {Kuramoto-Sivashinsky} equation},
journal = {Phys. Rev. E},
year = {2002},
volume = {65},
pages = {035203},
doi = {10.1103/physreve.65.035203},
}
@Article{CMRSY10,
Title = {Amplitude-phase synchronization at the onset of permanent spatiotemporal chaos},
Author = {Chian, A. C. and Miranda, R. A. and Rempel, E. L. and Saiki, Y. and Yamada, M.},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {254102},
Volume = {104},
DOI = {10.1103/PhysRevLett.104.254102}
}
@Article{CSRBHK07,
Title = {Chaos in driven Alfv\'en systems: {Unstable} periodic orbits and chaotic saddles},
Author = {Chian, A. C.-L. and Santana, W. M. and Rempel, E. L. and Borotto, F. A. and Hada, T. and Kamide, Y.},
Journal = {Nonlin. Proc. Geophys.},
Year = {2007},
Pages = {17--29},
Volume = {14},
Abstract = { The chaotic dynamics of Alfv\'en waves in space plasmas governed
by the derivative nonlinear Schr\"odinger equation, in the low-dimensional
limit described by stationary spatial solutions, is studied. A bifurcation
diagram is constructed, by varying the driver amplitude, to identify
a number of nonlinear dynamical processes including saddle-node bifurcation,
boundary crisis, and interior crisis. The roles played by unstable
periodic orbits and chaotic saddles in these transitions are analyzed,
and the conversion from a chaotic saddle to a chaotic attractor in
these dynamical processes is demonstrated. In particular, the phenomenon
of gap-filling in the chaotic transition from weak chaos to strong
chaos via an interior crisis is investigated. A coupling unstable
periodic orbit created by an explosion, within the gaps of the chaotic
saddles embedded in a chaotic attractor following an interior crisis,
is found numerically. The gap-filling unstable periodic orbits are
responsible for coupling the banded chaotic saddle (BCS) to the surrounding
chaotic saddle (SCS), leading to crisis-induced intermittency. The
physical relevance of chaos for Alfv\'en intermittent turbulence
observed in the solar wind is discussed. },
DOI = {10.5194/npg-14-17-2007}
}
@Book{Chicone2006,
Title = {Ordinary Differential Equations with Applications},
Author = {C. Chicone},
Publisher = {Springer},
Year = {2006},
Address = {New York}
}
@Article{Chillingworth2000,
author = {D. Chillingworth},
title = {Generic multiparameter bifurcation from a manifold},
journal = {Dyn. Stab. Syst.},
year = {2000},
volume = {15},
pages = {101--137},
doi = {10.1080/02681110050032119},
}
@Article{Chirikov79,
Title = {A universal instability of many-dimensional oscillator system},
Author = {B. V. Chirikov},
Journal = {Phys. Rep.},
Year = {1979},
Pages = {263--379},
Volume = {52},
DOI = {10.1016/0370-1573(79)90023-1}
}
@Article{ChoGuck99,
author = {W. G. Choe and J. Guckenheimer},
title = {Computing periodic orbits with high accuracy},
journal = {Computer Meth. Appl. Mech. and Engin.},
year = {1999},
volume = {170},
pages = {331--341},
doi = {10.1016/S0045-7825(98)00201-1},
}
@Article{ChPeCa90,
Title = {A general classification of three-dimensional flow fields},
Author = {{Chong}, M.~S. and {Perry}, A.~E. and {Cantwell}, B.~J.},
Journal = {Phys. Fluids},
Year = {1990},
Pages = {765--777},
Volume = {2}
}
@Article{Choss93,
Title = {Forced reflectional symmetry breaking of an {O(2)}-symmetric homoclinic tangle},
Author = {Chossat, P.},
Journal = {Nonlinearity},
Year = {1993},
Pages = {723--731},
Volume = {6},
DOI = {10.1088/0951-7715/6/5/003}
}
@Article{Choss01,
Title = {The bifurcation of heteroclinic cycles in systems of hydrodynamic type},
Author = {Chossat, P.},
Journal = {Dyn. Contin. Discr. Impul. Syst., Ser. A.},
Year = {2001},
Pages = {575--590},
Volume = {8},
URL = {http://online.watsci.org/fulltext_a_pdf/2001v8/v8n4a-pdf/p7.pdf}
}
@Article{Choss02,
Title = {The reduction of equivariant dynamics to the orbit space for compact group actions},
Author = {Chossat, P.},
Journal = {Acta Appl. Math.},
Year = {2002},
Pages = {71--94},
Volume = {70},
DOI = {10.1023/A:101397001420}
}
@Book{Chossat94,
Title = {The {Taylor-Couette} Problem},
Author = {P. Chossat and G. Iooss},
Publisher = {Springer},
Year = {1994},
Address = {New York}
}
@Book{ChossLaut00,
title = {{Methods in Equivariant Bifurcations and Dynamical Systems}},
publisher = {World Scientific},
year = {2000},
author = {P. Chossat and R. Lauterbach},
address = {Singapore},
isbn = {978-981-02-3828-5},
doi = {10.1142/4062},
}
@Article{ChMaSh98,
Title = {Traveling waves in lattice dynamical systems},
Author = {Chow, S.-N. and Mallet-Paret, J. and Shen, W.},
Journal = {J. Diff. Equ.},
Year = {1998},
Pages = {248--291},
Volume = {149},
DOI = {10.1006/jdeq.1998.3478}
}
@Article{ChMaVanV96,
Title = {Pattern formation and spatial chaos in spatially discrete evolution equations},
Author = {Chow, S.-N. and Mallet-Paret, J. and Van Vleck, E. S.},
Journal = {Random Comput. Dynam.},
Year = {1996},
Pages = {109--178},
Volume = {4},
DOI = {10.1.1.52.3402}
}
@PhdThesis{FreddyThesis,
author = {Christiansen, F.},
title = {{Periodic Orbits in Classical and Quantum Chaos}},
school = {Copenhagen Univ.},
year = {1992},
address = {Copenhagen},
}
@Article{CC92,
Title = {Periodic orbit quantization of the anisotropic {Kepler} problem},
Author = {F. Christiansen and P. Cvitanovi{\'c}},
Journal = {Chaos},
Year = {1992},
Pages = {61--69},
Volume = {2},
DOI = {10.1063/1.165899}
}
@Article{Christiansen97,
Title = {{Spatiotemporal} chaos in terms of unstable recurrent patterns},
Author = {F. Christiansen and P. Cvitanovi{\'c} and V. Putkaradze},
Journal = {Nonlinearity},
Year = {1997},
Pages = {55--70},
Volume = {10},
DOI = {10.1088/0951-7715/10/1/004}
}
@Article{Christiansen96,
Title = {Hopf's last hope: {Spatiotemporal} chaos in terms of unstable recurrent patterns},
Author = {F. Christiansen and P. Cvitanovi{\'c} and V. Putkaradze},
Journal = {Nonlinearity},
Year = {1997},
Addendum = {\arXiv{chao-dyn/9606016}},
Pages = {55--70},
Volume = {10},
DOI = {10.1088/0951-7715/10/1/004}
}
@Article{CCR,
Title = {The spectrum of the period-doubling operator in terms of cycles},
Author = {Christiansen, F. and Cvitanovi{\'c}, P. and Rugh, H. H.},
Journal = {J. Phys. A},
Year = {1999},
Pages = {713--717},
Volume = {23},
DOI = {10.1088/0305-4470/23/14/005}
}
@Article{chr95gen,
Title = {Generating partition for the standard map},
Author = {F. Christiansen and A. Politi},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {3811--3814},
Volume = {51}
}
@Article{ChPo96,
Title = {Symbolic encoding in symplectic maps},
Author = {F. Christiansen and A. Politi},
Journal = {Nonlinearity},
Year = {1996},
Pages = {1623--1640},
Volume = {9}
}
@Article{ChPo97,
author = {F. Christiansen and A. Politi},
title = {Guidelines for the constuction of a generating partition in the standard map},
journal = {Physica D},
year = {1997},
volume = {109},
pages = {32--41},
doi = {10.1016/s0167-2789(97)00156-5},
}
@Article{ChRu97,
Title = {Computing {Lyapunov} spectra with continuous {Gram-Schmidt} orthonormalization},
Author = {Christiansen, F. and Rugh, H. H.},
Journal = {Nonlinearity},
Year = {1997},
Pages = {1063--1072},
Volume = {10}
}
@Article{ChrLueOtt11,
author = {{Christov}, I. C. and {Lueptow}, R. M. and {Ottino}, J. M.},
title = {{Stretching and folding versus cutting and shuffling: {An} illustrated perspective on mixing and deformations of continua}},
journal = {Amer. J. Physics},
year = {2011},
volume = {79},
pages = {359--367},
doi = {10.1119/1.3533213},
}
@Article{ChKuRo83,
author = {Churchill, R. C. and Kummer, M. and Rod, D. L.},
title = {On averaging, reduction, and symmetry in {Hamiltonian} systems},
journal = {J. Diff. Eqn.},
year = {1983},
volume = {49},
pages = {359--414},
doi = {10.1016/0022-0396(83)90003-7},
}
@Article{cima_algebraic_1997,
author = {A. Cima},
title = {Algebraic properties of the {Lyapunov} and period constants},
journal = {Rocky Mountain J. Math.},
year = {1997},
volume = {27},
pages = {471--501},
doi = {10.1216/rmjm/1181071923},
}
@Article{cima_relation_1998,
Title = {On the relation between index and multiplicity},
Author = {A. Cima},
Journal = {J. London Math. Soc.},
Year = {1998},
Pages = {757--768},
Volume = {57}
}
@Article{cima_dynamics_2006,
Title = {Dynamics of some rational discrete dynamical systems via invariants},
Author = {A. Cima},
Journal = {Int. J. Bifur. Chaos},
Year = {2006},
Pages = {631--646},
Volume = {16}
}
@Article{cima_number_2008,
Title = {On the number of critical periods for planar polynomial systems},
Author = {A. Cima},
Journal = {Nonlinear Anal.},
Year = {2008},
Pages = {1889--1903},
Volume = {69}
}
@Article{cima_studying_2008,
author = {A. Cima and A. Gasull and V. Manosa},
title = {Studying discrete dynamical systems through differential equations},
journal = {J. Diff. Eqn.},
year = {2008},
volume = {244},
pages = {630--648},
doi = {10.1016/j.jde.2007.10.013},
}
@Article{cima_periodic_2007,
author = {A. Cima and A. Gasull and F. Manosas},
title = {Periodic orbits in complex {Abel} equations},
journal = {J. Diff. Eqn.},
year = {2007},
volume = {232},
pages = {314--328},
doi = {10.1016/j.jde.2006.09.002},
}
@Article{Cimasoni10,
Title = {A generalized {Kac-Ward} formula},
Author = {Cimasoni, D.},
Journal = {J. Stat. Mech.},
Year = {2010},
Pages = {P07023},
Volume = {2010},
DOI = {10.1088/1742-5468/2010/07/P07023}
}
@Article{Cimasoni12,
Title = {The critical {Ising} model via {Kac-Ward} matrices},
Author = {Cimasoni, D.},
Journal = {Commun. Math. Phys.},
Year = {2012},
Pages = {99--126},
Volume = {316},
DOI = {10.1007/s00220-012-1575-z}
}
@Article{CiDiPu14,
Title = {Existence of standing waves for the complex {Ginzburg-Landau} equation},
Author = {{Cipolatti}, R. and {Dickstein}, F. and {Puel}, J. P},
Journal = {J. Math. Analysis and Applications},
Year = {2015},
Pages = {579--593},
Volume = {422},
DOI = {10.1016/j.jmaa.2014.08.057}
}
@Article{Jaime2013,
Title = {Intermittent explosions of dissipative solitons and noise-induced crisis},
Author = {Cisternas, J. and Descalzi, O.},
Journal = {Phys. Rev. E},
Year = {2013},
Pages = {022903},
Volume = {88},
DOI = {10.1103/PhysRevE.88.022903}
}
@Article{Cisternas2016,
Title = {Anomalous diffusion of dissipative solitons in the cubic-quintic complex {Ginzburg-Landau} equation in two spatial dimensions},
Author = {Cisternas, J. and Descalzi, O. and Albers, T. and Radons, G.},
Journal = {Phys. Rev. Lett.},
Year = {2016},
Pages = {203901},
Volume = {116},
DOI = {10.1103/PhysRevLett.116.203901}
}
@Article{Jaime2012,
Title = {The transition to explosive solitons and the destruction of invariant tori},
Author = {Cisternas, J. and Descalzi, O. and Cartes, C.},
Journal = {Cent. Eur. J. Phys.},
Year = {2012},
Pages = {660--668},
Volume = {10},
DOI = {10.2478/s11534-012-0023-1}
}
@Article{Clair14,
Title = {The {Ihara} zeta function of the infinite grid},
Author = {Clair, B.},
Journal = {Electron. J. Combin.},
Year = {2014},
Pages = {P2--16},
Volume = {21},
URL = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i2p16}
}
@Article{CB92,
Title = {Three-dimensional convection in a horizontal layer subjected to constant shear},
Author = {R. M. Clever and F. H. Busse},
Journal = {J. Fluid Mech.},
Year = {1992},
Pages = {511--527},
Volume = {234}
}
@Article{CB97,
Title = {Tertiary and quaternary solutions for plane {Couette} flow},
Author = {Clever, R. M. and Busse, F. H.},
Journal = {J. Fluid Mech.},
Year = {1997},
Pages = {137--153},
Volume = {344},
Abstract = {The manifold of Nagata steady solutions is explored in the parameter
space of the problem and their instabilities are investigated. These
instabilities usually lead to time-periodic solutions whose properties
do not differ much from those of the steady solutions except that
the amplitude varies in time. In some cases travelling wave solutions
which are asymmetric with respect to the midplane of the layer are
found as quaternary states of flow. Similarities with longitudinal
vortices recently observed in experiments are discussed.}
}
@Article{CoKrTeRo76,
Title = {Non-linear saturation of the dissipative trapped ion mode by mode coupling},
Author = {B. I. Cohen and J. A. Krommers and W. M. Tang and M. N. Rosenbluth},
Journal = {Nucl. Fusion},
Year = {1976},
Pages = {971--992},
Volume = {16}
}
@Article{cohen72,
Title = {Non-linear saturation of the dissipative trapped-ion mode by mode coupling},
Author = {B. I. Cohen and J. A. Krommes and W. M. Tang and M. N. Rosenbluth},
Journal = {Nucl. Fusion},
Year = {1972},
Pages = {971--991},
Volume = {16}
}
@Book{CoVanLo88,
Title = {Handbook for Matrix Computations},
Author = {Coleman, T. F. and Van Loan, C.},
Publisher = {SIAM},
Year = {1988},
Address = {Philadelphia}
}
@Article{CdV73,
Title = {Spectre du {Laplacien} et longeurs des g\`eod\`esiques p\`eriodiques, II.},
Author = {Colin de Verdi\`ere, Y.},
Journal = {Compositio. Math.},
Year = {1973},
Pages = {159--184},
Volume = {27}
}
@Article{CEEksgl93,
author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe},
title = {A global attracting set for the {Kuramoto-Sivashinsky} equation},
journal = {Commun. Math. Phys.},
year = {1993},
volume = {152},
pages = {203--214},
doi = {10.1007/bf02097064},
}
@Article{CEEks93,
author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe},
title = {Analyticity for the {Kuramoto-Sivashinsky} equation},
journal = {Physica D},
year = {1993},
volume = {67},
pages = {321--326},
doi = {10.1016/0167-2789(93)90168-z},
}
@Article{collet80,
Title = {Universal Properties of Maps on an interval},
Author = {P. Collet and J.-P. Eckmann and O. E. Lanford},
Journal = {Commun. Math. Phys.},
Year = {1980},
Pages = {211},
Volume = {76}
}
@Article{CoLe84,
Title = {Ergodic properties of the {Lozi} mappings},
Author = {P. Collet and Y. Levy},
Journal = {Commun. Math. Phys.},
Year = {1984},
Pages = {461},
Volume = {93}
}
@Article{Coma06,
Title = {Forced symmetry breaking from {SO(3)} to {SO(2)} for rotating waves on a sphere},
Author = {A. N. Comanici},
Journal = {Nonlinearity},
Year = {2006},
Pages = {999--1019},
Volume = {19},
DOI = {10.1088/0951-7715/19/5/001}
}
@Article{Constantin97,
Title = {The elusive singularity},
Author = {P. Constantin},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1997},
Pages = {12761},
Volume = {94},
DOI = {10.1073/pnas.94.24.12761}
}
@Article{CoDoe92,
Title = {Energy dissipation in shear driven turbulence},
Author = {P. Constantin and C. R. Doering},
Journal = {Phys. Rev. Lett},
Year = {1992},
Pages = {1648--1651},
Volume = {69},
DOI = {10.1103/PhysRevLett.69.1648}
}
@Article{CoDoe95,
Title = {Variational bounds in dissipative systems},
Author = {P. Constantin and C. R. Doering},
Journal = {Physica D},
Year = {1995},
Pages = {221--228},
Volume = {82},
DOI = {10.1016/0167-2789(94)00237-K}
}
@Article{const85,
author = {Constantin, P. and Foias, C. and Manley, O. P. and T{\'e}mam, R.},
title = {Determining modes and fractal dimension of turbulent flows},
journal = {J. Fluid Mech.},
year = {1985},
volume = {150},
pages = {427--440},
doi = {10.1017/S0022112085000209},
}
@Book{constantin_integral_1989,
title = {Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations},
publisher = {Springer},
year = {1989},
author = {P. Constantin and C. Foias and B. Nicolaenko and R. T{\'e}mam},
isbn = {9780387967295},
address = {New York},
doi = {10.1007/978-1-4612-3506-4},
}
@Book{contebook,
Title = {The {Painlev\'e} Property: One Century Later},
Author = {R. Conte},
Publisher = {Springer},
Year = {1999},
Address = {New York}
}
@Article{CoMu89,
author = {R. Conte and M. Musette},
title = {Painlev\'e analysis and {Backlund} transformations in the {Kuramoto-Sivashinsky} equation},
journal = {J. Phys. A.},
year = {1989},
volume = {22},
pages = {169--177},
doi = {10.1088/0305-4470/22/2/006},
}
@Book{CBG16,
Title = {{The Symmetries of Things}},
Author = {Conway, J. H. and Burgiel, H. and Goodman-Strauss, C.},
Publisher = {CRC Press},
Year = {2016},
Address = {Boca Raton, FL},
ISBN = {9781439864890}
}
@Article{CopKadZha01,
Title = {Reversible {Boolean} networks {I:} distribution of cycle lengths},
Author = {S.N. Coppersmith and L. P. Kadanoff and Z. Zhang},
Journal = {Physica D},
Year = {2001},
Pages = {11--29},
Volume = {149},
DOI = {10.1016/S0167-2789(00)00198-6}
}
@Book{Cornwell97,
Title = {Group Theory in Physics: An introduction},
Author = {Cornwell, J. F.},
Publisher = {Academic},
Year = {1997},
Address = {New York}
}
@Article{CosGre13,
Title = {Extending the length and time scales of {Gram-Schmidt Lyapunov} vector computations},
Author = {A. B. Costa and J. R. Green},
Journal = {J. Comput. Phys.},
Year = {2013},
Pages = {113--122},
Volume = {246},
DOI = {10.1016/j.jcp.2013.03.051}
}
@Article{daCosta16,
Title = {The {Feynman} identity for planar graphs},
Author = {da Costa, G. A. T. F.},
Journal = {Lett. Math. Phys.},
Year = {2016},
Pages = {1089--1107},
Volume = {106},
DOI = {10.1007/s11005-016-0858-2}
}
@Book{Cotton08,
Title = {Chemical applications of group theory},
Author = {Cotton, F. A.},
Publisher = {Wiley},
Year = {2008},
Address = {New York}
}
@Book{CoLiSh96,
Title = {Ideals, Varieties and Algorithms},
Author = {D. A. Cox and J. B. Little and D. 0'Shea},
Publisher = {Springer},
Year = {1996},
Address = {New York}
}
@Article{cox02jcomp,
Title = {Exponential time differencing for stiff systems},
Author = {Cox, S. M. and Matthews, P. C.},
Journal = {J. Comput. Phys.},
Year = {2002},
Pages = {430--455},
Volume = {176},
DOI = {10.1006/jcph.2002.6995}
}
@Book{Coxeter12,
title = {{Regular Polytopes}},
publisher = {Dover},
year = {1948},
author = {H. S. M. Coxeter},
isbn = {9780486141589},
address = {New York},
}
@Misc{CrDaGo16,
Title = {Minimal cover of high-dimensional chaotic attractors by embedded coherent structures},
Author = {Crane, D. L. and {Davidchack}, R. L. and {Gorban}, A. N.},
Year = {2016},
URL = {https://arxiv.org/abs/1607.02180}
}
@Article{crawford91,
author = {J. D. Crawford},
title = {Introduction to bifurcation theory},
journal = {Rev. Modern Phys.},
year = {1991},
volume = {63},
pages = {991--1037},
doi = {10.1103/revmodphys.63.991},
}
@Article{crawford97,
author = {J. D. Crawford},
title = {Amplitude equations for electrostatic waves: {Universal} singular behavior in the limit of weak instability},
journal = {Phys. Plasmas},
year = {1995},
volume = {2},
pages = {97--128},
doi = {10.1063/1.871120},
}
@Article{crawford89,
Title = {Application of the method of spectral deformation to the {Vlasov-Poisson} system},
Author = {J. D. Crawford and P. D. Hislop},
Journal = {Ann. Phys.},
Year = {1989},
Pages = {265--317},
Volume = {189},
DOI = {10.1016/0003-4916(89)90166-8}
}
@Article{CraKno91,
Title = {Symmetry and symmetry-breaking bifurcations in fluid dynamics},
Author = {J. D. Crawford and E. Knobloch},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1991},
Pages = {341--387},
Volume = {23},
DOI = {10.1146/annurev.fl.23.010191.002013}
}
@Article{Creagh93,
Title = {Semiclassical mechanics of symmetry reduction},
Author = {S. C. Creagh},
Journal = {J. Phys. A},
Year = {1993},
Pages = {95--118},
Volume = {26},
Abstract = {The author discusses semiclassical approximations that are adapted
to given symmetry classes in quantum mechanics. Arbitrary abelian
symmetries and also rotational symmetry are treated. Semiclassical
approximations are derived for the projected propagator and energy
dependent Green's function associated with a given irreducible representation
of the symmetry group. From these they derive trace formulae, analogous
to the usual trace formula, that determine the energy levels in a
given symmetry class in terms of classical orbits.}
}
@Article{Creagh94,
Title = {Quantum zeta function for perturbed cat maps},
Author = {S. C. Creagh},
Journal = {Chaos},
Year = {1995},
Pages = {477--493},
Volume = {5},
DOI = {10.1063/1.166119}
}
@Article{Creagh91,
Title = {Semiclassical trace formulas in the presence of continuous symmetries},
Author = {S. C. Creagh and R. G. Littlejohn},
Journal = {Phys. Rev. A},
Year = {1991},
Pages = {836--850},
Volume = {44}
}
@Article{Creagh92,
Title = {Semiclassical trace formulas for systems with non-Abelian symmetry},
Author = {S. C. Creagh and R. G. Littlejohn},
Journal = {J. Phys. A},
Year = {1992},
Pages = {1643--1669},
Volume = {25}
}
@Book{latt,
Title = {Quantum Fields on the Computer},
Author = {M. Creutz},
Publisher = {World Scientific},
Year = {1992},
Address = {Singapore}
}
@Article{Cristad06,
Title = {Fractal diffusion coefficient from dynamical zeta functions},
Author = {G. Cristadoro},
Journal = {J. Phys. A},
Year = {2006},
Pages = {L151},
Volume = {39},
DOI = {10.1088/0305-4470/39/10/L01}
}
@Article{CriKnDeEsp12,
author = {Cristadoro, G. and Knight, G. and Degli Esposti, M.},
title = {Follow the fugitive: an application of the method of images to open systems},
journal = {J. Phys. A},
year = {2013},
volume = {46},
pages = {272001},
doi = {10.1088/1751-8113/46/27/272001},
}
@Phdthesis{Crockett10,
Title = {Orbit Space Reduction for Symmetric Dynamical Systems with an Application to Laser Dynamics},
Author = {Crockett, V. J.},
School = {Univ. of Exeter},
Year = {2010},
Address = {Exeter, UK},
URL = {http://hdl.handle.net/10036/3310}
}
@Phdthesis{Crofts07thesis,
Title = {Efficient method for detection of periodic orbits in chaotic maps and flows},
Author = {J. J. Crofts},
School = {Department of Mathematics, Univ of Leicester},
Year = {2007},
Address = {Leicester, UK},
URL = {http://arXiv.org/abs/nlin.CD/0706.1940}
}
@Article{CroDav06,
Title = {Efficient detection of periodic orbits in chaotic systems by stabilizing transformations},
Author = {J. J. Crofts and R. L. Davidchack},
Journal = {SIAM J. Sci. Comp.},
Year = {2006},
Pages = {1275--1288},
Volume = {28},
DOI = {10.1137/050623401}
}
@Article{CroDav09,
Title = {On the use of stabilizing transformations for detecting unstable periodic orbits in high-dimensional flows},
Author = {J. J. Crofts and R. L. Davidchack},
Journal = {Chaos},
Year = {2009},
Pages = {033138},
Volume = {19},
DOI = {10.1063/1.3222860}
}
@Article{cross93,
Title = {Pattern formation outside of equilibrium},
Author = {Cross, M. C. and Hohenberg, P. C.},
Journal = {Rev. Mod. Phys.},
Year = {1993},
Pages = {851--1112},
Volume = {65},
DOI = {10.1103/RevModPhys.65.851}
}
@Article{cross94sp,
author = {Cross, M. C. and Hohenberg, P. C.},
title = {Spatiotemporal Chaos},
journal = {Science},
year = {1994},
volume = {263},
pages = {1569--1570},
doi = {10.1126/science.263.5153.1569},
}
@Article{CCW05,
Title = {A new property of a class of {Jacobi} polynomials},
Author = {G. Csordas and M. Charalambides and F. Waleffe},
Journal = {Proc. Amer. Math. Soc.},
Year = {2005},
Pages = {3551--3560},
Volume = {133}
}
@Article{CuSoAk02,
Title = {Experimental evidence for soliton explosions},
Author = {Cundiff, S. T. and Soto-Crespo, J. M. and Akhmediev, N.},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Pages = {073903},
Volume = {88},
DOI = {10.1103/PhysRevLett.88.073903}
}
@Article{Curry78,
Title = {A generalized {Lorenz} system},
Author = {Curry, J. H.},
Journal = {Commun. Math. Phys.},
Year = {1978},
Pages = {193--204},
Volume = {60}
}
@Book{CushBat97,
title = {{Global Aspects of Classical Integrable Systems}},
publisher = {Birkh{\"{a}}user},
year = {1997},
author = {Cushman, R. H. and Bates, L. M.},
address = {Boston},
doi = {10.1007/978-3-0348-8891-2},
}
@Article{Cutkosky84,
Title = {The {Gribov} horizon},
Author = {Cutkosky, R. E.},
Journal = {Phys. Rev. D},
Year = {1984},
Pages = {447--454},
Volume = {30},
DOI = {10.1103/PhysRevD.30.447}
}
@Article{inv,
Title = {Invariant measurement of strange sets in terms of cycles},
Author = {P. Cvitanovi{\'c}},
Journal = {Phys. Rev. Lett.},
Year = {1988},
Pages = {2729--2732},
Volume = {61},
DOI = {10.1103/PhysRevLett.61.2729}
}
@Book{cvt89b,
Title = {Universality in Chaos},
Author = {P. Cvitanovi{\'c}},
Publisher = {Adam Hilger},
Year = {1989},
Address = {Bristol},
ISBN = {9780852742600}
}
@Article{skeleton,
Title = {Periodic orbits as the skeleton of classical and quantum chaos},
Author = {Cvitanovi{\'c}, P.},
Journal = {Physica D},
Year = {1991},
Pages = {138--151},
Volume = {51},
DOI = {10.1016/0167-2789(91)90227-Z}
}
@Article{CFTsketch,
Title = {{Chaotic Field Theory}: {A} sketch},
Author = {Cvitanovi{\'c}, P.},
Journal = {Physica A},
Year = {2000},
Pages = {61--80},
Volume = {288},
DOI = {10.1016/S0378-4371(00)00415-5}
}
@Book{PCgr,
Title = {{Group Theory} - {Birdtracks}, {Lie}'s, and {Exceptional Groups}},
Author = {P. Cvitanovi{\'c}},
Publisher = {Princeton Univ. Press},
Year = {2008},
Address = {Princeton NJ},
ISBN = {0691118361},
URL = {http://birdtracks.eu}
}
@Article{focusPOT,
Title = {Recurrent flows: {The} clockwork behind turbulence},
Author = {Cvitanovi{\'c}, P.},
Journal = {J. Fluid Mech. Focus Fluids},
Year = {2013},
Pages = {1--4},
Volume = {726},
DOI = {10.1017/jfm.2013.198}
}
@Incollection{CBook:projects,
Title = {Appendix: {Projects}},
Author = {P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#projects}
}
@Incollection{aver_dasbuch,
Title = {Averaging},
Author = {P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#average}
}
@Incollection{CBcount,
Title = {Counting},
Author = {P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#count}
}
@Incollection{koopmania,
Title = {Implementing evolution},
Author = {P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#appendMeasure}
}
@Incollection{CBcontinuous,
Title = {Relativity for cyclists},
Author = {P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
Chapter = {12},
URL = {http://ChaosBook.org/paper.shtml#continuous}
}
@Incollection{CBtrace,
author = {P. Cvitanovi{\'c}},
title = {Trace formulas},
booktitle = {Chaos: Classical and Quantum},
publisher = {Niels Bohr Inst.},
year = {2017},
editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay},
address = {Copenhagen},
url = {http://ChaosBook.org/paper.shtml#trace},
}
@Incollection{DasBuchMirror,
Title = {World in a mirror},
Author = {P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#discrete}
}
@Article{SCD07,
author = {Cvitanovi{\'c}, P. and Davidchack, R. L. and Siminos, E.},
title = {On the state space geometry of the {Kuramoto-Sivashinsky} flow in a periodic domain},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2010},
volume = {9},
pages = {1--33},
doi = {10.1137/070705623},
}
@InProceedings{etc12,
author = {Cvitanovi{\'c}, P. and Gibson, J. F.},
title = {Geometry of state space in plane {Couette} flow},
booktitle = {{Advances in Turbulence XII}},
year = {2009},
editor = {B. Eckhardt},
series = {Proc. 12\textsuperscript{th} EUROMECH Eur. Turb. Conf., Marburg},
pages = {75--78},
address = {Berlin},
publisher = {Springer},
doi = {10.1007/978-3-642-03085-7-17},
}
@Article{CviGib10,
Title = {Geometry of turbulence in wall-bounded shear flows: {Periodic} orbits},
Author = {Cvitanovi{\'c}, P. and Gibson, J. F.},
Journal = {Phys. Scr. T},
Year = {2010},
Pages = {014007},
Volume = {142},
DOI = {10.1088/0031-8949/2010/T142/014007}
}
@Article{SumRules,
Title = {Beyond the periodic orbit theory},
Author = {Cvitanovi{\'c}, P. and Hansen, Kim and Rolf, J. and Vattay, G.},
Journal = {Nonlinearity},
Year = {1998},
Pages = {1209--1232},
Volume = {11},
DOI = {10.1088/0951-7715/11/5/003}
}
@Inproceedings{CvitLanCrete02,
author = {P. Cvitanovi{\'c} and Y. Lan},
title = {Turbulent fields and their recurrences},
booktitle = {{Correlations and Fluctuations in QCD : Proceedings of 10. International Workshop on Multiparticle Production}},
year = {2003},
editor = {N. Antoniou},
isbn = {978-981-238-455-3},
pages = {313--325},
address = {Singapore},
publisher = {World Scientific},
doi = {10.1142/9789812704641_0032},
}
@Incollection{CBook:appendApplic,
Title = {Transport of vector fields},
Author = {P. Cvitanovi{\'c} and G. Vattay},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#appendApplic}
}
@Incollection{CVW96,
author = {Cvitanovi{\'c}, P. and Vattay, G. and Wirzba, A.},
title = {Quantum fluids and classical determinants},
booktitle = {Classical, Semiclassical and Quantum Dynamics in Atoms},
publisher = {Springer},
year = {1997},
editor = {H. Friedrich and B. Eckhardt},
pages = {29--62},
address = {New York},
doi = {10.1007/bfb0105968},
}
@InProceedings{CvWiAv12,
author = {Cvitanovi{\'c}, P. and Willis, A. P. and Avila, M.},
title = {Revealing the state space of turbulent pipe flow by symmetry reduction},
booktitle = {Proceed. ICTAM 2012 Intern. Congr. Theor. and Appl. Mech.},
year = {2012},
editor = {Jianxiang Wang},
doi = {10.1017/jfm.2013.75},
}
@Unpublished{Cvi07,
Title = {Continuous symmetry reduced trace formulas},
Author = {P. Cvitanovi\'{c}},
Note = {Unpublished},
Year = {2007},
URL = {http://ChaosBook.org/~predrag/papers/Cvi07.pdf}
}
@Incollection{symb_dyn,
Title = {Charting the state space},
Author = {P. Cvitanovi\'{c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#knead}
}
@Book{DasBuch,
Title = {Chaos: {Classical and Quantum}},
Author = {P. Cvitanovi\'{c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay},
Publisher = {Niels Bohr Inst.},
Year = {2017},
Address = {Copenhagen},
URL = {http://ChaosBook.org}
}
@Article{CE91,
Title = {Periodic orbit expansions for classical smooth flows},
Author = {P. Cvitanovi\'{c} and B. Eckhardt},
Journal = {J. Phys. A},
Year = {1991},
Pages = {L237--L241},
Volume = {24},
DOI = {10.1088/0305-4470/24/5/005}
}
@Article{pre88top,
Title = {Topological and metric properties of {H\'{e}non}-type strange attractors},
Author = {P. Cvitanovi\'{c} and G. H. Gunaratne and I. Procaccia},
Journal = {Phys. Rev. A},
Year = {1988},
Pages = {1503},
Volume = {38}
}
@Article{FredDet,
author = {Cvitanovi\'{c}, P. and Rosenqvist, P. E. and G. Vattay and Rugh, H. H.},
title = {A {Fredholm} determinant for semiclassical quantization},
journal = {Chaos},
year = {1993},
volume = {3},
pages = {619--636},
doi = {10.1063/1.165992},
}
@Article{PCar,
Title = {Group theory for {Feynman} diagrams in non-{Abelian} gauge theories},
Author = {P. Cvitanovi\'c},
Journal = {Phys. Rev. D},
Year = {1976},
Pages = {1536--1553},
Volume = {14}
}
@Article{PlanFieldThe,
Title = {Planar perturbation expansion},
Author = {Cvitanovi\'c, P.},
Journal = {Phys. Lett. B},
Year = {1981},
Pages = {49},
Volume = {99}
}
@Article{Cvi92chaos,
Title = {Periodic orbit theory in classical and quantum mechanics},
Author = {Cvitanovi\'c, P.},
Journal = {Chaos},
Year = {1992},
Pages = {1--4},
Volume = {2},
DOI = {10.1063/1.165921}
}
@Article{atlas12,
Title = {Cartography of high-dimensional flows: {A} visual guide to sections and slices},
Author = {Cvitanovi\'c, P. and Borrero-Echeverry, D. and Carroll, K. and Robbins, B. and Siminos, E.},
Journal = {Chaos},
Year = {2012},
Pages = {047506},
Volume = {22},
DOI = {10.1063/1.4758309}
}
@Article{CE89,
author = {Cvitanovi\'c, P. and Eckhardt, B.},
title = {Periodic orbit quantization of chaotic systems},
journal = {Phys. Rev. Lett.},
year = {1989},
volume = {63},
pages = {823--826},
doi = {10.1103/physrevlett.63.823},
}
@Article{CvitaEckardt,
author = {Cvitanovi\'c, P. and Eckhardt, B.},
title = {Symmetry decomposition of chaotic dynamics},
journal = {Nonlinearity},
year = {1993},
volume = {6},
pages = {277--311},
doi = {10.1088/0951-7715/6/2/008},
}
@Article{LorentzDiff,
author = {Cvitanovi\'c, P. and Eckmann, J.-P. and Gaspard, P.},
title = {Transport properties of the {Lorentz} gas in terms of periodic orbits},
journal = {Chaos Solit. Fract.},
year = {1995},
volume = {6},
pages = {113--120},
doi = {10.1016/0960-0779(95)80018-C},
}
@Article{CGS92,
Title = {Investigation of the {Lorentz} gas in terms of periodic orbits},
Author = {Cvitanovi\'c, P. and Gaspard, P. and Schreiber, T.},
Journal = {Chaos},
Year = {1992},
Pages = {85--90},
Volume = {2},
DOI = {10.1063/1.165902}
}
@Unpublished{CvGr12,
Title = {Slicing a heart to keep it ticking: {Dreams Of Grand Schemes}},
Author = {Cvitanovi\'c, P. and Grigoriev, R. O.},
Note = {In preparation},
Year = {2012}
}
@Article{CGV,
Title = {On the mode-locking universality for critical circle maps},
Author = {P. Cvitanovi\'c and G. H. Gunaratne and M. J. Vinson},
Journal = {Nonlinearity},
Year = {1990},
Pages = {873},
Volume = {3},
Abstract = {The conjectured universality of the Hausdorff dimension of the fractal
set formed by the set of the irrational winding parameter values
for critical circle maps is shown to follow from the universal scalings
for quadratic irrational winding numbers.}
}
@Inproceedings{CviLip12,
author = {P. Cvitanovi\'c and D. Lippolis},
title = {Knowing when to stop: {How} noise frees us from determinism},
booktitle = {Let's Face Chaos through Nonlinear Dynamics},
year = {2012},
editor = {M. Robnik and V. G. Romanovski},
pages = {82--126},
address = {Melville, NY},
publisher = {American Institute of Physics},
doi = {10.1063/1.4745574},
}
@Article{CV93,
author = {P. Cvitanovi\'c and G. Vattay},
title = {Entire {Fredholm} determinants for evaluation of semiclassical and thermodynamical spectra},
journal = {Phys. Rev. Lett.},
year = {1993},
volume = {71},
pages = {4138--4141},
doi = {10.1103/physrevlett.71.4138},
}
@Article{CviPik93,
author = {Cvitanovic, P. and Pikovsky, A.},
title = {Cycle expansion for power spectrum},
journal = {Proc. SPIE},
year = {1993},
volume = {2038},
pages = {290--298},
doi = {10.1117/12.162683},
}
@Article{AlIsPo91,
Title = {Geometric properties of the pruning front},
Author = {D'Alessandro, G. and Isola, S. and Politi, A.},
Journal = {Progr. Theor. Phys.},
Year = {1991},
Pages = {1149--1157},
Volume = {86},
DOI = {10.1143/ptp/86.6.1149},
Mrnumber = {93a:58052}
}
@Article{DAlesPol90,
author = {G. D'Alessandro and A. Politi},
title = {Hierarchical approach to complexity with applications to dynamical systems},
journal = {Phys. Rev. Lett.},
year = {1990},
volume = {64},
pages = {1609},
doi = {10.1103/physrevlett.64.1609},
}
@Article{SouMar99,
Title = {Thermodynamically reversible generalization of diffusion limited aggregation},
Author = {D'Souza, R. M. and Margolus, N. H.},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {264--274},
Volume = {60},
DOI = {10.1103/PhysRevE.60.264}
}
@Article{Dahlqv94,
Title = {Determination of resonance spectra for bound chaotic systems},
Author = {P. Dahlqvist},
Journal = {J. Phys. A},
Year = {1994},
Pages = {763--785},
Volume = {27},
DOI = {10.1088/0305-4470/27/3/020}
}
@Article{Dahlqvist95,
Title = {Approximate zeta functions for the {Sinai} billiard and related systems},
Author = {P. Dahlqvist},
Journal = {Nonlinearity},
Year = {1995},
Pages = {11},
Volume = {8},
DOI = {10.1088/0951-7715/8/1/002}
}
@Article{DR_prl,
Title = {Existence of stable orbits in the {$x^{2}y^{2}$} potential},
Author = {P. Dahlqvist and G. Russberg},
Journal = {Phys. Rev. Lett.},
Year = {1990},
Pages = {2837--2838},
Volume = {65},
DOI = {10.1103/PhysRevLett.65.2837}
}
@Article{DR91a,
Title = {Periodic orbit quantization of bound chaotic systems},
Author = {P. Dahlqvist and G. Russberg },
Journal = {J. Phys. A},
Year = {1991},
Pages = {4763--4778},
Volume = {24},
DOI = {10.1088/0305-4470/24/20/012}
}
@Article{dana89,
Title = {Hamiltonian transport on unstable periodic orbits},
Author = {Dana},
Journal = {Physica D},
Year = {1989},
Pages = {205},
Volume = {39},
DOI = {10.1016/0167-2789(89)90005-5}
}
@Article{Dana02,
Title = {General quantization of canonical maps on a two-torus},
Author = {I. Dana},
Journal = {J. Phys. A},
Year = {2002},
Pages = {3447},
Volume = {35},
DOI = {10.1088/0305-4470/35/15/307}
}
@Article{Dana13,
author = {Dana, I.},
title = {Classical and quantum transport in one-dimensional periodically kicked systems},
journal = {Canadian J. Chem.},
year = {2014},
volume = {92},
pages = {77--84},
doi = {10.1139/cjc-2013-0374},
}
@Article{DaMuPe88,
Title = {Resonances and diffusion in periodic {Hamiltonian} maps},
Author = {I. Dana and N. V. Murray and I. C. Percival},
Journal = {Phys. Rev. Lett.},
Year = {1988},
Pages = {233},
Volume = {62},
DOI = {10.1103/PhysRevLett.62.233}
}
@Article{Dang86,
Title = {Steady-state mode interactions in the presence of {O(2)}-symmetry},
Author = {Dangelmayr, G.},
Journal = {Dyn. Sys.},
Year = {1986},
Pages = {159--185},
Volume = {1},
DOI = {10.1080/02681118608806011}
}
@Article{DaVuDel00,
Title = {Spatial heteroclinic bifurcations of time periodic solutions to the {Ginzburg-Landau} equation},
Author = {H. Dang-Vu and C. Delcarte},
Journal = {Quart. Appl. Math.},
Year = {2000},
Pages = {459--472},
Volume = {58},
DOI = {10.1090/qam/1770649}
}
@Article{DHBEks96,
author = {H. Dankowicz and P. Holmes and G. Berkooz and J. Elezgaray},
title = {Local models of spatio-temporally complex fields},
journal = {Physica D},
year = {1996},
volume = {90},
pages = {387--407},
doi = {10.1016/0167-2789(95)00245-6},
}
@Article{DV2000,
Title = {Phase space analysis of a dynamical model for the subcritical transition to turbulence in plane {Couette} flow},
Author = {O. Dauchot and N. Vioujard},
Journal = {Eur. Phys. J. B},
Year = {2000},
Pages = {377--381},
Volume = {14}
}
@Book{DauPey06,
Title = {{Physics of Solitons}},
Author = {Dauxois, T. and Peyrard, M.},
Publisher = {Cambridge Univ. Press},
Year = {2006},
Address = {Cambridge},
ISBN = {9780521854214}
}
@Article{DLBconv92,
author = {F. Daviaud and J. Lega and P. Berg\'{e} and P. Coullet and M. Dubois},
title = {Spatio-temporal intermittency in a 1{D} convective pattern: theoretical model and experiments},
journal = {Physica D},
year = {1992},
volume = {55},
pages = {287--308},
doi = {10.1016/0167-2789(92)90061-q},
}
@Unpublished{Davidchack_priv,
Title = {{Kuramoto-Sivashinsky $O(2)$} quotienting},
Author = {R. L. Davidchack},
Note = {Unpublished},
Year = {2007}
}
@Article{mfind,
author = {R. L. Davidchack and Y-C Lai},
title = {Efficient algorithm for detecting unstable periodic orbits in chaotic systems},
journal = {Phys. Rev. E},
year = {1999},
volume = {60},
pages = {6172},
doi = {10.1103/physreve.60.6172},
}
@Article{dlbd00,
Title = {Estimating generating partitions of chaotic systems by unstable periodic orbits},
Author = {R. L. Davidchack and Y-C Lai and E. M. Bollt and M. Dhamala},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {1353},
Volume = {61}
}
@Article{davies2009,
Title = {Laser absorption by overdense plasmas in the relativistic regime},
Author = {Davies, J. R.},
Journal = {Plasma Phys. Control. Fusion},
Year = {2009},
Pages = {014006},
Volume = {51},
DOI = {10.1088/0741-3335/51/1/014006}
}
@Article{DaMacKaSa1991,
Title = {{Markov} shifts in the {H\'enon} family},
Author = {M.J. Davis and R.S. MacKay and A. Sannami},
Journal = {Physica D},
Year = {1991},
Pages = {171--178},
Volume = {52},
DOI = {10.1016/0167-2789(91)90119-T}
}
@Article{DaGrSaYo94,
author = {S. P. Dawson and C. Grebogi and T. Sauer and J. A. Yorke},
title = {Obstructions to shadowing when a {Lyapunov} exponent is near zero},
journal = {Phys. Rev. Lett.},
year = {1994},
volume = {73},
pages = {1927},
doi = {10.1103/PhysRevLett.73.1927},
}
@Article{dawson_collections_1997,
author = {S. P. Dawson and A. M. Mancho},
title = {Collections of heteroclinic cycles in the {Kuramoto-Sivashinsky} equation},
journal = {Physica D},
year = {1997},
volume = {100},
pages = {231--256},
doi = {10.1016/s0167-2789(96)00209-6},
}
@Article{DeArKo04,
author = {De Ara\'ujo, G. A. and Koiller, J.},
title = {Self-propulsion of {N}-hinged ``{Animats}'' at low {Reynolds} number},
journal = {Qualitative Theory of Dynamical Systems},
year = {2004},
volume = {4},
pages = {139--167},
doi = {10.1007/bf02970856},
}
@Article{DePSWP12,
Title = {Bifurcation control of a parametric pendulum},
Author = {De Paula, A. S. and Savi, M. A. and Wiercigroch, M.N and Pavlovskaia, E.},
Journal = {Int. J. Bifur. Chaos},
Year = {2012},
Pages = {1250111},
Volume = {22},
DOI = {10.1142/S0218127412501118}
}
@Phdthesis{DeWitte13,
Title = {Computational analysis of bifurcations of periodic orbits},
Author = {De Witte, V.},
School = {Ghent University},
Year = {2013}
}
@Article{DWRGK13,
Title = {Numerical periodic normalization for codim 2~{b}ifurcations of limit cycles: {Computational} formulas, numerical implementation, and examples},
Author = {De Witte, V. and Rossa, F. and Govaerts, W. and Kuznetsov, Yu. A.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2013},
Pages = {722--788},
Volume = {12},
DOI = {10.1137/120874904}
}
@Article{Dehaye05,
author = {P.-O. Dehaye},
title = {Averages over classical {Lie} groups, twisted by characters},
journal = {J. Combin. Theory A},
year = {2007},
volume = {114},
pages = {1278 - 1292},
doi = {10.1016/j.jcta.2007.01.008},
}
@Article{Deissler1994,
Title = {Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex {Ginzburg-Landau} equation},
Author = {R. J. Deissler and H. R. Brand},
Journal = {Phys. Rev. Lett.},
Year = {1994},
Pages = {478--481},
Volume = {72},
DOI = {10.1103/PhysRevLett.72.478}
}
@Article{DellAnZwan91,
Title = {Every gauge orbit passes inside the {Gribov} horizon},
Author = {Dell'Antonio, G. and Zwanziger, D.},
Journal = {Commun. Math. Phys.},
Year = {1991},
Pages = {291--299},
Volume = {138},
DOI = {10.1007/BF02099494}
}
@Article{DePoHoo96,
Title = {{Lyapunov} instability in a system of hard disks in equilibrium and nonequilibrium steady states},
Author = {Dellago, C. and Posch, H. A. and Hoover, W. G.},
Journal = {Phys. Rev. E},
Year = {1996},
Pages = {1485},
Volume = {53}
}
@Article{Dembo1982,
author = {R. S. Dembo and S. C. Eisenstat and T. Steihaug},
title = {Inexact {Newton} methods},
journal = {SIAM J. Numer. Anal.},
year = {1982},
volume = {19},
pages = {400--408},
doi = {10.1137/0719025},
}
@Misc{DemChaos,
Title = {Chaotic maps},
Author = {E. Demidov},
Note = {www.ibiblio.org/e-notes},
Year = {2009},
URL = {http://www.ibiblio.org/e-notes/Chaos/contents.htm}
}
@Book{Demidovich1967,
Title = {Lectures on Stability Theory},
Author = {B. P. Demidovich},
Publisher = {Nauka},
Year = {1967},
Address = {Moscow},
Note = {in Russian}
}
@Article{DDF00,
author = {J.W. Demmel and L. Dieci and M.J. Friedman},
title = {Computing connecting orbits via an improved algorithm for continuing invariant spaces},
journal = {SIAM J. Sci. Comput.},
year = {2000},
volume = {22},
pages = {81--94},
doi = {10.1137/s1064827598344868},
}
@Article{DRSB12,
Title = {High-precision continuation of periodic orbits},
Author = {Dena, {\'A}. and Rodr{\'i}guez, M. and Serrano, S. and Barrio, R.},
Journal = {Abst. Appl. Analysis},
Year = {2012},
Pages = {716024},
Volume = {2012},
DOI = {10.1155/2012/716024}
}
@Book{Dennis96,
title = {{Numerical Methods for Unconstrained Optimization and Nonlinear Equations}},
publisher = {SIAM},
year = {1996},
author = {Dennis, J. E. and Schnabel, R. B.},
address = {Philadelphia},
doi = {10.1137/1.9781611971200},
}
@Article{Desai06,
Title = {Subsystem entropy for {$Z^d$} sofic shifts},
Author = {Desai, A.},
Journal = {Indag. Math.},
Year = {2006},
Pages = {353--359},
Volume = {17},
DOI = {10.1016/S0019-3577(06)80037-6}
}
@Article{Descalzi05,
Title = {Static, oscillating modulus, and moving pulses in the one-dimensional quintic complex {Ginzburg-Landau} equation: {An} analytical approach},
Author = {Descalzi, O.},
Journal = {Phys. Rev. E},
Year = {2005},
Pages = {046210},
Volume = {72},
DOI = {10.1103/PhysRevE.72.046210}
}
@Article{Descalzi03,
Title = {Saddle-node bifurcation: {Appearance} mechanism of pulses in the subcritical complex {Ginzburg-Landau} equation},
Author = {Descalzi, O. and Argentina, M. and Tirapegui, E.},
Journal = {Phys. Rev. E},
Year = {2003},
Pages = {015601},
Volume = {67},
DOI = {10.1103/PhysRevE.67.015601}
}
@Article{Descalzi10,
Title = {Transition from modulated to exploding dissipative solitons: {Hysteresis}, dynamics, and analytic aspects},
Author = {Descalzi, O. and Brand, H. R.},
Journal = {Phys. Rev. E},
Year = {2010},
Pages = {026203},
Volume = {82},
DOI = {10.1103/PhysRevE.82.026203}
}
@Article{DesBra13,
Title = {Quasi-one-dimensional solutions and their interaction with two-dimensional dissipative solitons},
Author = {Descalzi, O. and Brand, H. R.},
Journal = {Phys. Rev. E},
Year = {2013},
Pages = {022915},
Volume = {87},
DOI = {10.1103/PhysRevE.87.022915}
}
@Article{Orazio2011,
Title = {Exploding dissipative solitons: {The} analog of the {Ruelle-Takens} route for spatially localized solutions},
Author = {Descalzi, O. and Cartes, C. and Cisternas, J. E. and Brand, H. R.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {056214},
Volume = {83},
DOI = {10.1103/PhysRevE.83.056214}
}
@Article{Dettm14,
author = {Dettmann, C. P.},
title = {Diffusion in the {Lorentz} gas},
journal = {Commun. Theor. Phys},
year = {2014},
volume = {62},
pages = {521--540},
doi = {10.1088/0253-6102/62/4/10},
}
@Article{carl97int,
Title = {Cycle expansions for intermittent diffusion},
Author = {C. P. Dettmann and P. Cvitanovi\'{c}},
Journal = {Phys. Rev. E},
Year = {1997},
Pages = {6687},
Volume = {56}
}
@Article{DM97,
Title = {Stability ordering of cycle expansions},
Author = {C. P. Dettmann and G. P. Morriss},
Journal = {Phys. Rev. Lett.},
Year = {1997},
Pages = {4201--4204},
Volume = {78},
DOI = {10.1103/PhysRevLett.78.4201}
}
@Article{DeNi79,
Title = {Shift automorphisms in the {H\'enon} mapping},
Author = {Devaney, R. and Nitecki, Z.},
Journal = {Commun. Math. Phys.},
Year = {1979},
Pages = {137--146},
Volume = {67},
DOI = {10.1007/BF01221362}
}
@Book{devnmap,
Title = {An Introduction to Chaotic Dynamical systems},
Author = {R. L. Devaney},
Publisher = {Wesley},
Year = {1989},
Address = {Redwood City}
}
@Book{deva87,
title = {{An Introduction to Chaotic Dynamical systems}},
publisher = {Westview Press},
year = {2008},
author = {R. L. Devaney},
edition = {2},
isbn = {9780786722679},
doi = {10.2307/3619398},
}
@Article{DhaLai99,
Title = {Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles},
Author = {Dhamala, M. and Lai, Y.-C.},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {6176--6179},
Volume = {60},
DOI = {10.1103/PhysRevE.60.6176}
}
@Article{DhoPatZhi15,
Title = {The action of the special orthogonal group on planar vectors: integrity bases via a generalization of the symbolic interpretation of Molien functions},
Author = {G. Dhont and F. Patra and B. I. Zhilinski\'is},
Journal = {J. Phys. A},
Year = {2015},
Pages = {035201},
Volume = {48},
DOI = {10.1088/1751-8113/48/3/035201}
}
@Article{DhoZhi13,
Title = {The action of the orthogonal group on planar vectors: invariants, covariants and syzygies},
Author = {G. Dhont and B. I. Zhilinski\'i},
Journal = {J. Phys. A},
Year = {2013},
Pages = {455202},
Volume = {46},
DOI = {10.1088/1751-8113/46/45/455202}
}
@Article{DhGoKu03,
Title = {{MATCONT: A MATLAB} package for numerical bifurcation analysis of {ODEs}},
Author = {Dhooge, A. and Govaerts, W. and Kuznetsov, Yu. A.},
Journal = {ACM Trans. Math. Softw.},
Year = {2003},
Pages = {141--164},
Volume = {29},
DOI = {10.1145/779359.779362}
}
@Book{Diacu96,
Title = {{Celestial Encounters: The Origins of Chaos and Stability}},
Author = {Diacu, F. and Holmes, P.},
Publisher = {Princeton Univ. Press},
Year = {1996},
Address = {Princeton NJ}
}
@Article{lfind,
author = {F. K. Diakonos and P. Schmelcher and O. Biham},
title = {Systematic computation of the least unstable periodic orbits in chaotic attractors},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {81},
pages = {4349},
doi = {10.1103/physrevlett.81.4349},
}
@Article{DiEl08,
Title = {{SVD} algorithms to approximate spectra of dynamical systems},
Author = {Dieci, L. and Elia, C.},
Journal = {Math. Comput. Simul.},
Year = {2008},
Pages = {1235--1254},
Volume = {79}
}
@Article{DJRV07,
author = {Dieci, L. and Jolly, M. S. and Rosa, R. and Van Vleck, E. S.},
title = {Error in approximation of {Lyapunov} exponents on inertial manifolds: {The Kuramoto-Sivashinsky} equation},
journal = {Discrete Continuous Dyn. Syst. Ser. B},
year = {2007},
volume = {9},
pages = {555--580},
doi = {10.3934/dcdsb.2008.9.555},
}
@Article{DiLoRu91,
Title = {Numerical calculation of invariant tori},
Author = {L. Dieci and J. Lorenz and R. D. Russell},
Journal = {SIAM J. Sci. Stat. Comput.},
Year = {1991},
Pages = {607--647},
Volume = {12},
DOI = {10.1137/0912033}
}
@Article{DiRuVl97,
author = {Dieci, L. and Russell, R. D. and Van Vleck, E. S.},
title = {On the compuation of {Lyapunov} exponents for continuous dynamical systems},
journal = {SIAM J. Numer. Anal.},
year = {1997},
volume = {34},
pages = {402--423},
doi = {10.1137/s0036142993247311},
}
@Article{DiVl02,
author = {Dieci, L. and Van Vleck, E. S.},
title = {{Lyapunov} Spectral Intervals: Theory and Computation},
journal = {SIAM J. Numer. Anal.},
year = {2002},
volume = {40},
pages = {516--542},
doi = {10.1137/s0036142901392304},
}
@Article{diepenbeek_persistence_????,
author = {L. U. C. Diepenbeek and F. Dumortier and H. Broer and J. P. Gossez and J. Mawhin and Vanderbauwhede, A. and S. V. Lunel},
title = {Persistence of {Hamiltonian} relative periodic orbits},
note = {Unknown reference},
}
@Article{DCTSCD14,
Title = {Estimating the dimension of the inertial manifold from unstable periodic orbits},
Author = {Ding, X. and Chat{\'e}, H. and Cvitanovi\'c, P. and Siminos, E. and Takeuchi, K. A.},
Journal = {Phys. Rev. Lett.},
Year = {2016},
Pages = {024101},
Volume = {117},
DOI = {10.1103/PhysRevLett.117.024101}
}
@Article{DingCvit14,
Title = {Periodic eigendecomposition and its application in {Kuramoto-Sivashinsky} system},
Author = {Ding, X. and Cvitanovi{\'c}, P.},
Journal = {{SIAM} J. Appl. Dyn. Syst.},
Year = {2016},
Pages = {1434--1454},
Volume = {15},
DOI = {10.1137/15M1037299}
}
@Misc{DingCvit16,
author = {Ding, X. and Cvitanovi{\'c}, P.},
title = {Exploding relative periodic orbits in cubic-quintic complex {Ginzburg--Landau} equation},
year = {2017},
note = {In preparation},
}
@Misc{DingKang16,
author = {X. Ding and S. H. Kang},
title = {Adaptive time-stepping exponential integrators for cubic-quintic complex {Ginzburg--Landau} equations},
year = {2017},
url = {http://arxiv.org/abs/1703.09622},
}
@Book{ditt01cq,
Title = {Classical and Quantum Dynamics: From Classical Paths to Path Integrals},
Author = {W. Dittrich and M. Reuter},
Publisher = {Springer},
Year = {2001},
Address = {New York}
}
@Article{doeb94nls,
Title = {Properties of nonlinear Schr{\"{o}}dinger equations associated with diffeomorphism group representations},
Author = {H.-D. Doebner and G. A. Goldin},
Journal = {J. Phys. A},
Year = {1994},
Pages = {1771--1780},
Volume = {27}
}
@Manual{auto,
Title = {AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with {HomCont})},
Author = {Doedel, E. J. and Champneys, A. R. and Fairgrieve, T. F. and Kuznetsov, Y. A. and Sandstede, B. and Wang, X.},
Year = {1998}
}
@Techreport{orbit,
Title = {On locating homoclinic and heteroclinic orbits},
Author = {Doedel, E. J. and Friedman, M. J. and Monteiro, A. C.},
Institution = {Center for Applied Mathematics, Cornell University},
Year = {1993}
}
@Article{doedel_computation_2003,
Title = {Computation of Periodic Solutions of Conservative Systems with Application to the 3\mbox{-}{B}ody Problem},
Author = {Doedel, E. J. and R. C. Paffenroth and H. B. Keller and D. J. Dichmann and Galan, J. and Vanderbauwhede, A.},
Journal = {Int. J. Bifur. Chaos},
Year = {2003},
Pages = {1353--1381},
Volume = {13}
}
@Article{doedel_elemental_2007,
Title = {Elemental periodic orbits associated with the libration points in the circular restricted 3\mbox{-}{b}ody problem},
Author = {Doedel, E. J. and V. A. Romanov and R. C. Paffenroth and H. B. Keller and D. J. Dichmann and Galan, J. and Vanderbauwhede, A.},
Journal = {Int. J. Bifur. Chaos},
Year = {2007},
Pages = {2625--2678},
Volume = {17}
}
@Article{doelman89,
Title = {Slow time-periodic solutions of the {Ginzburg-Landau} equation},
Author = {A. Doelman},
Journal = {Physica D},
Year = {1989},
Pages = {156--172},
Volume = {40},
DOI = {10.1016/0167-2789(89)90060-2}
}
@Article{doelman91n,
Title = {Finite-dimensional models of the {Ginzburg-Landau} equation},
Author = {A. Doelman},
Journal = {Nonlinearity},
Year = {1991},
Pages = {231--250},
Volume = {4},
DOI = {10.1088/0951-7715/4/2/003}
}
@Article{symmcgl,
Title = {Breaking the hidden symmetry in the {Ginzburg-Landau} equation},
Author = {A. Doelman},
Journal = {Physica D},
Year = {1996},
Pages = {398--428},
Volume = {97},
DOI = {10.1016/0167-2789(95)00303-7}
}
@Article{doercgl87,
Title = {Exact {Lyapunov} dimension of the universal attractor for the complex {Ginzburg-Landau} equation},
Author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Number = {26},
Pages = {2911--2914},
Volume = {59},
DOI = {10.1103/physrevlett.59.2911}
}
@Article{doercgl88,
Title = {Low-dimensional behaviour in the complex {Ginzburg-Landau} equation},
Author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko},
Journal = {Nonlinearity},
Year = {1988},
Pages = {279--309},
Volume = {1},
DOI = {10.1088/0951-7715/1/2/001}
}
@Article{Dolgopyat04,
Title = {On differentiability of {SRB} states for partially hyperbolic systems},
Author = {Dolgopyat, D.},
Journal = {Inv. Math.},
Year = {2004},
Pages = {389--449},
Volume = {155},
DOI = {10.1007/s00222-003-0324-5}
}
@Article{DFGHMS86,
Title = {Chaotic streamlines in the {ABC} flows},
Author = {Dombre, T. and Frisch, U. and Greene, J. M. and H\'enon, M. and Mehr, A. and Soward, A. M.},
Journal = {J. Fluid Mech.},
Year = {1986},
Pages = {353--391},
Volume = {167},
DOI = {10.1017/S0022112086002859}
}
@Article{Donaldson09c,
Title = {Vector symmetry reduction},
Author = {Donaldson, A. F.},
Journal = {Electronic Notes in Theoretical Computer Science},
Year = {2009},
Note = {{Proceedings of the Eighth International Workshop on Automated Verification of Critical Systems (AVoCS 2008)}},
Pages = {3--18},
Volume = {250},
DOI = {10.1016/j.entcs.2009.08.014}
}
@Article{DoLa14a,
Title = {A variational approach to connecting orbits in nonlinear dynamical systems},
Author = {C. Dong and Y. Lan},
Journal = {Phys. Lett. A},
Year = {2014},
Pages = {705--712},
Volume = {378},
DOI = {10.1016/j.physleta.2014.01.001}
}
@Article{DoLa14,
Title = {Organization of spatially periodic solutions of the steady {Kuramoto-Sivashinsky} equation},
Author = {C. Dong and Y. Lan},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2014},
Pages = {2140--2153},
Volume = {19},
DOI = {10.1016/j.cnsns.2013.09.040}
}
@Article{Donnay89,
Title = {Geodesic flow on the two-sphere, Part {I}: {Positive} measure entropy},
Author = {Donnay, V.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {1989},
Pages = {531--553},
Volume = {8}
}
@Incollection{Donnay88,
Title = {Geodesic flow on the two-sphere, Part {II}: {Ergodicity}},
Author = {Donnay, V. J.},
Booktitle = {Dynamical Systems},
Publisher = {Springer},
Year = {1988},
Address = {New York},
Editor = {Alexander, J. C.},
Pages = {112--153},
Series = {Lect. Notes Math.},
Volume = {1342},
DOI = {10.1007/BFb0082827}
}
@Article{Dormand78,
Title = {New {Runge-Kutta} algorithms for numerical simulation in dynamical astronomy},
Author = {Dormand, J. R. and Prince, P. J.},
Journal = {Celest. Mech.},
Year = {1978},
Pages = {223--232},
Volume = {18},
DOI = {10.1007/BF01230162}
}
@Article{Dormand86,
Title = {A family of embedded {Runge-Kutta} formulae},
Author = {Dormand, J. R. and Prince, P. J.},
Journal = {J. Comput. Appl. Math.},
Year = {1986},
Pages = {203--211},
Volume = {15},
DOI = {10.1016/0771-050X(80)90013-3}
}
@Article{Dragt05,
Title = {The symplectic group and classical mechanics},
Author = {Dragt, A. J.},
Journal = {Ann. New York Acad. Sci.},
Year = {2005},
Pages = {291--307},
Volume = {1045},
DOI = {10.1196/annals.1350.025}
}
@Unpublished{Dragt11,
Title = {Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics},
Author = {A. J. Dragt},
Year = {2011},
Institution = {Physics Department, U. of Maryland},
URL = {http://www.physics.umd.edu/dsat/dsatliemethods.html}
}
@Techreport{Dragt11bad,
Title = {Lie methods for nonlinear dynamics with applications to accelerator physics},
Author = {Dragt, A. J.},
Institution = {{Physics Department, U. of Maryland}},
Year = {2011},
URL = {http://www.physics.umd.edu/dsat/dsatliemethods.html}
}
@Misc{DraHab08,
author = {Dragt, A. J. and Habib, S.},
title = {How {Wigner} functions transform under symplectic maps},
year = {1998},
url = {http://arXiv.org/abs/quant-ph/9806056},
}
@Book{DR81,
Title = {Hydrodynamic Stability},
Author = {P. Drazin and W. H. Reid},
Publisher = {Cambridge Univ. Press},
Year = {1981},
Address = {Cambridge}
}
@Book{Dresselhaus07,
title = {{Group Theory: Application to the Physics of Condensed Matter}},
publisher = {Springer},
year = {2007},
author = {Dresselhaus, M. S. and Dresselhaus, G. and Jorio, A.},
address = {New York},
doi = {10.1007/978-3-540-32899-5},
}
@Book{Driebe99,
Title = {Fully Chaotic Maps and Broken Time Symmetry},
Author = {Driebe, D.J.},
Publisher = {Springer},
Year = {1999},
Address = {New York},
ISBN = {0792355644}
}
@Article{dromey12,
Title = {Coherent synchrotron emission from electron nanobunches formed in relativistic laser-plasma interactions},
Author = {Dromey, B. and Rykovanov, S. and Yeung, M. and H\"orlein, R. and Jung, D. and Gautier, D. C. and Dzelzainis, T. and Kiefer, D. and Palaniyppan, S. and Shah, R. and Schreiber, J. and Ruhl, H. and Fernandez, J. C. and Lewis, C. L. S. and Zepf, M. and Hegelich, B. M.},
Journal = {Nature Phys.},
Year = {2012},
Pages = {804--808},
Volume = {8},
DOI = {10.1038/nphys2439},
}
@Article{DruCip00,
Title = {Application of {Lie} algebras to visual servoing},
Author = {T. Drummond and R. Cipolla},
Journal = {Int. J. Computer Vision},
Year = {2000},
Pages = {21--41},
Volume = {37}
}
@Article{du87,
author = {M. L. Du and J. B. Delos},
title = {Effect of closed classical orbits on quantum spectra: {Ionization} of atoms in a magnetic field},
journal = {Phys. Rev. Lett.},
year = {1987},
volume = {58},
pages = {1731},
doi = {10.1103/physrevlett.58.1731},
}
@Article{du_growth06,
Title = {Growth rates for fast kinematic dynamo instabilities of chaotic fluid flows},
Author = {Y. Du and E. Ott},
Journal = {J. Fluid Mech.},
Year = {2006},
Pages = {265--288},
Volume = {257},
DOI = {10.1017/S0022112093003076}
}
@Article{duguet08,
author = {Duguet, Y. and Pringle, C. C. T. and Kerswell, R. R.},
title = {Relative periodic orbits in transitional pipe flow},
journal = {Phys. Fluids},
year = {2008},
volume = {20},
pages = {114102},
doi = {10.1063/1.3009874},
}
@Article{duguet07,
Title = {Transition in pipe flow: the saddle structure on the boundary of turbulence},
Author = {Duguet, Y. and Willis, A. P. and Kerswell, R. R.},
Journal = {J. Fluid Mech.},
Year = {2008},
Pages = {255--274},
Volume = {613},
DOI = {10.1017/S0022112008003248}
}
@Misc{DuisterDSsymm,
Title = {Dynamical Systems with Symmetry},
Author = {J. J. Duistermaat}
}
@Article{DuiGui75,
Title = {The spectrum of positive elliptic operators and periodic bicharacteristics},
Author = {Duistermaat, J. J. and Guillemin, V. W.},
Journal = {Inv. Math.},
Year = {1975},
Pages = {39--79},
Volume = {29},
DOI = {10.1007/BF01405172}
}
@Book{DuiKol00,
Title = {Lie Groups},
Author = {Duistermaat, J. J. and Kolk, J. A. C.},
Publisher = {Springer},
Year = {2000},
Address = {New York}
}
@Article{DuLoMe12,
author = {H. R. Dullin and H. E. Lomel{\'{i}} and J. D. Meiss},
title = {Symmetry reduction by lifting for maps},
journal = {Nonlinearity},
year = {2012},
volume = {25},
pages = {1709},
doi = {10.1088/0951-7715/25/6/1709},
}
@Article{dullin-2008,
Title = {Quadratic volume-preserving maps: {Invariant} circles and bifurcations},
Author = {H. R. Dullin and J. D. Meiss},
Journal = {SIAM J. Appl. Dyn. Sys.},
Year = {2008},
Pages = {76--128},
Volume = {8},
DOI = {10.1137/080728160}
}
@Article{Dullin99,
author = {H. R. Dullin and J. D. Meiss and D. Sterling},
title = {Generic twistless bifurcations},
journal = {Nonlinearity},
year = {1999},
volume = {13},
pages = {203--224},
doi = {10.1088/0951-7715/13/1/310},
}
@Article{SteDuMei04,
author = {H. R. Dullin and J. D. Meiss and D. G. Sterling},
title = {Symbolic codes for rotational orbits},
journal = {SIAM J. Appl. Dyn. Sys.},
year = {2005},
volume = {4},
pages = {515--562},
doi = {10.1137/040612877},
}
@Article{DSM00,
author = {H. R. Dullin and D. Sterling and J. D. Meiss},
title = {Self-rotation number using the turning angle},
journal = {Physica D},
year = {2000},
volume = {145},
pages = {25--46},
doi = {10.1016/s0167-2789(00)00093-2},
}
@Article{DuIbKo06,
Title = {Cocoon bifurcation in three-dimensional reversible vector fields},
Author = {Dumortier, F. and Ibanez, S. and Kokubu, H.},
Journal = {Nonlinearity},
Year = {2006},
Pages = {305--328},
Volume = {19},
DOI = {10.1088/0951-7715/19/2/004}
}
@Article{Duval88,
author = {J.-P. Duval},
title = {Generation d'une section des classes de conjugaison et arbre des mots de {L}yndon de longueur born\'e},
journal = {Theoret. Comput. Sci.},
year = {1988},
volume = {60},
pages = {255--283},
doi = {10.1016/0304-3975(88)90113-2},
}
@Article{DysFal92,
Title = {Period of a discrete cat mapping},
Author = {F. J. Dyson and H. Falk},
Journal = {Amer. Math. Monthly},
Year = {1992},
Pages = {603--614},
Volume = {99},
DOI = {10.2307/2324989}
}
@Article{EaPoSa10,
author = {J. Early and J. Pohjanpelto and R. Samelson},
title = {Group foliation of equations in geophysical fluid dynamics},
journal = {Discrete Continuous Dyn. Syst. Ser. A},
year = {2010},
volume = {27},
pages = {1571--1586},
doi = {10.3934/dcds.2010.27.1571},
}
@Article{Eckhardt87,
Title = {Fractal properties of scattering singularities},
Author = {B. Eckhardt},
Journal = {J. Phys. A},
Year = {1987},
Pages = {5971},
Volume = {20},
DOI = {10.1088/0305-4470/20/17/030}
}
@Article{EM99,
Title = {Transition to turbulence in a shear flow},
Author = {B. Eckhardt and A. Mersmann},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {509--517},
Volume = {60}
}
@Article{eckhardt94,
Title = {Periodic orbit analysis of the {Lorenz} flow},
Author = {B. Eckhardt and G. Ott},
Journal = {Z. Phys. B},
Year = {1994},
Pages = {259--266},
Volume = {93}
}
@Incollection{CERRS,
Title = {Pinball scattering},
Author = {B. Eckhardt and G. Russberg and P. Cvitanovi\'c and P. E. Rosenqvist and P. Scherer},
Booktitle = {Quantum Chaos: Between Order and Disorder},
Publisher = {Cambridge Univ. Press},
Year = {1995},
Address = {Cambridge},
Editor = {G. Casati and B. Chirikov},
Pages = {483}
}
@Article{EckWi90,
Title = {Symbolic description of periodic orbits for the quadratic {Zeeman} effect},
Author = {B. Eckhardt and D. Wintgen},
Journal = {J. Phys. B},
Year = {1990},
Pages = {355},
Volume = {23}
}
@Article{eck81,
author = {J.-P. Eckmann},
title = {Roads to turbulence in dissipative dynamical systems},
journal = {Rev. Mod. Phys.},
year = {1981},
volume = {53},
pages = {643--654},
doi = {10.1103/revmodphys.53.643},
}
@Book{eckman80map,
Title = {Iterated Maps on the Interval as Dynamical Systems},
Author = {J.-P. Eckmann and P. Collet},
Publisher = {Birkh{\"{a}}user},
Year = {1980},
Address = {Boston}
}
@Article{EckGat00,
Title = {Hydrodynamic {Lyapunov modes} in translation-invariant systems},
Author = {Eckmann, J.-P. and Gat, O.},
Journal = {J. Stat. Phys.},
Year = {2000},
Pages = {775--798},
Volume = {98}
}
@Article{EKR87,
Title = {Recurrence plots of dynamical systems},
Author = {Eckmann, J.-P. and Kamphorst, S. O. and Ruelle, D. },
Journal = {Europhys. Lett.},
Year = {1987},
Pages = {973},
Volume = {4},
DOI = {10.1209/0295-5075/4/9/004}
}
@Article{EckKamp86,
Title = {Liapunov exponents from time series},
Author = {Eckmann, J.-P. and Kamphorst, S. O. and Ruelle, D. and Ciliberto, S.},
Journal = {Phys. Rev. A},
Year = {1986},
Pages = {4971--4979},
Volume = {34},
DOI = {10.1103/PhysRevA.34.4971}
}
@Article{EckmannRuelle1985,
Title = {Ergodic theory of chaos and strange attractors},
Author = {J.-P. Eckmann and D. Ruelle},
Journal = {Rev. Mod. Phys.},
Year = {1985},
Pages = {617--656},
Volume = {57},
DOI = {10.1103/RevModPhys.57.617}
}
@Article{EckmannRuelle1992,
Title = {Fundamental limitations for estimating dimensions and {Lyapunov} exponents in dynamical systems},
Author = {J.-P. Eckmann and D. Ruelle},
Journal = {Physica D},
Year = {1992},
Pages = {185--187},
Volume = {56},
DOI = {10.1016/0167-2789(92)90023-G},
URL = {http://www.ihes.fr/~ruelle/PUBLICATIONS/[106].pdf}
}
@Article{ecklp88,
Title = {Liapunov spectra for infinite chains of nonlinear oscillators},
Author = {J.-P. Eckmann and C. E. Wayne},
Journal = {J. Stat. Phys.},
Year = {1988},
Pages = {853--878},
Volume = {50}
}
@Book{Efst05,
Title = {Metamorphoses of {Hamiltonian} systems with symmetries},
Author = {K. Efstathiou},
Publisher = {Springer},
Year = {2005},
Address = {New York}
}
@Article{egolf94,
author = {D. A. Egolf and H. S. Greenside},
title = {Relation between fractal dimension and spatial correlation length for extensive chaos},
journal = {Nature},
year = {1994},
volume = {369},
pages = {129--131},
doi = {10.1038/369129a0},
}
@Article{EGtran95,
author = {D. A. Egolf and H. S. Greenside},
title = {Characterization of the transition from defect to phase turbulence},
journal = {Phys. Rev. Lett.},
year = {1995},
volume = {74},
pages = {1751--1754},
doi = {10.1103/physrevlett.74.1751},
}
@Article{egolf98,
author = {D. A. Egolf and I. V. Melnikov and E. Bodenschatz},
title = {Importance of local pattern properties in spiral defect chaos},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {80},
pages = {3228--3231},
doi = {10.1103/physrevlett.80.3228},
}
@Article{egolf00,
author = {D. A. Egolf and I. V. Melnikov and W. Pesch and R. E. Ecke},
title = {Mechanisms of extensive spatiotemporal chaos in {Rayleigh-B\'{e}nard} convection},
journal = {Nature},
year = {2000},
volume = {404},
pages = {733--736},
doi = {10.1038/35008013},
}
@Article{ave99,
Title = {Average patterns of spatiotemporal chaos: {A} boundary effect},
Author = {V. M. Egu\'{i}luz and P. Alstr{\o}m and E. Hern\'{a}ndez-Garc\'{\i}a and O. Piro},
Journal = {Phys. Rev. E},
Year = {1999},
Number = {3},
Pages = {2822},
Volume = {59}
}
@Article{Eisenstat1994,
author = {S. C. Eisenstat and H. F. Walker},
title = {Globally convergent inexact {Newton} methods},
journal = {SIAM J. Optim.},
year = {1994},
volume = {4},
pages = {293--442},
doi = {10.1137/0804022},
}
@Article{ElXiDeMa95,
Title = {Spatiotemporal chaos in the damped {Kuramoto-Sivashinsky} equation},
Author = {Elder, K. R. and Xi, H. and Deans, M. and Gunton, J. D.},
Journal = {AIP Conf. Proc.},
Year = {1995},
Pages = {702--708},
Volume = {342},
DOI = {10.1063/1.48763}
}
@Article{ElWu96,
Title = {Stability of cellular states of the {Kuramoto-Sivashinsky} equation},
Author = {Elgin, J. and Wu, X.},
Journal = {SIAM J. Appl. Math.},
Year = {1996},
Pages = {1621--1638},
Volume = {56},
DOI = {10.1137/S0036139994263689}
}
@Book{ELLIOTT,
Title = {Symmetry in Physics},
Author = {Elliott, J. P. and Dawber, P. G.},
Publisher = {MacMillan},
Year = {1979},
Address = {Surrey},
Volume = {2}
}
@Unpublished{EllGaHoRa09,
author = {Ellis, D. C. P. and Gay-Balmaz, F. and Holm, D. D. and Ratiu, T. S.},
title = {{Lagrange-Poincar\'e} field equations},
note = {Submitted to J. Geometry and Physics},
year = {2009},
doi = {10.1016/j.geomphys.2011.06.007},
}
@Article{Elyutin04,
Title = {{Lyapunov} exponent for a gas of soft scatterers},
Author = {Elyutin, P. V.},
Journal = {Phys. Lett. A },
Year = {2004},
Pages = {153--156},
Volume = {331},
DOI = {10.1016/j.physleta.2004.08.043}
}
@Article{EmmRom89,
Title = {Orbifolds as configuration spaces of systems with gauge symmetries},
Author = {Emmrich, C. and Romer, H.},
Journal = {Commun. Math. Phys.},
Year = {1990},
Pages = {69},
Volume = {129},
DOI = {10.1007/BF02096779}
}
@Article{EDASRU14,
Title = {Coherent backscattering in {Fock} space: {A} signature of quantum many-body interference in interacting bosonic systems},
Author = {Engl, T. and Dujardin, J. and Arg{\"u}elles, A. and Schlagheck, P. and Richter, K. and Urbina, J. D.},
Journal = {Phys. Rev. Lett.},
Year = {2014},
Pages = {140403},
Volume = {112},
DOI = {10.1103/PhysRevLett.112.140403}
}
@Article{EPUR14,
Title = {The semiclassical propagator in fermionic {Fock} space},
Author = {Engl, T. and Pl{\"o}ss, P. and Urbina, J. D. and Richter, K.},
Journal = {Theor. Chem. Acc.},
Year = {2014},
Pages = {1563},
Volume = {133},
DOI = {10.1007/s00214-014-1563-9}
}
@Article{EnUrRi15,
Title = {Complex scattering as canonical transformation: {A} semiclassical approach in {Fock} space},
Author = {Engl, T. and Urbina, J. D. and Hummel, Q. and Richter, K.},
Journal = {Ann. Phys.},
Year = {2015},
Pages = {737--747},
Volume = {527},
DOI = {10.1002/andp.201500151}
}
@Article{EDUR15,
Title = {The semiclassical propagator in {Fock} space: dynamical echo and many-body interference},
Author = {Engl, T. and Urbina, J. D. and Richter, K.},
Journal = {Philos. Trans. Royal Soc. A},
Year = {2016},
Pages = {20150159},
Volume = {374},
DOI = {10.1098/rsta.2015.0159}
}
@Article{ErshPot98,
Title = {On the concept of stationary {Lyapunov} basis},
Author = {S. V. Ershov and A. B. Potapov},
Journal = {Physica D},
Year = {1998},
Pages = {167--198},
Volume = {118},
DOI = {10.1016/S0167-2789(98)00013-X}
}
@Article{esarey09,
Title = {Physics of laser-driven plasma-based electron accelerators},
Author = {Esarey, E. and Schroeder, C. B. and Leemans, W. P.},
Journal = {Rev. Mod. Phys.},
Year = {2009},
Pages = {1229--1285},
Volume = {81},
DOI = {10.1103/RevModPhys.81.1229}
}
@Article{EyHaLe04,
Title = {Ruelle's linear response formula, ensemble adjoint schemes and {L\'evy} flights},
Author = {Eyink, G. L. and Haine, T. W. N. and Lea, D. J.},
Journal = {Nonlinearity},
Year = {2004},
Pages = {1867},
Volume = {17},
DOI = {10.1088/0951-7715/17/5/016}
}
@Article{ERTW91,
Title = {Semiclassical cycle expansion for the helium atom},
Author = {Ezra, G. S. and Richter, K. and Tanner, G. and Wintgen, D.},
Journal = {J. Phys. B},
Year = {1991},
Pages = {L413--L420},
Volume = {24}
}
@Article{Faddeev09,
author = {L. D. Faddeev},
title = {{Faddeev-Popov} ghosts},
journal = {Scholarpedia},
year = {2009},
volume = {4},
pages = {7389},
doi = {10.4249/scholarpedia.7389},
}
@Article{aabdls,
author = {Fairweather, G. and Gladwell, I.},
title = {Algorithms for almost block diagonal linear systems},
journal = {SIAM Rev.},
year = {2004},
volume = {46},
pages = {49--58},
doi = {10.1137/s003614450240506x},
}
@Article{FE03,
Title = {Traveling waves in pipe flow},
Author = {H. Faisst and B. Eckhardt},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Pages = {224502},
Volume = {91},
DOI = {10.1103/PhysRevLett.91.224502}
}
@Article{fl92,
Title = {Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors},
Author = {C. Falcolini and R. de la Llave},
Journal = {J. Stat. Phys.},
Year = {1992},
Pages = {645--666},
Volume = {67}
}
@Article{Fang94,
Title = {Dynamics for a two-dimensional antisymmetric map},
Author = {H.P. Fang},
Journal = {J. Phys. A},
Year = {1994},
Pages = {5187--5200},
Volume = {27}
}
@Article{Faraz15,
Title = {An adjoint-based approach for finding invariant solutions of {Navier-Stokes} equations},
Author = {Farazmand, M.},
Journal = {J. Fluid M.},
Year = {2016},
Pages = {278--312},
Volume = {795},
DOI = {10.1017/jfm.2016.203}
}
@Misc{FarCvi16,
Title = {An adjoint-based approach for finding symmetry-invariant solutions of {Kuramoto-Sivashinsky} equation},
Author = {Farazmand, M. and Cvitanovi{\'c}, P.},
Note = {In preparation},
Year = {2016}
}
@Article{Haller11err,
Title = {Erratum and addendum to ``A variational theory of hyperbolic Lagrangian coherent structures''},
Author = {Farazmand, M. and Haller, G.},
Journal = {Physica D},
Year = {2011},
Pages = {439--441}
}
@Article{FaHa12,
Title = {Computing {Lagrangian} coherent structures from their variational theory},
Author = {M. Farazmand and G. Haller},
Journal = {Chaos},
Year = {2012},
Pages = {013128},
Volume = {22},
DOI = {10.1063/1.3690153}
}
@Incollection{FaOttYo83,
author = {J. D. Farmer and E. Ott and J. A. Yorke},
title = {The dimension of chaotic attractors},
booktitle = {The Theory of Chaotic Attractors},
publisher = {Springer},
year = {1983},
editor = {Hunt, B. R. and Li, T.-Y. and Kennedy, J. A. and Nusse, H. E.},
pages = {142--169},
address = {New York},
doi = {10.1007/978-0-387-21830-4_11},
isbn = {978-0-387-21830-4},
}
@Article{farmer87,
author = {J. D. Farmer and J. J. Sidorowich},
title = {Predicting chaotic time series},
journal = {Phys. Rev. Lett.},
year = {1987},
volume = {59},
pages = {845},
doi = {10.1103/physrevlett.59.845},
}
@Article{Faure07,
Title = {Prequantum chaos: {Resonances} of the prequantum cat map},
Author = {F. Faure},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {255--285},
Volume = {1},
DOI = {10.3934/jmd.2007.1.255}
}
@Article{Faure11,
author = {Faure, F.},
title = {Semiclassical origin of the spectral gap for transfer operators of a partially expanding map},
journal = {Nonlinearity},
year = {2011},
volume = {24},
pages = {1473--1498},
doi = {10.1088/0951-7715/24/5/005},
}
@Article{FaRoSj08,
author = {Faure, F. and Roy, N. and Sj{\"o}strand, J.},
title = {Semi-classical approach for {Anosov} diffeomorphisms and {Ruelle} resonances},
journal = {Open Math. J.},
year = {2008},
volume = {1},
pages = {35--81},
url = {https://hal.archives-ouvertes.fr/hal-00383044},
}
@Misc{FauTsu12,
author = {Faure, F. and Tsujii, M.},
title = {Prequantum transfer operator for symplectic {Anosov} diffeomorphism},
year = {2012},
url = {https://hal.archives-ouvertes.fr/hal-00703234/},
}
@Article{FauTsu13,
author = {Faure, F. and Tsujii, M.},
title = {Band structure of the {Ruelle} spectrum of contact {Anosov} flows},
journal = {C.R. Math.},
year = {2013},
volume = {351},
pages = {385--391},
doi = {10.1016/j.crma.2013.04.022},
}
@Article{faure04,
Title = {A laser-plasma accelerator producing monoenergetic electron beams},
Author = {Faure, J. and Glinec, Y. and Pukhov, A. and Kiselev, S. and Gordienko, S. and Lefebvre, E. and Rousseau, J.-P. and Burgy, F. and Malka, V.},
Journal = {Nature},
Year = {2004},
Number = {7008},
Pages = {541--544},
Volume = {431},
DOI = {10.1038/nature02963}
}
@Article{FOP15,
Title = {Symmetry reduction of turbulent pipe flows},
Author = {Fedele, F. and Abessi, O. and Roberts, P. J.},
Journal = {J. Fluid Mech.},
Year = {2015},
Pages = {390--410},
Volume = {779},
DOI = {10.1017/jfm.2015.423}
}
@Article{Feffer83,
Title = {The uncertainty principle},
Author = {C. L. Fefferman},
Journal = {Bull. Amer. Math. Soc.},
Year = {1983},
Pages = {129--206},
Volume = {9}
}
@Misc{Fefferman2000,
author = {Fefferman, C. L.},
title = {Existence and smoothness of the {Navier-Stokes} equation},
year = {2000},
journal = {The Millennium Prize Problems},
pages = {1--6},
url = {http://www.claymath.org/millennium-problems/navier%E2%80%93stokes-equation},
}
@Article{feigen78,
Title = {Quantitative universality for a class of nonlinear transformations},
Author = {M. J. Feigenbaum},
Journal = {J. Stat. Phys.},
Year = {1978},
Pages = {25--52},
Volume = {19},
DOI = {10.1007/BF01020332}
}
@Article{Feigenbaum87,
Title = {Some characterizations of strange sets},
Author = {Feigenbaum, M. J.},
Journal = {J. Stat. Phys.},
Year = {1987},
Pages = {919--924},
Volume = {46},
DOI = {10.1007/BF01011148}
}
@Article{Feigenbaum88a,
Title = {Presentation functions and scaling function theory for circle maps},
Author = {M. J. Feigenbaum},
Journal = {Nonlinearity},
Year = {1988},
Pages = {577--602},
Volume = {1},
DOI = {10.1088/0951-7715/1/4/005}
}
@Article{Feigenbaum88,
Title = {Presentation functions, fixed points, and a theory of scaling function dynamics},
Author = {Feigenbaum, M. J.},
Journal = {J. Stat. Phys.},
Year = {1988},
Pages = {527--569},
Volume = {52},
DOI = {10.1007/BF01019716}
}
@Article{Feiste1994,
Title = {18 {GHZ} all-optical frequency locking and clock recovery using a self-pulsating two-section laser},
Author = {U. Feiste and D. J. As and A. Erhardt},
Journal = {IEEE Photon. Technol. Lett.},
Year = {1994},
Pages = {106--108},
Volume = {6}
}
@Article{FelsOlver98,
Title = {Moving coframes: {I. A} practical algorithm},
Author = {M. Fels and P. J. Olver},
Journal = {Acta Appl. Math.},
Year = {1998},
Number = {2},
Pages = {161--213},
Volume = {51},
DOI = {10.1023/A:1005878210297}
}
@Article{FelsOlver99,
Title = {Moving coframes: {II. Regularization} and theoretical foundations},
Author = {M. Fels and P. J. Olver},
Journal = {Acta Appl. Math.},
Year = {1999},
Pages = {127--208},
Volume = {55},
DOI = {10.1023/A:1006195823000}
}
@Article{Feniche71,
Title = {Persistence and smoothness of invariant manifolds for flows},
Author = {Fenichel, N.},
Journal = {Indiana Univ. Math. J.},
Year = {1971},
Pages = {193--226},
Volume = {21},
DOI = {10.1512/iumj.1972.21.21017}
}
@Article{Fernandez14,
Title = {Breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps},
Author = {Fernandez, B.},
Journal = {J. Stat. Phys.},
Year = {2014},
Pages = {999--1029},
Volume = {154},
DOI = {10.1007/s10955-013-0903-9}
}
@Article{FerGui04,
Title = {Route to chaotic synchronisation in coupled map lattices: {Rigorous} results},
Author = {B. Fernandez and P. Guiraud},
Journal = {Discrete Continuous Dyn. Syst. Ser. B},
Year = {2004},
Pages = {435--456},
Volume = {4},
DOI = {10.3934/dcdsb.2004.4.435}
}
@Article{FerJia04,
Title = {Coupling two unimodal maps with simple kneading sequences},
Author = {B. Fernandez and M. Jiang},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {2004},
Pages = {107--125},
Volume = {24},
DOI = {10.1017/S0143385703000312}
}
@Article{FiSaScWu96,
Title = {Bifurcation from relative equilibria of noncompact group actions: {Skew} products, meanders, and drifts},
Author = {Fiedler, B. and Sandstede, B. and Scheel, A. and Wulff, C.},
Journal = {Doc. Math.},
Year = {1996},
Pages = {479--505},
Volume = {141}
}
@Article{FiTu98,
Title = {Normal forms, resonances, and meandering tip motions near relative equilibria of {Euclidean} group actions},
Author = {Fiedler, B. and Turaev, D.},
Journal = {Arch. Rational Mech. Anal.},
Year = {1998},
Pages = {129--159},
Volume = {145}
}
@Article{Field70,
Title = {Equivariant dynamical systems},
Author = {M. Field},
Journal = {Bull. Amer. Math. Soc.},
Year = {1970},
Pages = {1314--1318},
Volume = {76},
DOI = {10.1090/S0002-9947-1980-0561832-4}
}
@Incollection{Field88,
Title = {Local structure of equivariant dynamics},
Author = {M. Field},
Booktitle = {Singularity Theory and its Applications: Warwick 1989, Part II: Singularities, Bifurcations and Dynamics},
Publisher = {Springer},
Year = {1996},
Address = {New York},
Editor = {M. Roberts and I. Stewart},
Pages = {142--166},
DOI = {10.1007/BFb0085422},
ISBN = {9783540470472}
}
@Article{Field96,
author = {M. Field},
title = {Symmetry breaking for compact {Lie} groups},
journal = {Memoirs Amer. Math. Soc.},
year = {1996},
volume = {120},
number = {574},
pages = {R8},
doi = {10.1090/memo/0574},
}
@Article{Field80,
Title = {Equivariant dynamical systems},
Author = {Field, M. J.},
Journal = {Trans. Amer. Math. Soc.},
Year = {1980},
Pages = {185--205},
Volume = {259},
DOI = {10.1090/S0002-9947-1980-0561832-4}
}
@Book{Field07,
Title = {Dynamics and Symmetry},
Author = {Field, M. J.},
Publisher = {Imperial College Press},
Year = {2007},
Address = {London}
}
@Article{FigHar12,
Title = {Reliable computation of robust response tori on the verge of breakdown},
Author = {J.-L. Figueras and \`{A}. Haro},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2012},
Pages = {597--628},
Volume = {11},
DOI = {10.1137/100809222}
}
@Article{Fisher61,
Title = {Statistical mechanics of dimers on a plane lattice},
Author = {Fisher, M. E.},
Journal = {Phys. Rev.},
Year = {1961},
Pages = {1664--1672},
Volume = {124},
DOI = {10.1103/PhysRev.124.1664}
}
@Article{Fisher66,
Title = {On the dimer solution of planar {Ising} models},
Author = {Fisher, M. E.},
Journal = {J. Math. Phys.},
Year = {1966},
Pages = {1776--1781},
Volume = {7},
DOI = {10.1063/1.1704825}
}
@Article{Fisher67,
Title = {The theory of condensation and the critical point},
Author = {Fisher, M. E.},
Journal = {Physics},
Year = {1967},
Pages = {255--283},
Volume = {3},
URL = {http://inspirehep.net/record/1304501/files/vol3p255-283_001.pdf}
}
@Article{PhysToday04,
Title = {New experiments set the scale for the onset of turbulence in pipe flow},
Author = {R. Fitzgerald},
Journal = {Phys. Today},
Year = {2004},
Pages = {21--23},
Volume = {57}
}
@Article{Flannery11,
Title = {The elusive {d'Alembert-Lagrange} dynamics of nonholonomic systems},
Author = {M. R. Flannery},
Journal = {Amer. J. Phys.},
Year = {2011},
Pages = {932--944},
Volume = {79},
DOI = {10.1119/1.3563538}
}
@Article{Fleisch00,
author = {Fleischhack, C.},
title = {Stratification of the generalized gauge orbit space},
journal = {Communications in Mathematical Physics},
year = {2000},
volume = {214},
pages = {607--649},
doi = {10.1007/s002200000286},
}
@Article{Fl89,
Title = {New exact-solutions of the complex {Lorenz} equations},
Author = {Flessas, G. P.},
Journal = {J. Phys. A},
Year = {1989},
Pages = {L137--L141},
Volume = {22}
}
@Article{FlLe91,
Title = {A completely integrable case in the complex {Lorenz} equations},
Author = {Flessas, G. P. and Leach, P. G. L.},
Journal = {Phys. Lett. A},
Year = {1991},
Pages = {127--130},
Volume = {154}
}
@Article{Floquet1883,
author = {Floquet, G.},
title = {Sur les {\'e}quations diff{\'e}rentielles lin{\'e}aires \`a coefficients p{\'e}riodiques},
journal = {Ann. Sci. Ec. Norm. S{\'e}r},
year = {1883},
volume = {12},
pages = {47--88},
url = {http://www.numdam.org/item?id=ASENS_1883_2_12__47_0},
}
@Article{Flor11,
author = {Floratos, E.},
title = {Matrix quantization of turbulence},
journal = {Int. J. Bifurcation Chaos},
year = {2012},
volume = {22},
pages = {1250213},
doi = {10.1142/s0218127412502136},
}
@Article{FogRen09,
Title = {Minimum action method for the {Kardar-Parisi-Zhang} equation},
Author = {Fogedby, H. C. and Ren, W.},
Journal = {Phys. Rev. E},
Year = {2009},
Pages = {041116},
Volume = {80},
DOI = {10.1103/PhysRevE.80.041116}
}
@Article{fogleman01,
Title = {Lagrangian chaos and correlated {Levy} flights in a non-{Beltrami} flow: {Transient} versus long-term transport},
Author = {M. A. Fogleman and M. J. Fawcett and T. H. Solomon},
Journal = {Phys. Rev. E},
Year = {2001},
Pages = {020101},
Volume = {63},
Abstract = {Long-range transport is studied numerically in a time-independent,
three-dimensional (3D) fluid flow composed of the superposition of
two chains of alternating vortices, one horizontal and the other
vertical. Tracers in this flow follow chaotic trajectories composed
of correlated L\'evy flights with varying velocities. Locations of
the chaotic regimes in the flow are compared with recent theories
of chaos in non-Beltrami 3D flows. Growth of the variance of a distribution
of tracers is divided into transient and long-term regimes, each
with different growth exponents.}
}
@Article{FJolly95,
Title = {On the numerical algebraic approximation of global attractors},
Author = {C. Foias and M. S. Jolly},
Journal = {Nonlinearity},
Year = {1995},
Pages = {295--319},
Volume = {8},
Abstract = {An algebraic approximation of the global attractors is developed for
the {L}orenz and KS system.}
}
@Article{foias88,
Title = {On the computation of inertial manifolds},
Author = {C. Foias and M. S. Jolly and I. G. Kevrekidis and G. R. Sell and E. S. Titi},
Journal = {Phys. Lett. A},
Year = {1988},
Pages = {433--436},
Volume = {131},
DOI = {10.1016/0375-9601(88)90295-2}
}
@Book{foias2001,
title = {{{Navier--Stokes} Equations and Turbulence}},
publisher = {Cambridge Univ. Press},
year = {2001},
author = {Foias, C. and Manley, O. and Rosa, R. and T{\'e}mam, R.},
isbn = {9781139428996},
address = {Cambridge},
}
@Article{FMTT83,
author = {C. Foias and O.P. Manley and R. T{\'e}mam and Y.M. Treve},
title = {Asymptotic analysis of the {Navier-Stokes} equations},
journal = {Physica D},
year = {1983},
volume = {9},
pages = {157--188},
doi = {10.1016/0167-2789(83)90297-X},
}
@Article{Foiasks88,
author = {C. Foias and B. Nicolaenko and G. R. Sell and R. T{\'e}mam},
title = {{Kuramoto-Sivashinsky} equation},
journal = {J. Math. Pures et Appl.},
year = {1988},
volume = {67},
pages = {197},
}
@Article{FNSTks85,
author = {C. Foias and B. Nicolaenko and G. R. Sell and R. T{\'e}mam},
title = {Inertial manifold for the {Kuramoto-Sivashinsky} equation},
journal = {C. R. Acad. Sci. Paris, Ser. I},
year = {1985},
volume = {301},
number = {6},
pages = {285--288},
url = {http://gallica.bnf.fr/ark:/12148/bpt6k6446253z/f299},
}
@Article{FNSTks88,
author = {C. Foias and B. Nicolaenko and G. R. Sell and R. T{\'e}mam},
title = {Inertial manifolds for the {Kuramoto-Sivashinsky} equation and an estimate of their lowest dimension},
journal = {J. Math. Pure Appl.},
year = {1988},
volume = {67},
pages = {197--226},
url = {http://purl.umn.edu/4494},
}
@Article{Foias1988a,
author = {Foias, C. and Sell, G. R. and T{\'e}mam, R.},
title = {Inertial manifolds for nonlinear evolutionary equations},
journal = {J. Diff. Equ.},
year = {1988},
volume = {73},
pages = {309--353},
doi = {10.1016/0022-0396(88)90110-6},
}
@Article{FoLlMa11,
Title = {Dynamical systems on lattices with decaying interaction {I: A} functional analysis framework},
Author = {E. Fontich and de la Llave, R. and P. Mart{\'{i}}n},
Journal = {J. Diff. Equ.},
Year = {2011},
Pages = {2838--2886},
Volume = {250},
DOI = {10.1016/j.jde.2010.07.023}
}
@Article{Forrester13,
Title = {{Lyapunov} exponents for products of complex {Gaussian} random matrices},
Author = {Forrester, P. J.},
Journal = {J. Stat. Phys.},
Year = {2013},
Pages = {796--808},
Volume = {151},
DOI = {10.1007/s10955-013-0735-7}
}
@Article{ForKas72,
Title = {On the random-cluster model: {I. Introduction} and relation to other models},
Author = {C.M. Fortuin and P.W. Kasteleyn},
Journal = {Physica},
Year = {1972},
Pages = {536--564},
Volume = {57},
DOI = {10.1016/0031-8914(72)90045-6}
}
@Article{Foster94,
author = {Foster, L.},
title = {{Gauss}ian elimination with partial pivoting can fail in practice},
journal = {SIAM J. Matrix Anal. Appl.},
year = {1994},
volume = {15},
pages = {1354--1362},
doi = {10.1137/s0895479892239755},
}
@Article{FoBaBiBi10,
Title = {Alternative stable scroll waves and conversion of autowave turbulence},
Author = {A. J. Foulkes and D. Barkley and V. N. Biktashev and I. V. Biktasheva},
Journal = {Chaos},
Year = {2010},
Pages = {043136},
Volume = {20},
DOI = {10.1063/1.3517079}
}
@Article{FouBik10,
author = {A. J. Foulkes and V. N. Biktashev},
title = {Riding a spiral wave: {Numerical} simulation of spiral waves in a comoving frame of reference},
journal = {Phys. Rev. E},
year = {2010},
volume = {81},
pages = {046702},
doi = {10.1103/physreve.81.046702},
}
@Article{FouBik10a,
author = {A. J. Foulkes and V. N. Biktashev},
title = {Riding a spiral wave: {Numerical} simulation of spiral waves in a co-moving frame of reference},
journal = {Physical Review E},
year = {2010},
volume = {81},
doi = {10.1103/physreve.81.046702},
}
@Article{FowlerCLE82,
author = {Fowler , A. C. and {Gibbon}, J. D. and {McGuinness}, M. J.},
title = {The complex {Lorenz} equations},
journal = {Physica D},
year = {1982},
volume = {4},
pages = {139--163},
doi = {10.1016/0167-2789(82)90057-4},
}
@Article{FowlerCLE83,
author = {Fowler , A. C. and Gibbon, J. D. and McGuinness, M. J.},
title = {The real and complex {Lorenz} equations and their relevance to physical systems},
journal = {Physica D},
year = {1983},
volume = {7},
pages = {139--163},
doi = {10.1016/0167-2789(83)90123-9},
}
@Article{FoMcGui84,
author = {Fowler , A. C. and McGuinness, M. J.},
title = {On the nature of the torus in the complex {Lorenz} equations},
journal = {SIAM J. Appl. Math.},
year = {1984},
volume = {44},
pages = {681--700},
doi = {10.1137/0144049},
}
@Phdthesis{FoxPhDthesis,
Title = {Destruction of Invariant Tori in Volume-Preserving Maps},
Author = {Fox, A. M.},
School = {Applied Math, U. Colorado},
Year = {2013},
Address = {Boulder},
ISBN = {9781303093715},
URL = {http://search.proquest.com/docview/1367595114}
}
@Unpublished{FoxCvi14,
Title = {A brief life and death of a torus: {Computation} of quasiperiodic solutions to the {Kuramoto-Sivashinsky} equation},
Author = {Fox, A. M.},
Note = {In preparation},
Year = {2015}
}
@Article{Fox14,
Title = {Critical invariant circles in asymmetric and multiharmonic generalized standard maps},
Author = {Fox, A. M. and Meiss, J. D.},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2014},
Pages = {1004--1026},
Volume = {19},
DOI = {10.1016/j.cnsns.2013.07.028}
}
@Article{FoxMei16,
Title = {Computing the conjugacy of invariant tori for volume-preserving maps},
Author = {A. M. Fox and J. D. Meiss},
Journal = {SIAM J. Appl. Dyn. Sys.},
Year = {2016},
Pages = {557--579},
Volume = {15},
DOI = {10.1137/15M1022859}
}
@Article{FGZ93,
Title = {Characterization of the {Lorenz} attractor by unstable periodic orbits},
Author = {V. Franceschini and C. Giberti and Z. M. Zheng},
Journal = {Nonlinearity},
Year = {1993},
Pages = {251--258},
Volume = {6},
DOI = {10.1088/0951-7715/6/2/006}
}
@Article{FrRu81,
Title = {Stable and unstable manifolds of the {H\'enon} mapping},
Author = {Franceschini, V. and Russo, L.},
Journal = {J. Stat. Phys.},
Year = {1981},
Pages = {757--769},
Volume = {25},
DOI = {10.1007/BF01022365}
}
@Article{Francis61,
Title = {The {QR} transformation: {A} unitary analogue to the {LR} transformation. \textup{I}},
Author = {Francis, J. G. F.},
Journal = {Comput. J.},
Year = {1961},
Pages = {265--271},
Volume = {4},
DOI = {10.1093/comjnl/4.3.265}
}
@Misc{franzosi-2004,
author = {R. Franzosi and P. Poggi and M. Cerruti-Sola},
title = {{Lyapunov} exponents from unstable periodic orbits in the {FPU}-beta model},
year = {2004},
url = {http://arXiv.org/abs/nlin/0408056},
}
@Article{FrPoCe05,
Title = {{Lyapunov} exponents from unstable periodic orbits},
Author = {R. Franzosi and P. Poggi and M. Cerruti-Sola},
Journal = {Phys. Rev. E},
Year = {2005},
Pages = {036218},
Volume = {71},
DOI = {10.1103/PhysRevE.71.036218}
}
@Article{FKYY83,
Title = {The {Liapunov} dimension of strange attractors},
Author = {P. Frederickson and J. L. Kaplan and E. D. Yorke and J. A. Yorke},
Journal = {J. Diff. Eqn.},
Year = {1983},
Pages = {185--207},
Volume = {49},
Abstract = {... the question of estimating the dimension of the attractor is
addressed. While more general conjectures are made here, particular
attention is paid to the idea that if the Jacobian determinant of a map
is greater than one and a ball is mapped into itself, then generically,
the attractor will have positive two-dimensional measure, and most of
this paper is devoted to presenting cases with such Jacobians for which
the attractors are proved to have non-empty interior. },
DOI = {10.1016/0022-0396(83)90011-6}
}
@Article{freire_limit_2007,
Title = {Limit cycles and {Lie} symmetries},
Author = {E. Freire},
Journal = {Bull. Sci. Mathematiques},
Year = {2007},
Pages = {501--517},
Volume = {131}
}
@Article{Fried95,
Title = {Meromorphic zeta functions for analytic flows},
Author = {Fried, D.},
Journal = {Commun. Math. Phys.},
Year = {1995},
Pages = {161--190},
Volume = {174},
DOI = {10.1007/BF02099469}
}
@Article{Friedland97,
Title = {On the entropy of {$Z^d$} subshifts of finite type},
Author = {Friedland, S.},
Journal = {Linear Algebra Appl.},
Year = {1997},
Pages = {199--220},
Volume = {252},
DOI = {10.1016/0024-3795(95)00676-1}
}
@Incollection{Friedli1978,
author = {Friedli, A.},
title = {Verallgemeinerte {Runge-Kutta Verfahren} zur {L\"oesung} steifer {Differentialgleichungssysteme}},
booktitle = {Numerical Treatment of Differential Equations: Proceedings of a Conference, Held at Oberwolfach, July 4--10, 1976},
publisher = {Springer},
year = {1978},
editor = {Bulirsch, R. and Grigorieff, R. D. and Schr{\"o}der, J.},
pages = {35--50},
address = {Berlin},
doi = {10.1007/BFb0067462},
}
@Article{FriedmanDoedelConnections91,
Title = {Numerical computation of invariant manifolds connecting fixed points},
Author = {Friedman, M. J. and Doedel, E. J.},
Journal = {SIAM J. Numer. Anal.},
Year = {1991},
Number = {3},
Pages = {789--808},
Volume = {28}
}
@Article{Frigo05,
author = {M. Frigo and S. G. Johnson},
title = {The Design and Implementation of {FFTW3}},
journal = {Proc. IEEE},
year = {2005},
volume = {93},
pages = {216--231},
doi = {10.1109/jproc.2004.840301},
}
@Article{friou2013,
Title = {Saturation mechanisms of backward stimulated Raman scattering in a one-dimensional geometry},
Author = {Friou, A. and B\'enisti, D. and Gremillet, L. and Lefebvre, E. and Morice, O. and Siminos, E. and Strozzi, D. J.},
Journal = {Phys. Plasmas},
Year = {2013},
Pages = {103103},
Volume = {20},
DOI = {10.1063/1.4823714}
}
@Book{frisch,
Title = {Turbulence},
Author = {U. Frisch},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Address = {Cambridge}
}
@Article{frisch86,
author = {U. Frisch and B. Hasslacher and Y. Pomeau},
title = {Lattice-gas automata for the navier-stokes equation},
journal = {Phys. Rev. Lett.},
year = {1986},
volume = {56},
pages = {1505--1508},
doi = {10.1103/physrevlett.56.1505},
}
@Article{frisch87,
author = {U. Frisch and Z. S. She and P.-L. Sulem},
title = {Large-scale flow driven by the anisotropic kinetic alpha effect},
journal = {Physica D},
year = {1987},
volume = {28},
pages = {382--392},
doi = {10.1142/9789814434348_0044},
}
@Article{FSTks86,
Title = {Viscoelastic behavior of cellular solutions to the {Kuramoto-Sivashinsky} model},
Author = {U. Frisch and Z. S. She and O. Thual},
Journal = {J. Fluid Mech.},
Year = {1986},
Pages = {221--240},
Volume = {168},
DOI = {10.1017/S0022112086000356}
}
@Incollection{Froeh10,
Author = {Froehlich, S.},
Booktitle = {{ChaosBook.org/projects}},
Publisher = {Georgia Inst. of Technology},
Year = {2010},
Chapter = {Reducing continuous symmetries with linear slice},
URL = {http://ChaosBook.org/projects/index.shtml#Froehlich}
}
@Article{FrCv11,
author = {Froehlich, S. and Cvitanovi{\'c}, P.},
title = {Reduction of continuous symmetries of chaotic flows by the method of slices},
journal = {Commun. Nonlinear Sci. Numer. Simul.},
year = {2012},
volume = {17},
pages = {2074--2084},
doi = {10.1016/j.cnsns.2011.07.007},
}
@Article{FrHuMoWa12,
Title = {Computing covariant vectors, {Lyapunov} vectors, {Oseledets} vectors, and dichotomy projectors: {A} comparative numerical study},
Author = {{Froyland}, G. and {H{\"u}ls}, T. and {Morriss}, G. P. and {Watson}, T. M.},
Journal = {Physica D},
Year = {2013},
Pages = {18--39},
Volume = {247},
DOI = {10.1016/j.physd.2012.12.005}
}
@Article{FuchSchSch94,
author = {Fuchs, J. and Schmidt, M. G. and Schweigert, C.},
title = {On the configuration space of gauge theories},
journal = {Nucl. Phys.},
year = {1994},
volume = {B426},
pages = {107--128},
doi = {10.1016/0550-3213(94)90128-7},
}
@InProceedings{FuOn08,
Title = {On balanced realization and finite-dimensional approximation for infinite-dimensional nonlinear systems},
Author = {Fujimoto, K. and Ono, S.},
Booktitle = {47. IEEE Conf. on Decision and Control. CDC 2008},
Year = {2008},
Organization = {IEEE},
Pages = {4215--4220},
Publisher = {Institute of Electrical and Electronics Engineers ({IEEE})},
DOI = {10.1109/cdc.2008.4739031}
}
@Article{FuKr97,
author = {M. Fulmek and C. Krattenthaler},
title = {Lattice path proofs for determinant formulas for symplectic and orthogonal characters},
journal = {J. Combin. Theory A},
year = {1997},
volume = {77},
pages = {3--50},
doi = {10.1006/jcta.1996.2711},
url = {www.mat.univie.ac.at/~kratt/artikel/symporth.html},
}
@Book{Fulton91,
Title = {Representation Theory},
Author = {W. Fulton and J. Harris},
Publisher = {Springer},
Year = {1991},
Address = {Berlin}
}
@Article{AGIP90,
Title = {On the topology of the {H\'enon} map},
Author = {G. D'Alessandro, P. Grassberger, S. Isola and A. Politi},
Journal = {J. Phys. A},
Year = {1990},
Pages = {5285},
Volume = {23},
DOI = {10.1088/0305-4470/23/22/017}
}
@Article{HamGomez02,
author = {A. G{\'o}mez and J. D. Meiss},
title = {Reversible polynomial automorphisms of the plane: {The} involutory case},
journal = {Phys. Lett. A},
year = {2003},
volume = {312},
pages = {49--58},
doi = {10.1016/s0375-9601(03)00605-4},
}
@Article{GadAmr93,
Title = {Spatially periodic orbits in coupled-map lattices},
Author = {Gade, P. M. and Amritkar, R. E.},
Journal = {Phys. Rev. E},
Year = {1993},
Pages = {143--154},
Volume = {47},
DOI = {10.1103/PhysRevE.47.143}
}
@Article{Gaeta92,
Title = {Reduction and {Equivariant Branching Lemma}: {Dynamical} systems, evolution {PDEs}, and gauge theories},
Author = {Gaeta, G.},
Journal = {Acta Appl. Math.},
Year = {1992},
Pages = {43--68},
Volume = {28},
DOI = {10.1007/BF00047030}
}
@Article{Gaeta95,
Title = {A splitting lemma for equivariant dynamics},
Author = {Gaeta, G.},
Journal = {Lett. Math. Phys.},
Year = {1995},
Pages = {313--320},
Volume = {33},
DOI = {10.1007/BF00749685}
}
@Article{Gaeta08,
Title = {Breaking of linear symmetries and {Michel}'s theory: {Grassmann} manifolds, and invariant subspaces},
Author = {Gaeta, G.},
Journal = {Int. J. Mod. Phys. A},
Year = {2008},
Pages = {547--565},
Volume = {23},
DOI = {10.1142/S0217751X08038639}
}
@Article{GaeRod96a,
author = {G. Gaeta and M. A. Rodr\'iguez},
title = {Determining discrete symmetries of differential equations},
journal = {Nuovo Cim. B},
year = {1996},
volume = {111},
pages = {879--891},
doi = {10.1007/BF02749018},
}
@Article{GaeRod96,
Title = {Discrete symmetries of differential equations},
Author = {G. Gaeta and M. A. Rodr\'iguez},
Journal = {J. Phys. A},
Year = {1996},
Pages = {859},
Volume = {29},
DOI = {10.1088/0305-4470/29/4/013}
}
@Article{galan_stability_2002,
author = {Galan, J. and Munoz-Almaraz, F. J. and Freire, E. and Doedel, E. J. and Vanderbauwhede, A.},
title = {Stability and bifurcations of the figure-8~{s}olution of the three-body problem},
journal = {Phys. Rev. Lett.},
year = {2002},
volume = {88},
pages = {241101},
doi = {10.1103/physrevlett.88.241101},
}
@Article{Gallavotti76,
Title = {Funzioni zeta ed insiemi basilari},
Author = {Gallavotti, G.},
Journal = {Accad. Lincei. Rend. Sc. Fis. Mat. e Nat},
Year = {1976},
Pages = {309--317},
Volume = {61}
}
@Misc{GKM03,
Title = {Topological characterization of spatial-temporal chaos},
Author = {M. Gameiro and W. Kalies and K. Mischaikow},
Year = {2003}
}
@Misc{marcio03,
Title = {Topological characterization of spatial-temporal chaos},
Author = {M. Gameiro and W. Kalies and K. Mischaikow},
Year = {2003}
}
@Article{GaXiLa11,
author = {{Gao}, A. and {Xie}, J. and {Lan}, Y.},
title = {Accelerating cycle expansions by dynamical conjugacy},
journal = {J. Stat. Phys.},
year = {2012},
volume = {146},
pages = {56--66},
doi = {10.1007/s10955-011-0369-6},
}
@Article{GGLTL09,
Title = {Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-{Lyapunov} way},
Author = {F. Gao and H. Gao and Zh. Li and H. Tong and J.-J. Lee},
Journal = {Chaos Solit. Fract.},
Year = {2009},
Pages = {2450--2463},
Volume = {42},
DOI = {10.1016/j.chaos.2009.03.119}
}
@Article{GarSar04,
author = {Garc{\'i}a-Mata, I. and Saraceno, M.},
title = {Spectral properties and classical decays in quantum open systems},
journal = {Phys. Rev. E},
year = {2004},
volume = {69},
pages = {056211},
doi = {10.1103/PhysRevE.69.056211},
}
@Article{postgal89,
author = {B. Garc\'{i}a-Archilla and J. Novo and E. S. Titi},
title = {Postprocessing the {G\"{a}lerkin} method: {A} novel approach to approximate inertial manifolds},
journal = {SIAM J. Numer. Anal.},
year = {1998},
volume = {35},
pages = {941--972},
abstract = {{G}{\"{a}}lerkin method},
doi = {10.1137/s0036142995296096},
}
@Article{garcia_geometrical_1996,
Title = {Geometrical conditions for the stability of orbits in planar systems},
Author = {R. Garcia},
Journal = {Math. Proc. Cambridge Philos. Soc.},
Year = {1996},
Pages = {499--520},
Volume = {120}
}
@Article{GaRuBa10,
Title = {Complex networks and symmetry: {A} review},
Author = {Garlaschelli, D. and Ruzzenenti, F. and Basosi, R.},
Journal = {Symmetry},
Year = {2010},
Pages = {1683--1709},
Volume = {2},
DOI = {10.3390/sym2031683}
}
@Article{garnier,
author = {N. Garnier and A. Chiffaudel and F. Daviaud and A. Prigent},
title = {Nonlinear dynamics of waves and modulated waves in 1{D} thermocapillary flows: {I. General} presentation and periodic solutions},
journal = {Physica D},
year = {2003},
volume = {174},
pages = {1--29},
doi = {10.1016/S0167-2789(02)00680-2},
}
@Article{Garnier2006,
author = {Garnier, N. and W{\'o}jcik, D.},
title = {{Spatiotemporal chaos: the microscopic perspective}},
journal = {Phys. Rev. Lett.},
year = {2006},
volume = {96},
pages = {114101},
doi = {10.1103/physrevlett.96.114101},
}
@Article{GaChi88,
Title = {Geometrical phases from global gauge invariance of nonlinear classical field theories},
Author = {Garrison, J. C. and Chiao, R. Y.},
Journal = {Phys. Rev. Lett.},
Year = {1988},
Pages = {165--168},
Volume = {60}
}
@Article{Gaspard92,
Title = {Diffusion, effusion, and chaotic scattering: {An} exactly solvable {Liouvillian} dynamics},
Author = {Gaspard, P.},
Journal = {J. Stat. Phys.},
Year = {1992},
Pages = {673--747},
Volume = {68},
DOI = {10.1007/BF01048873}
}
@Incollection{Gaspard92a,
author = {Gaspard, P.},
title = {From dynamical chaos to diffusion},
booktitle = {{From Phase Transitions to Chaos: Topics in Modern Statistical Physics}},
publisher = {World Scientific},
year = {1992},
editor = {Gy{\"o}rgyi, G. and Kondor, I. and Sasv{\'a}ri, L. and T{\'e}l, T.},
pages = {322--334},
address = {Singapore},
doi = {10.1142/9789814355872_0026},
}
@Article{gasp02,
Title = {Trace formula for noisy flows},
Author = {P. Gaspard},
Journal = {J. Stat. Phys.},
Year = {2002},
Pages = {57},
Volume = {106},
DOI = {10.1023/A:1013167928166}
}
@Article{GaspAlon93,
Title = {{$\hbar$}-expansion for the periodic-orbit quantization of hyperbolic systems},
Author = {P. Gaspard and D. Alonso},
Journal = {Phys. Rev. A},
Year = {1993},
Pages = {R3468--R3471},
Volume = {47}
}
@Article{GasBar95,
Title = {Chaotic scattering and diffusion in the {Lorentz} gas},
Author = {Gaspard, P. and Baras, F.},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {5332--5352},
Volume = {51},
DOI = {10.1103/PhysRevE.51.5332}
}
@InProceedings{GaBaMaHo92,
Title = {Dynamical chaos underlying diffusion in the {Lorentz} gas},
Author = {Gaspard, P. and Baras, F. and Mareschal, M. and Holian, B.},
Booktitle = {Microscopic simulations of complex hydrodynamic phenomena: {Proceedings} of {ASI}},
Year = {1992},
Address = {New York},
Pages = {301--322},
Publisher = {Plenum}
}
@Article{GasNic90,
Title = {Transport properties, {Lyapunov} exponents, and entropy per unit time},
Author = {Gaspard, P. and Nicolis, G.},
Journal = {Phys. Rev. Lett.},
Year = {1990},
Pages = {1693--1696},
Volume = {65},
DOI = {10.1103/PhysRevLett.65.1693}
}
@Article{GaspRice89c,
Title = {Exact quantization of the scattering from a classically chaotic repellor},
Author = {P. Gaspard and S. A. Rice},
Journal = {J. Chem. Phys.},
Year = {1989},
Pages = {2255--2262},
Volume = {90},
DOI = {10.1063/1.456019}
}
@Article{GaspRice89a,
Title = {Scattering from a classically chaotic repellor},
Author = {P. Gaspard and S. A. Rice},
Journal = {J. Chem. Phys.},
Year = {1989},
Pages = {2225--2241},
Volume = {90},
DOI = {10.1063/1.456017}
}
@Article{GaspRice89b,
Title = {Semiclassical quantization of the scattering from a classically chaotic repellor},
Author = {P. Gaspard and S. A. Rice},
Journal = {J. Chem. Phys.},
Year = {1989},
Pages = {2242--2254},
Volume = {90},
DOI = {10.1063/1.456018}
}
@Article{gasull_stability_2008,
Title = {On the stability of periodic orbits for differential systems in {$\mathbb{R}^n$}},
Author = {A. Gasull and H. Giacomini and M. Grau},
Journal = {Discrete Continuous Dyn. Syst. Ser. B},
Year = {2008},
Pages = {495--509},
Volume = {10},
DOI = {10.3934/dcdsb.2008.10.495}
}
@Book{gatermannHab,
Title = {{Computer Algebra Methods for Equivariant Dynamical Systems}},
Author = {Gatermann, K.},
Publisher = {Springer},
Year = {2000},
Address = {New York},
ISBN = {9783540671619}
}
@Article{GatGuy99,
Title = {Gr{\"o}bner bases, invariant theory and equivariant dynamics},
Author = {K. Gatermann and F. Guyard},
Journal = {J. Symbolic Comp.},
Year = {1999},
Pages = {275--302},
Volume = {28},
DOI = {10.1006/jsco.1998.0277}
}
@Article{GBHMRV10,
Title = {Invariant higher-order variational problems},
Author = {{Gay-Balmaz}, F. and {Holm}, D.~D. and {Meier}, D.~M. and {Ratiu}, T.~S. and {Vialard}, {F.-X.}},
Journal = {Commun. Math. Phys.},
Year = {2012},
Pages = {413--458},
Volume = {309},
DOI = {10.1007/s00220-011-1313-y}
}
@Article{GeLe98,
Title = {Construction of invariant torus using {Toeplitz Jacobian} matrices/fast {Fourier} transform approach},
Author = {Ge, T. and Leung, A. Y. T.},
Journal = {Nonlinear Dyn.},
Year = {1998},
Pages = {283--305},
Volume = {15},
DOI = {10.1023/A:1008246602555}
}
@Article{geddes04,
Title = {High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding},
Author = {Geddes, C. G. R. and Toth, Cs and van Tilborg, J. and Esarey, E. and Schroeder, C. B. and Bruhwiler, D. and Nieter, C. and Cary, J. and Leemans, W. P.},
Journal = {Nature},
Year = {2004},
Pages = {538--541},
Volume = {431},
Abstract = {Laser-driven accelerators, in which particles are accelerated by the
electric field of a plasma wave (the wakefield) driven by an intense
laser, have demonstrated accelerating electric fields of hundreds
of {GV} m-1 (refs 1?3). These fields are thousands of times greater
than those achievable in conventional radio-frequency accelerators,
spurring interest in laser accelerators as compact next-generation
sources of energetic electrons and radiation. To date, however, acceleration
distances have been severely limited by the lack of a controllable
method for extending the propagation distance of the focused laser
pulse. The ensuing short acceleration distance results in low-energy
beams with 100 per cent electron energy spread, which limits potential
applications. Here we demonstrate a laser accelerator that produces
electron beams with an energy spread of a few per cent, low emittance
and increased energy (more than 109 electrons above 80 {MeV).} Our
technique involves the use of a preformed plasma density channel
to guide a relativistically intense laser, resulting in a longer
propagation distance. The results open the way for compact and tunable
high-brightness sources of electrons and radiation.},
DOI = {10.1038/nature02900}
}
@Article{Geist01051990,
Title = {Comparison of different methods for computing {Lyapunov} exponents},
Author = {Geist, K. and Parlitz, U. and Lauterborn, W.},
Journal = {Progr. Theor. Phys.},
Year = {1990},
Pages = {875--893},
Volume = {83},
DOI = {10.1143/PTP.83.875}
}
@Article{GeZe84,
Title = {Models of representations of classical groups and their hidden symmetries},
Author = {Gel'fand, I. M. and Zelevinskii, A. V.},
Journal = {Funct. Anal. Appl.},
Year = {1984},
Pages = {183--198},
Volume = {18}
}
@Book{Georgi99,
Title = {{Lie} Algebras in Particle Physics},
Author = {H. Georgi},
Publisher = {Perseus Books},
Year = {1999},
Address = {Reading, MA}
}
@Article{GeDeAl12,
author = {Georgiou, O. and Dettmann, C. P. and Altmann, E. G.},
title = {Faster than expected escape for a class of fully chaotic maps},
journal = {Chaos},
year = {2012},
volume = {22},
pages = {043115},
doi = {10.1063/1.4766723},
}
@Article{GeOgSk11,
author = {Gerlach, E. and Eggl, S. and {Skokos}, C.},
title = {Efficient integration of the variational equations of multi-dimensional {Hamiltonian} systems: {Application} to the {Fermi-Pasta-Ulam} lattice},
journal = {Int. J. Bifurcation Chaos},
year = {2012},
volume = {22},
pages = {1250216},
doi = {10.1142/s0218127412502161},
}
@Article{heron87,
Title = {Dimension of the attractors associated to the {Ginzburg-Landau} partial differential equation},
Author = {J. M. Ghidaglia and B. H\'{e}ron},
Journal = {Physica D},
Year = {1987},
Pages = {282--304},
Volume = {28},
DOI = {10.1016/0167-2789(87)90020-0}
}
@Article{GiLePo95,
Title = {Statistical properties of bidimensional patterns generated from delayed and extended maps},
Author = {Giacomelli, G. and Lepri, S. and Politi, A.},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {3939--3944},
Volume = {51},
DOI = {10.1103/PhysRevE.51.3939}
}
@Article{GiaPol91,
Title = {Spatio-temporal chaos and localization},
Author = {G. Giacomelli and A. Politi},
Journal = {Europhys. Lett.},
Year = {1991},
Pages = {387--392},
Volume = {15},
DOI = {10.1209/0295-5075/15/4/004}
}
@Article{GiacoOtto05,
Title = {New bounds for the {Kuramoto-Sivashinsky} equation},
Author = {L. Giacomelli and F. Otto},
Journal = {Commun. Pure Appl. Math.},
Year = {2005},
Pages = {297--318},
Volume = {58},
DOI = {10.1002/cpa.20031}
}
@Misc{GiPaPe11,
author = {{Giacomin}, G. and {Pakdaman}, K. and {Pellegrin}, X.},
title = {Global attractor and asymptotic dynamics in the {Kuramoto} model for coupled noisy phase oscillators},
year = {2011},
url = {http://arXiv.org/abs/1107.4501},
}
@Misc{GiKuLeTa11,
author = {{Giardina}, C. and {Kurchan}, J. and {Lecomte}, V. and {Tailleur}, J.},
title = {Simulating rare events in dynamical processes},
year = {2011},
url = {http://arXiv.org/abs/1106.4929},
}
@Article{GibMcCLE82,
author = {Gibbon, J. D. and McGuinness, M. J.},
title = {The real and complex {Lorenz} equations in rotating fluids and lasers},
journal = {Physica D},
year = {1982},
volume = {5},
pages = {108--122},
doi = {10.1016/0167-2789(82)90053-7},
}
@Article{GibMcCLE83,
Title = {The real and complex {Lorenz} equations},
Author = {Gibbon, J. D. and McGuinness, M. J.},
Journal = {Proc. R. Irish. Acad., Ser. A},
Year = {1983},
Pages = {17--22},
Volume = {83}
}
@Article{GibVer94,
Title = {Normally attracting manifolds and periodic behavior in one-dimensional and two-dimensional coupled map lattices},
Author = {Giberti, C. and Vernia, C.},
Journal = {Chaos},
Year = {1994},
Pages = {651--663},
Volume = {4},
DOI = {10.1063/1.166042}
}
@Phdthesis{GibsonPhD,
Title = {Dynamical-systems Models of Wall-bounded, Shear-flow Turbulence},
Author = {J. F. Gibson},
School = {Cornell Univ.},
Year = {2002}
}
@Techreport{channelflow,
Title = {{Channelflow}: {A} spectral {Navier-Stokes} simulator in {C}++},
Author = {J. F. Gibson},
Institution = {U. New Hampshire},
Year = {2013},
Note = {{\tt {Channelflow.org}}},
Publisher = {J. F. Gibson},
URL = {http://Channelflow.org}
}
@Techreport{GibsonMovies,
Title = {Movies of plane {Couette}},
Author = {Gibson, J. F. and Cvitanovi{\'c}, P.},
Institution = {Georgia Inst. of Technology},
Year = {2015},
URL = {http://ChaosBook.org/tutorials}
}
@Article{GHCW07,
Title = {Visualizing the geometry of state-space in plane {Couette} flow},
Author = {J. F. Gibson and J. Halcrow and P. Cvitanovi{\'c}},
Journal = {J. Fluid Mech.},
Year = {2008},
Pages = {107--130},
Volume = {611},
DOI = {10.1017/S002211200800267X}
}
@Article{HGC08,
Title = {Equilibrium and traveling-wave solutions of plane {Couette} flow},
Author = {J. F. Gibson and J. Halcrow and P. Cvitanovi{\'c}},
Journal = {J. Fluid Mech.},
Year = {2009},
Pages = {243--266},
Volume = {638},
DOI = {10.1017/S0022112009990863}
}
@Book{CGdynamo,
Title = {{Stretch, Twist, Fold: the Fast Dynamo}},
Author = {Gilbert, A. D. and Childress, S.},
Publisher = {Springer},
Year = {1995},
Address = {Berlin},
DOI = {10.1007/978-3-540-44778-8},
ISBN = {978-3-662-14014-7}
}
@Article{GilbLef08,
author = {Gilbert, T. and Lefevere, R.},
title = {Heat conductivity from molecular chaos hypothesis in locally confined billiard systems},
journal = {Phys. Rev. Lett.},
year = {2008},
volume = {101},
pages = {200601},
doi = {10.1103/PhysRevLett.101.200601},
}
@Book{Gill82,
Title = {Atmosphere-ocean dynamics},
Author = {A. E. Gill},
Publisher = {Academic},
Year = {1982},
Address = {London}
}
@Book{gilmore74,
Title = {Lie Groups, {L}ie Algebras, and some of their Applications},
Author = {R. Gilmore},
Publisher = {Wiley},
Year = {1974},
Address = {New York}
}
@Book{gilmore08,
Title = {Lie Groups, Physics, and Geometry},
Author = {R. Gilmore},
Publisher = {Cambridge Univ. Press},
Year = {2008},
Address = {Cambridge}
}
@Article{GGJLF10,
Title = {Connecting curves for dynamical systems},
Author = {R. Gilmore and J.-M. Ginoux and T. Jones and C. Letellier and U. S. Freitas},
Journal = {J. Phys. A},
Year = {2010},
Pages = {255101},
Volume = {43},
DOI = {10.1088/1751-8113/43/25/255101}
}
@Book{gilmore2003,
Title = {The Topology of Chaos},
Author = {R. Gilmore and M. Lefranc},
Publisher = {Wiley},
Year = {2003},
Address = {New York}
}
@Book{GL-Gil07b,
title = {{The Symmetry of Chaos}},
publisher = {Oxford Univ. Press},
year = {2007},
author = {R. Gilmore and C. Letellier},
address = {Oxford},
isbn = {9780195310658},
}
@Article{GiChLiPo12,
author = {Ginelli, F. and Chat\'{e}, H. and Livi, R. and Politi, A.},
title = {Covariant {Lyapunov} vectors},
journal = {J. Phys. A},
year = {2013},
volume = {46},
pages = {254005},
doi = {10.1088/1751-8113/46/25/254005},
}
@Article{ginelli-2007-99,
author = {Ginelli, F. and Poggi, P. and Turchi, A. and Chat\'e, H. and Livi, R. and Politi, A.},
title = {Characterizing dynamics with covariant {Lyapunov} vectors},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {99},
pages = {130601},
doi = {10.1103/PhysRevLett.99.130601},
}
@Article{GiKaChPoAl11,
author = {Ginelli, F. and Takeuchi, K. A. and Chat\'{e}, H. and Politi, A. and Torcini A.},
title = {Chaos in the {Hamiltonian} mean-field model},
journal = {Phys. Rev. E},
year = {2011},
volume = {84},
pages = {066211},
doi = {10.1103/physreve.84.066211},
}
@Article{Ginzburg04,
Title = {{Nobel Lecture}: On superconductivity and superfluidity (what I have and have not managed to do) as well as on the ``physical minimum'' at the beginning of the {XXI} century},
Author = {Ginzburg, V. L.},
Journal = {Rev. Mod. Phys.},
Year = {2004},
Pages = {981--998},
Volume = {76},
DOI = {10.1103/RevModPhys.76.981}
}
@Article{GioAdr98,
author = {M. Giona and A. Adrover},
title = {Nonuniform stationary measure of the invariant unstable foliation in {H}amiltonian and fluid mixing systems},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {81},
pages = {3864},
doi = {10.1103/physrevlett.81.3864},
}
@Article{GioCer05,
Title = {Connecting the spatial structure of periodic orbits and invariant manifolds in hyperbolic area-preserving systems},
Author = {M. Giona and S. Cerbelli},
Journal = {Phys. Lett. A},
Year = {2005},
Pages = {200--207},
Volume = {347},
DOI = {10.1016/j.physleta.2005.08.005}
}
@Article{GiPo91,
Title = {Homoclinic tangencies, generating partitions and curvature of invariant manifolds},
Author = {F. Giovannini and A. Politi},
Journal = {J. Phys. A},
Year = {1991},
Pages = {1837--1848},
Volume = {24},
Abstract = {A method to compute the curvature of the unstable manifold is introduced
and applied to H\'enon map and Duffing attractor, showing that it
allows the authors to locate the homoclinic tangencies and, in turn,
to construct a generating partition.}
}
@Article{GiPo92,
Title = {Generating partitions in {H\'enon}-type maps},
Author = {F. Giovannini and A. Politi},
Journal = {Phys. Lett. A},
Year = {1992},
Pages = {332--336},
Volume = {161}
}
@Article{GloKR85,
author = {R. Glowinski and H. B. Keller and L. Rheinhart},
title = {Continuation-conjugate gradient methods for the least-squares solution of nonlinear boundary value problems},
journal = {SIAM J. Sci. Statist. Comput.},
year = {1985},
volume = {6},
pages = {793--832},
doi = {10.1137/0906055},
}
@Article{cgole92,
Title = {A new proof of the {Aubry-Mather}'s theorem},
Author = {C. Gol\'{e}},
Journal = {Math. Z.},
Year = {1992},
Pages = {441--448},
Volume = {210},
Abstract = {A auxiliary infinite gradient-like flow is constructed for the area-preserving
map such that orbits of the original system are rest points of the
new system. In this way, existence of orbits of any rotation number
is proved.}
}
@Article{GoSuOr87,
author = {Goldhirsch, I. and Sulem, P. L. and Orszag, S. A.},
title = {Stability and {Lyapunov} stability of dynamical systems: {A} differential approach and a numerical method},
journal = {Physica D},
year = {1987},
volume = {27},
pages = {311--337},
doi = {10.1016/0167-2789(87)90034-0},
}
@Article{GoSi94,
Title = {The one-dimensional complex {Ginzburg-Landau} equation in the low dissipation limit},
Author = {Goldman, D. and Sirovich, L.},
Journal = {Nonlinearity},
Year = {1994},
Pages = {417--439},
Volume = {7},
DOI = {10.1088/0951-7715/7/2/007}
}
@Misc{Goldobin12,
author = {Goldobin, D. S.},
title = {Limit distribution of averages over unstable periodic orbits forming chaotic attractor},
year = {2012},
url = {http://arXiv.org/abs/1208.1691},
}
@Misc{GoZa10,
Title = {Noise reduces disorder in chaotic dynamics},
Author = {Goldobin, D. S. and Zaks, M. A. },
Year = {2010},
URL = {http://arXiv.org/abs/1008.0073}
}
@Book{goldstein59,
Title = {Classical Mechanics},
Author = {Goldstein, H.},
Publisher = {Wesley},
Year = {1959},
Address = {Reading, MA}
}
@Book{goldstein80,
Title = {{Classical Mechanics}},
Author = {Goldstein, H.},
Publisher = {Wesley},
Year = {1980},
Address = {Reading, MA},
Edition = {2},
ISBN = {9788177582833}
}
@Book{goldstein01,
Title = {{Classical Mechanics}},
Author = {Goldstein, H. and Poole, C. P. and Safko, J. L.},
Publisher = {Wesley},
Year = {2001},
Address = {Reading, MA},
Edition = {3\textsuperscript{rd}}
}
@Article{golubord,
Title = {Order and disorder in fluid motion},
Author = {J. P. Gollub},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1995},
Pages = {6705--6711},
Volume = {92},
DOI = {10.1073/pnas.92.15.6705}
}
@Book{GoVanLo96,
Title = {Matrix Computations},
Author = {Golub, G. H. and Van Loan, C. F.},
Publisher = {J. Hopkins Univ. Press},
Year = {1996},
Address = {Baltimore, MD}
}
@Book{golubI,
Title = {{Singularities and Groups in Bifurcation Theory}},
Author = {M. Golubitsky and D. G. Schaeffer},
Publisher = {Springer},
Year = {1984},
Address = {New York},
DOI = {10.1007/978-1-4612-5034-0},
ISBN = {9781461250340},
Volume = {1}
}
@Book{golubitsky2002sp,
Title = {{The Symmetry Perspective}},
Author = {Golubitsky, M. and Stewart, I.},
Publisher = {Birkh{\"a}user},
Year = {2002},
Address = {Boston},
ISBN = {9783034881678}
}
@Book{golubII,
Title = {{Singularities and Groups in Bifurcation Theory}},
Author = {M. Golubitsky and I. Stewart and D. G. Schaeffer},
Publisher = {Springer},
Year = {1988},
Address = {New York},
DOI = {10.1007/978-1-4612-4574-2},
ISBN = {978-0-387-96652-6},
Volume = {2}
}
@Article{golubsym84,
author = {M. Golubitsky and J. W. Swift and Knobloch, J.},
title = {Symmetries and pattern selection in {Rayleigh-B\'{e}nard} convection},
journal = {Physica D},
year = {1984},
volume = {10},
pages = {249},
doi = {10.1016/0167-2789(84)90179-9},
}
@Article{GoPa11,
Title = {Numerical simulation of asymptotic states of the damped {Kuramoto-Sivashinsky} equation},
Author = {Gomez, H. and Paris, J.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {046702},
Volume = {83},
DOI = {10.1103/PhysRevE.83.046702}
}
@Article{Good94,
Title = {Stability of the {Kuramoto-Sivashinsky} and related systems},
Author = {J. Goodman},
Journal = {Commun. Pure Appl. Math.},
Year = {1994},
Pages = {293--306},
Volume = {47},
DOI = {10.1002/cpa.3160470304}
}
@Article{GDTR08,
author = {E. Gouillart and O. Dauchot and {J.-L.} Thiffeault and S. Roux},
title = {Open-flow mixing: {Experimental} evidence for strange eigenmodes},
journal = {Phys. Fluids},
year = {2009},
volume = {21},
pages = {023603},
doi = {10.1063/1.3080680},
}
@Book{Govaerts00,
Title = {Numerical Methods for Bifurcations of Dynamical Equilibria},
Author = {W. J. F. Govaerts},
Publisher = {SIAM},
Year = {2000},
Address = {Philadelphia}
}
@Article{GozReu94,
Title = {{Lyapunov} exponents, path-integrals and forms},
Author = {Gozzi, E. and Reuter, M.},
Journal = {Chaos Solit. Fract.},
Year = {1994},
Pages = {1117--1139},
Volume = {4},
DOI = {10.1016/0960-0779(94)90026-4}
}
@Book{GraRyz,
Title = {Tables of Integrals, Series and Products},
Author = {I. S. Gradshteyn and I. M. Ryzhik},
Publisher = {Academic},
Year = {1980},
Address = {New York}
}
@Incollection{GranatRBA,
author = {Granat, R. and Jonsson, I. and K{\aa}gstr\"{o}m, B.},
title = {Recursive blocked algorithms for solving periodic triangular {Sylvester}-type matrix equations},
booktitle = {{Applied Parallel Computing. State of the Art in Scientific Computing}},
publisher = {Springer},
year = {2007},
pages = {531--539},
address = {New York},
doi = {10.1007/978-3-540-75755-9_65},
}
@Article{GranatK06,
author = {R. Granat and B. K\r{a}gstr\"{o}m},
title = {Direct eigenvalue reordering in a product of matrices in periodic {Schur} form},
journal = {SIAM J. Matrix Anal. Appl.},
year = {2006},
volume = {28},
pages = {285--300},
doi = {10.1137/05062490x},
}
@Article{grant67,
Title = {{Fourier-{Hermit}e} solutions of the {Vlasov} equations in the linearized limit},
Author = {F. C. Grant and M. R. Feix},
Journal = {Phys. Fluids},
Year = {1967},
Pages = {696--702},
Volume = {10}
}
@Article{D_q,
Title = {Generalized dimensions of strange attractors},
Author = {P. Grassberger},
Journal = {Phys. Lett. A},
Year = {1983},
Pages = {227--230},
Volume = {97},
DOI = {10.1016/0375-9601(83)90753-3}
}
@Article{gras86,
Title = {Toward a quantitative theory of self-generated complexity},
Author = {Grassberger, P.},
Journal = {Int. J. Theor. Phys.},
Year = {1986},
Pages = {907--938},
Volume = {25},
DOI = {10.1007/BF00668821},
ISSN = {1572-9575}
}
@Article{grass88,
Title = {On symbolic dynamics of one-humped maps of the Iinterval},
Author = {Grassberger, P.},
Journal = {Z. Naturforsch. A},
Year = {1988},
Pages = {671--680},
Volume = {43},
DOI = {10.1515/zna-1988-0710}
}
@Article{Grassberger89,
Title = {Information content and predictability of lumped and distributed dynamical systems},
Author = {P. Grassberger},
Journal = {Phys. Scr.},
Year = {1989},
Pages = {346},
Volume = {40},
DOI = {10.1088/0031-8949/40/3/016}
}
@Article{GK85,
Title = {Generating partitions for the dissipative {H{\'e}non} map},
Author = {P. Grassberger and H. Kantz},
Journal = {Phys. Lett. A},
Year = {1985},
Pages = {235--238},
Volume = {113},
DOI = {10.1016/0375-9601(85)90016-7}
}
@Article{grass89,
author = {P. Grassberger and H. Kantz and U. Moenig},
title = {On the symbolic dynamics of {H{\'e}non} map},
journal = {J. Phys. A},
year = {1989},
volume = {22},
pages = {5217--5230},
doi = {10.1088/0305-4470/22/24/011},
}
@Article{GraPro83a,
Title = {Characterization of strange attractors},
Author = {Grassberger, P. and Procaccia, I.},
Journal = {Phys. Rev. Lett.},
Year = {1983},
Pages = {346--349},
Volume = {50},
DOI = {10.1103/PhysRevLett.50.346}
}
@Article{GraPro83,
Title = {Estimation of the {Kolmogorov} entropy from a chaotic signal},
Author = {Grassberger, P. and Procaccia, I.},
Journal = {Phys. Rev. A},
Year = {1983},
Pages = {2591--2593},
Volume = {28},
DOI = {10.1103/PhysRevA.28.2591}
}
@Article{GraPro83b,
Title = {Measuring the strangeness of strange attractors},
Author = {Grassberger, P. and Procaccia, I.},
Journal = {Physica D},
Year = {1983},
Pages = {189--208},
Volume = {9},
DOI = {10.1016/0167-2789(83)90298-1}
}
@Article{greb90shad,
author = {C. Grebogi and S. M. Hammel and J. A. Yorke and T. Sauer},
title = {Shadowing of physical trajectories in chaotic dynamics: {Containment} and refinement},
journal = {Phys. Rev. Lett.},
year = {1990},
volume = {65},
pages = {1527--1530},
doi = {10.1103/physrevlett.65.1527},
}
@Article{yorke2,
Title = {Unstable periodic orbits and the dimensions of multifractal chaotic attractors},
Author = {C. Grebogi and E. Ott and J. A. Yorke},
Journal = {Phys. Rev. A},
Year = {1988},
Pages = {1711--1724},
Volume = {37},
Abstract = {The probability measure generated by typical chaotic orbits of a dynamical
system can have an arbitrarily fine-scaled interwoven structure of
points with different singularity scalings. Recent work has characterized
such measures via a spectrum of fractal dimension values. In this
paper we pursue the idea that the infinite number of unstable periodic
orbits embedded in the support of the measure provides the key to
an understanding of the structure of the subsets with different singularity
scalings. In particular, a formulation relating the spectrum of dimensions
to unstable periodic orbits is presented for hyperbolic maps of arbitrary
dimensionality. Both chaotic attractors and chaotic repellers are
considered.},
DOI = {10.1103/PhysRevA.37.1711}
}
@Article{gree98,
Title = {Two-dimensional measure-preserving mappings},
Author = {J. M. Greene},
Journal = {J. Math. Phys.},
Year = {1968},
Pages = {760},
Volume = {9}
}
@Article{gree79,
Title = {A method for determining a stochastic transition},
Author = {J. M. Greene},
Journal = {J. Math. Phys.},
Year = {1979},
Pages = {1183--1201},
Volume = {20}
}
@Article{GreeKim87,
author = {J. M. Greene and J.-S. Kim},
title = {The calculation of {Lyapunov} spectra},
journal = {Physica D},
year = {1987},
volume = {24},
pages = {213--225},
doi = {10.1016/0167-2789(87)90076-5},
}
@Article{ksgreene88,
Title = {The steady states of the {Kuramoto-Sivashinsky} equation},
Author = {J. M. Greene and J.-S. Kim},
Journal = {Physica D},
Year = {1988},
Pages = {99--120},
Volume = {33},
Abtract = {Use Fourier modes to discuss the energy transport from long wavelength modes to short ones. The generation of steady states with periodic boundary condition is studied systematically with a bifurcation analysis. Their stability is investigated and the scaling in the limit of large system size is presented.},
DOI = {10.1016/S0167-2789(98)90013-6}
}
@Article{GrMaViFe81,
Title = {Universal behaviour in families of area-preserving maps},
Author = {J. M. Greene and R. S. MacKay and F. Vivaldi and M. J. Feigenbaum},
Journal = {Physica D},
Year = {1981},
Pages = {468--486},
Volume = {3},
DOI = {10.1016/0167-2789(81)90034-8}
}
@Book{Greensite11,
Title = {An introduction to the confinement problem},
Author = {Greensite, J.},
Publisher = {Springer},
Year = {2011},
Address = {New York},
Pages = {101--129}
}
@Book{greshosani,
Title = {Incompressible Flow and the Finite Element Method},
Author = {P. M. Gresho and R. L. Sani},
Publisher = {Wiley},
Year = {2000},
Address = {New York}
}
@Article{Gribov77,
Title = {Quantization of nonabelian gauge theories},
Author = {Gribov, V. N.},
Journal = {Nucl. Phys.},
Year = {1978},
Pages = {1--19},
Volume = {B139},
DOI = {10.1016/0550-3213(78)90175-X}
}
@Incollection{autod89,
Title = {On Automatic Differentiation},
Author = {A. Griewank},
Booktitle = {Mathematical Programming: Recent Developments and Applications},
Publisher = {Kluwer},
Year = {1989},
Address = {Dordrecht},
Editor = {M. Iri and K. Tanabe},
Pages = {83--108}
}
@Article{ksgrim91,
Title = {The non-existence of a certain class of travelling wave solutions of the {Kuramoto-Sivashinsky} equation},
Author = {R. Grimshaw and A. P. Hooper},
Journal = {Physica D},
Year = {1991},
Pages = {231--238},
Volume = {50},
Abstract = {If the effect of short-wave stability is small, there are no regular
shocks.},
DOI = {0.1016/0167-2789(91)90177-B}
}
@Article{Gritsun10,
Title = {Statistical characteristics of barotropic atmospeheric system and its unstable periodic solutions},
Author = {Gritsun, A.},
Journal = {Dokl. Earth Sciences},
Year = {2010},
Pages = {1688--1691},
Volume = {435},
Abstract = {This paper is devoted to the problem of approximating an invariant
measure and statistical characteristics of barotropic atmospheric
model with the help of its periodic trajectories. In this procedure
orbits are taken into account according to their weights defined
by the orbit instability characteristics. The method comes from the
dynamical systems theory where in several specific case (for hyperbolic
systems in particular) unstable periodic orbits define the system
invariant measure. In our study we show that the system PDF could
be reconstructed with the error less than 10\% provided that the
optimal orbit weight function is chosen.},
DOI = {10.1134/S1028334X10120287}
}
@Article{Gritsun11,
Title = {Connection of periodic orbits and variability patterns of circulation for the barotropic model of atmospheric dynamics},
Author = {Gritsun, A.},
Journal = {Dokl. Earth Sciences},
Year = {2011},
Pages = {636--640},
Volume = {438},
Abstract = {We have investigated the relationship between periodic trajectories
of barotropic atmospheric model and the modes of the model variability.
In particular, we have studied the nature of ``25 day'' mode of variability
(Branstator, 1987; Kushnir 1987). This mode arises as a first complex
empirical orthogonal function (or ``Hilbert EOF'' according to (H.
von Storch, Zwiers)) for a given system and is a dominant rotational
component of the system dynamics. It was shown that the mode structure
coincides with several least unstable periodic orbits of the system.
The phase portrait of the system in the plane of the first complex
EOF has regular shape with maximum of the probability density function
in the vicinity of these weakly unstable periodic orbits.},
DOI = {10.1134/S1028334X11050035}
}
@Article{Gritsun13,
Title = {Statistical characteristics, circulation regimes and unstable periodic orbits of a barotropic atmospheric model},
Author = {Gritsun, A.},
Journal = {Philos. Trans. Royal Soc. A},
Year = {2013},
Volume = {371},
DOI = {10.1098/rsta.2012.0336}
}
@Article{GrBrMa08,
Title = {Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem},
Author = {A. Gritsun and G. Branstator and A. Majda},
Journal = {J. Atmos. Sci.},
Year = {2008},
Pages = {2824--2841},
Volume = {65},
DOI = {10.1175/2007JAS2496.1}
}
@Article{LucGri16,
author = {A. Gritsun and V. Lucarini},
title = {Fluctuations, response, and resonances in a simple atmospheric model},
journal = {Physica D},
year = {2017},
volume = {349},
doi = {10.1016/j.physd.2017.02.015},
}
@Article{Gritsun08,
Title = {Unstable periodic trajectories of a barotropic model of the atmosphere},
Author = {Gritsun, A. S.},
Journal = {Russian J. Numer. Analysis and Math. Modelling},
Year = {2008},
Pages = {345--367},
Volume = {23},
Abstract = {Unstable periodic trajectories of a chaotic dissipative system belong
to the attractor of the system and are its important characteristics.
Many chaotic systems have an infinite number of periodic solutions
forming the skeleton of the system attractor. This allows one to
approximate the system trajectories and statistical characteristics
by using periodic solutions. The least unstable orbits may generate
local maxima of the system state distribution functions on the attractor.
With respect to atmospheric systems this means that orbits may determine
dynamic circulation regimes and typical variability modes of the
system. In some cases, given a small number of periodic solutions,
one can describe the dynamics on the attractor of the system and
the basic statistics with sufficient precision. Thus, the information
concerning periodic trajectories of a particular dynamic system may
be very important for analysis of its behavior. A search for periodic
trajectories is reduced to the solution of a system of nonlinear
equations with respect to the initial condition of an orbit and its
period. The choice of a numerical solution method and an initial
guess is an important aspect here. In this paper we consider the
problem of the calculation of periodic trajectories for a barotropic
model of the atmosphere. Several methods for determination of periodic
orbits of the model are formulated and implemented, including the
Newton method with step suppression, the Newton method with a second
order tensor correction, the quasi-Newton method with step suppression,
the quasi-Newton method with minimization of the error functional
and approximate Hessian inversion by the LBFG scheme and the GMRES
method. A comparison of the efficiency of these numerical methods
and different choices of initial conditions is performed. Various
factors influencing the rate of convergence of the methods are considered.},
DOI = {10.1515/RJNAMM.2008.021}
}
@Article{G00,
author = {S. Grossmann},
title = {The onset of shear turbulence},
journal = {Rev. Mod. Phys.},
year = {2000},
volume = {72},
pages = {603--618},
}
@Article{GroFuj82,
Title = {Diffusion in discrete nonlinear dynamical systems},
Author = {Grossmann, S. and Fujisaka, H.},
Journal = {Phys. Rev. A},
Year = {1982},
Pages = {1779--1782},
Volume = {26},
DOI = {10.1103/PhysRevA.26.1779}
}
@Article{Adler98,
author = {Adler, R. L.},
title = {Symbolic dynamics and {Markov} partitions},
journal = {Bull. Amer. Math. Soc.},
year = {1998},
volume = {35},
pages = {1--56},
doi = {10.1090/S0273-0979-98-00737-X},
}
@Article{Guckenh77,
Title = {On the bifurcation of maps of the interval},
Author = {J. Guckenheimer},
Journal = {Inv. Math.},
Year = {1977},
Pages = {165--178},
Volume = {39},
DOI = {10.1007/BF01390107}
}
@Article{Guck79,
Title = {Sensitive dependence to initial conditions for one dimensional maps},
Author = {Guckenheimer, J.},
Journal = {Commun. Math. Phys.},
Year = {1979},
Pages = {133--160},
Volume = {70},
Abstract = {This paper studies the iteration of maps of the interval which have
negative Schwarzian derivative and one critical point. The maps in
this class are classified up to topological equivalence. The equivalence
classes of maps which display sensitivity to initial conditions for
large sets of initial conditions are characterized.},
DOI = {10.1007/BF01982351}
}
@Book{guckb,
title = {{Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields}},
publisher = {Springer},
year = {1983},
author = {J. Guckenheimer and P. Holmes},
address = {New York},
doi = {10.1007/978-1-4612-1140-2},
}
@Article{GKOS15,
Title = {Invariant manifolds and global bifurcations},
Author = {J. Guckenheimer and B. Krauskopf and H. M. Osinga and B. Sandstede},
Journal = {Chaos},
Year = {2015},
Volume = {25},
DOI = {10.1063/1.4915528},
URL = {http://www.dam.brown.edu/people/sandsted/publications/gkos-survey.pdf}
}
@Article{GM00aut,
author = {J. Guckenheimer and B. Meloon},
title = {Computing periodic orbits and their bifurcations with automatic differentiation},
journal = {SIAM J. Sci. Comput.},
year = {2000},
volume = {22},
pages = {951--985},
doi = {10.1137/s1064827599359278},
}
@Incollection{GuIsLa08,
Title = {Ihara zeta functions for periodic simple graphs},
Author = {Guido, D. and Isola, T. and Lapidus, M. L.},
Booktitle = {{C*-algebras and Elliptic Theory II}},
Publisher = {Birkh{\"a}user},
Year = {2008},
Address = {Basel},
Editor = {Burghelea, D. and Melrose, R. and Mishchenko, A. S. and Troitsky, E. V.},
Pages = {103--121},
DOI = {10.1007/978-3-7643-8604-7_5},
ISBN = {978-3-7643-8604-7}
}
@Book{GuiSte90,
Title = {Symplectic Techniques in Physics},
Author = {V. Guillemin and S. Sternberg},
Publisher = {Cambridge Univ. Press},
Year = {1990},
Address = {Cambridge}
}
@Article{GuiUri87,
Title = {Reduction, the trace formula, and semiclassical asymptotics},
Author = {Guillemin, V. and Uribe, A.},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1987},
Pages = {7799--7801},
Volume = {84},
DOI = {10.1073/pnas.84.22.7799}
}
@Article{GuiUri89,
Title = {Circular symmetry and the trace formula},
Author = {Guillemin, V. and Uribe, A.},
Journal = {Inv. Math.},
Year = {1989},
Pages = {385--423},
Volume = {96},
DOI = {10.1007/BF01393968}
}
@Article{GuiUri90,
Title = {Reduction and the trace formula},
Author = {Guillemin, V. and Uribe, A.},
Journal = {J. Diff. Geom.},
Year = {1990},
Pages = {315},
Volume = {32},
URL = {http://projecteuclid.org/euclid.jdg/1214445310}
}
@Book{MiraGum80,
Title = {Recurrances and Discrete Dynamical Systems},
Author = {I. Gumowski and C. Mira},
Publisher = {Springer},
Year = {1980},
Address = {Berlin}
}
@Article{GunRan93I,
Title = {Spatio-temporal chaos. {I. Hyperbolicity}, structural stability, spatio-temporal shadowing and symbolic dynamics},
Author = {V. M. Gundlach and D. A. Rand},
Journal = {Nonlinearity},
Year = {1993},
Pages = {165},
Volume = {6},
URL = {http://stacks.iop.org/0951-7715/6/i=2/a=002}
}
@Book{Gurtin81,
Title = {An Introduction to Continuum Mechanics},
Author = {Gurtin, M. E.},
Publisher = {Academic},
Year = {1981},
Address = {New York}
}
@Misc{GHJSC16,
author = {B. Gutkin and L. Han and R. Jafari and A. K. Saremi and P. Cvitanovi{\'c}},
title = {Linear encoding of the spatiotemporal cat map},
year = {2017},
note = {In preparation},
}
@Article{GutOsi13,
Title = {Clustering of periodic orbits and ensembles of truncated unitary matrices},
Author = {Gutkin, B. and Osipov, V.},
Journal = {J. Stat. Phys.},
Year = {2013},
Pages = {1049--1064},
Volume = {153},
DOI = {10.1007/s10955-013-0859-9}
}
@Article{GutOsi13a,
Title = {Clustering of periodic orbits in chaotic systems},
Author = {Gutkin, B. and Osipov, V.},
Journal = {Nonlinearity},
Year = {2013},
Pages = {177},
Volume = {26},
DOI = {10.1088/0951-7715/26/1/177}
}
@Article{GutOsi15,
Title = {Classical foundations of many-particle quantum chaos},
Author = {Gutkin, B. and Osipov, V.},
Journal = {Nonlinearity},
Year = {2016},
Pages = {325--356},
Volume = {29},
DOI = {10.1088/0951-7715/29/2/325}
}
@Article{gutzwiller67,
author = {M. C. Gutzwiller},
title = {Phase-integral approximation in momentum space and the bound states of an atom},
journal = {J. Math. Phys.},
year = {1967},
volume = {8},
pages = {1979--2000},
doi = {10.1063/1.1705112},
}
@Article{gutzwiller69,
author = {M. C. Gutzwiller},
title = {Phase-integral approximation in momentum space and the bound states of an atom. {II}},
journal = {J. Math. Phys.},
year = {1969},
volume = {10},
pages = {1004--1020},
doi = {10.1063/1.1664927},
}
@Article{gutzwiller70,
author = {M. C. Gutzwiller},
title = {Energy spectrum according to classical mechanics},
journal = {J. Math. Phys.},
year = {1970},
volume = {11},
number = {6},
pages = {1791--1806},
doi = {10.1063/1.1665328},
}
@Article{gutzwiller71,
Title = {Periodic orbits and classical quantization conditions},
Author = {M. C. Gutzwiller},
Journal = {J. Math. Phys.},
Year = {1971},
Pages = {343--358},
Volume = {12},
DOI = {10.1063/1.1665596}
}
@Article{gut82,
Title = {The quantization of a classically ergodic system},
Author = {M. C. Gutzwiller},
Journal = {Physica D},
Year = {1982},
Pages = {183--207},
Volume = {5},
DOI = {10.1016/0167-2789(82)90017-3}
}
@Book{gutbook,
Title = {{Chaos in Classical and Quantum Mechanics}},
Author = {M. C. Gutzwiller},
Publisher = {Springer},
Year = {1990},
Address = {New York},
ISBN = {9781461209836}
}
@Book{henonrtb2,
Title = {Generating Families in the Restricted Three-Body Problem {II}. Quantitative Study of Bifurcations},
Author = {M. H\'{e}non},
Publisher = {Springer},
Year = {2001},
Address = {New York}
}
@Article{hhsys,
Title = {The applicability of the third integral of motion: {Some} numerical experiments},
Author = {M. H\'{e}non and C. Heiles},
Journal = {Astron. J.},
Year = {1964},
Pages = {73--79},
Volume = {69},
DOI = {10.1086/109234}
}
@Article{henon,
author = {M. H\'enon},
title = {A two-dimensional mapping with a strange attractor},
journal = {Commun. Math. Phys.},
year = {1976},
volume = {50},
pages = {94--102},
booktitle = {The Theory of Chaotic Attractors},
doi = {10.1007/978-0-387-21830-4_8},
}
@Article{HW90,
Title = {Spectral properties of strongly perturbed {Coulomb} systems: {Fluctuation} properties},
Author = {H\"onig, A. and Wintgen, D.},
Journal = {Phys. Rev. A},
Year = {1989},
Pages = {5642--5657},
Volume = {39},
DOI = {10.1103/PhysRevA.39.5642}
}
@Article{Huls16,
Title = {On the approximation of stable and unstable fiber bundles of (non)autonomous {ODEs} -- {A} contour algorithm},
Author = {H\"uls, T.},
Journal = {Int. J. Bifur. Chaos},
Year = {2016},
Pages = {1650118},
Volume = {26},
DOI = {10.1142/S0218127416501182}
}
@Book{HaCh08,
Title = {{Nonlinear Dynamical Systems and Control: A {Lyapunov}-Based Approach}},
Author = {Haddad, W. M. and Chellaboina, V.},
Publisher = {Princeton Univ. Press},
Year = {2008},
Address = {Princeton NJ}
}
@Article{HaFaHa13,
author = {{Hadjighasem}, A. and {Farazmand}, M. and {Haller}, G.},
title = {Detecting invariant manifolds, attractors, and generalized {KAM} tori in aperiodically forced mechanical systems},
journal = {Nonlinear Dyn.},
year = {2013},
volume = {73},
pages = {689--704},
doi = {10.1007/s11071-013-0823-x},
}
@Article{Hagen1839,
Title = {{\"U}ber die Bewegung des Wassers in engen cylindrischen R{\"o}hren},
Author = {G. Hagen},
Journal = {Ann. Phys.},
Year = {1839},
Pages = {423--442},
Volume = {122},
DOI = {10.1002/andp.18391220304}
}
@Article{HaShu04a,
Title = {An algorithm to prune the area-preserving {H\'enon} map},
Author = {Hagiwara, R. and Shudo, A.},
Journal = {J. Phys. A},
Year = {2004},
Number = {44},
Pages = {10521},
Volume = {37},
Abstract = {An explicit algorithm to provide the pruning front for the area-preserving
H\'enon map is presented. The procedure terminates within finitely
many steps when the map has hyperbolic structure. The only information
required to specify the pruning front is a bifurcation diagram of
homoclinic orbits, and it is obtained by tracking orbits from the
anti-integrable limit. The pruned region thus determined is used
to construct the Markov partition of the map, and the topological
entropy is evaluated as an application.},
DOI = {10.1088/0305-4470/37/44/005}
}
@Article{HaShu04b,
author = {Hagiwara, R. and Shudo, A.},
title = {Grammatical complexity for two-dimensional maps},
journal = {J. Phys. A},
year = {2004},
volume = {37},
pages = {10545},
doi = {10.1088/0305-4470/37/44/006},
abstract = {We calculate the grammatical complexity of the symbol sequences generated
from the {H\'enon} map and the Lozi map using the recently developed
methods to construct the pruning front. When the map is hyperbolic,
the language of symbol sequences is regular in the sense of the Chomsky
hierarchy and the corresponding grammatical complexity takes finite
values. It is found that the complexity exhibits a self-similar structure
as a function of the system parameter, and the similarity of the
pruning fronts is discussed as an origin of such self-similarity.
For non-hyperbolic cases, it is observed that the complexity monotonically
increases as we increase the resolution of the pruning front.},
}
@Book{Hairer06,
Title = {{Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations}},
Author = {Hairer, E. and Lubich, C. and Wanner, G.},
Publisher = {Springer},
Year = {2006},
Address = {Berlin},
DOI = {10.1007/3-540-30666-8},
Edition = {2}
}
@Article{HaiMaj10,
author = {M. Hairer and A. J. Majda},
title = {A simple framework to justify linear response theory},
journal = {Nonlinearity},
year = {2010},
volume = {23},
pages = {909--922},
doi = {10.1088/0951-7715/23/4/008},
}
@Article{HakenZeroLyap83,
Title = {At least one {Lyapunov} exponent vanishes if the trajectory of an attractor does not contain a fixed point},
Author = {H. Haken},
Journal = {Phys. Lett. A},
Year = {1983},
Pages = {71--72},
Volume = {94},
DOI = {10.1016/0375-9601(83)90209-8}
}
@Phdthesis{HalcrowThesis,
Title = {Geometry of turbulence: An exploration of the state-space of plane {Couette} flow},
Author = {Halcrow, J.},
School = {School of Physics, Georgia Inst. of Technology},
Year = {2008},
Address = {Atlanta},
URL = {http://ChaosBook.org/projects/theses.html}
}
@Article{GHCV08,
Title = {Heteroclinic connections in plane {Couette} flow},
Author = {Halcrow, J. and Gibson, J. F. and Cvitanovi{\'c}, P. and Viswanath, D.},
Journal = {J. Fluid Mech.},
Year = {2009},
Pages = {365--376},
Volume = {621},
DOI = {10.1017/S0022112008005065}
}
@Book{haleob,
Title = {{Ordinary Differential Equations}},
Author = {Hale, J.K.},
Publisher = {Dover},
Year = {1969},
Address = {New York},
ISBN = {9780486472119}
}
@Book{HaleKo91,
Title = {{Dynamics and Bifurcations}},
Author = {J. Hale and H. Ko{\c{c}}ak},
Publisher = {Springer},
Year = {1991},
Address = {New York},
ISBN = {9781461244264}
}
@Book{Hale63,
title = {{Oscillations in Nonlinear Systems}},
publisher = {Dover},
year = {1963},
author = {Hale, J. K.},
isbn = {9780486803265},
address = {New York},
}
@Book{Hall03,
Title = {Lie Groups, {Lie} Algebras, and Representations},
Author = {Hall, B. C},
Publisher = {Springer},
Year = {2003},
Address = {New York}
}
@Article{Hall93,
Title = {Fat one-dimensional representatives of pseudo-{Anosov} isotopy classes with minimal periodic orbit structure},
Author = {T. Hall},
Journal = {Nonlinearity},
Year = {1994},
Pages = {367},
Volume = {7},
DOI = {10.1088/0951-7715/7/2/004}
}
@Article{Hall94,
author = {T. Hall},
title = {The creation of horseshoes},
journal = {Nonlinearity},
year = {1994},
volume = {7},
pages = {861--924},
doi = {10.1088/0951-7715/7/3/008},
}
@Article{Haller11,
Title = {A variational theory of hyperbolic {Lagrangian Coherent Structures}},
Author = {Haller, G.},
Journal = {Physica D},
Year = {2011},
Pages = {574--598},
Volume = {240},
DOI = {10.1016/j.physd.2010.11.010}
}
@Article{HaMe98,
Title = {Reduction of three-dimensional, volume-preserving flows with symmetry},
Author = {G. Haller and I. Mezi{\'c}},
Journal = {Nonlinearity},
Year = {1998},
Pages = {319--339},
Volume = {11},
DOI = {10.1088/0951-7715/11/2/008}
}
@Article{haller2000,
Title = {Lagrangian coherent structures and mixing in two-dimensional turbulence},
Author = {Haller, G. and Yuan, G.},
Journal = {Physica D},
Year = {2000},
Pages = {352--370},
Volume = {147},
Abstract = {We introduce a Lagrangian definition for the boundaries of coherent
structures in two-dimensional turbulence. The boundaries are defined
as material lines that are linearly stable or unstable for longer
times than any of their neighbors. Such material lines are responsible
for stretching and folding in the mixing of passive tracers. We derive
an analytic criterion that can be used to extract coherent structures
with high precision from numerical or experimental data sets. The
criterion provides a rigorous link between the Lagrangian concept
of hyperbolicity, the {Okubo?Weiss} criterion, and vortex boundaries.
We apply the results to simulations of two-dimensional barotropic
turbulence.},
DOI = {10.1016/S0167-2789(00)00142-1}
}
@Article{HaKiWa95,
author = {J. Hamilton and J. Kim and F. Waleffe},
title = {Regeneration mechanisms of near-wall turbulence structures},
journal = {J. Fluid Mech.},
year = {1995},
volume = {287},
pages = {317--348},
doi = {10.1017/s0022112095000978},
}
@Article{HanBer80,
Title = {Quantization of linear maps on a torus -- {Fresnel} diffraction by a periodic grating},
Author = {J. H. Hannay and M. V. Berry},
Journal = {Physica D},
Year = {1980},
Pages = {267--290},
Volume = {1},
DOI = {10.1016/0167-2789(80)90026-3}
}
@Article{Hansen92b,
Title = {Pruning of orbits in four-disk and hyperbola billiards},
Author = {Hansen, K. T.},
Journal = {Chaos},
Year = {1992},
Pages = {71--75},
Volume = {2},
DOI = {10.1063/1.165900}
}
@Article{hansen92,
Title = {Remarks on the symbolic dynamics for the {H\'enon} map},
Author = {Hansen, K. T.},
Journal = {Phys. Lett. A},
Year = {1992},
Pages = {100--104},
Volume = {165},
DOI = {10.1016/0375-9601(92)90083-X}
}
@Phdthesis{hansen,
Title = {Symbolic Dynamics in Chaotic systems},
Author = {Hansen, K. T.},
School = {Univ. of Oslo},
Year = {1993},
Address = {Oslo, Norway},
URL = {http://ChaosBook.org/projects/KTHansen/thesis}
}
@Article{Hansen92-1,
Title = {Symbolic dynamics. {I. Finite} dispersive billiards},
Author = {Hansen, K. T.},
Journal = {Nonlinearity},
Year = {1993},
Pages = {753--769},
Volume = {6},
DOI = {10.1088/0951-7715/6/5/005}
}
@Article{Hansen92-2,
Title = {Symbolic dynamics. {II. Bifurcations} in billiards and smooth potentials},
Author = {Hansen, K. T.},
Journal = {Nonlinearity},
Year = {1993},
Pages = {771--778},
Volume = {6},
DOI = {10.1088/0951-7715/6/5/006}
}
@Article{Hansen95,
author = {Hansen, K. T.},
title = {Alternative method to find orbits in chaotic systems},
journal = {Phys. Rev. E},
year = {1995},
volume = {52},
pages = {2388--2391},
doi = {10.1103/PhysRevE.52.2388},
}
@Misc{stadium95,
author = {Hansen, K. T. and Cvitanovi{\'c}, P.},
title = {Symbolic dynamics and {Markov} partitions for the stadium billiard},
year = {1995},
note = {{\em J. Stat. Phys.}, accepted 1996, revised version still not resubmitted},
url = {http://arXiv.org/abs/chao-dyn/9502005},
}
@Article{hansen1d,
Title = {Bifurcation structures in maps of {H\'enon} type},
Author = {Hansen, K. T. and Cvitanovi{\'c}, P.},
Journal = {Nonlinearity},
Year = {1998},
Pages = {1233--1261},
Volume = {11},
DOI = {10.1088/0951-7715/11/5/004}
}
@Book{hao89,
title = {Elementary Symbolic Dynamics and Chaos in Dissipative Systems},
publisher = {World Scientific},
year = {1989},
author = {B.-L. Hao},
address = {Singapore},
doi = {10.1142/0674},
}
@Book{hao90b,
title = {Chaos {II}},
publisher = {World Scientific},
year = {1990},
author = {B.-L. Hao},
address = {Singapore},
doi = {10.1142/1001},
}
@Book{hao98,
title = {Applied Symbolic Dynamics and Chaos},
publisher = {World Scientific},
year = {1998},
author = {B.-L. Hao and W.-M. Zheng},
address = {Singapore},
doi = {10.1142/3830},
}
@Article{vHaFrLuPr00,
Title = {Transient chaotic mixing during a baroclinic life cycle},
Author = {J. von Hardenberg and K. Fraedrich and F. Lunkeit and A. Provenzale},
Journal = {Chaos},
Year = {2000},
Pages = {122--134},
Volume = {10},
DOI = {10.1063/1.166491}
}
@Book{Harrison70,
Title = {Solid State Theory},
Author = {Harrison, W. A.},
Publisher = {Dover},
Year = {1980},
Address = {New York}
}
@Article{Hart79,
Title = {Finite amplitude baroclinic instability},
Author = {Hart, J. E.},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1979},
Pages = {147--172},
Volume = {11},
DOI = {10.1146/annurev.fl.11.010179.001051}
}
@Book{Harter93,
title = {Principles of Symmetry, Dynamics, and Spectroscopy},
publisher = {Wiley},
year = {1993},
author = {Harter, W. G.},
address = {New York},
doi = {10.1063/1.2808676},
}
@Book{hartmanb,
title = {Ordinary Differential Equations},
publisher = {Wiley},
year = {1964},
author = {P. Hartman},
address = {New York},
doi = {10.1137/1.9780898719222},
}
@Article{Hasha05,
Title = {A search for baroclinic structures},
Author = {A. E. Hasha},
Journal = {Proceed. 2005 WHOI Summer. Geophysical Fluid Dynamics Program},
Year = {2005}
}
@Article{Hashimoto89,
Title = {Zeta functions of finite graphs and representations of p-adic groups},
Author = {Hashimoto, K.},
Journal = {Adv. Stud. Pure Math.},
Year = {1989},
Pages = {211--280},
Volume = {15},
DOI = {10.1016/B978-0-12-330580-0.50015-X}
}
@Inbook{HaCho10,
pages = {1--8},
title = {Connection vector fields and optimized coordinates for swimming systems at low and high {Reynolds} numbers},
publisher = {ASME},
year = {2010},
author = {Hatton, R. L. and Choset, H.},
address = {New York},
booktitle = {ASME 2010 Dynamic Systems and Control Conference},
doi = {10.1115/dscc2010-4003},
}
@Article{MvH98,
author = {van Hecke, M.},
title = {Building blocks of spatiotemporal intermittency},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {80},
pages = {1896--1899},
doi = {10.1103/physrevlett.80.1896},
}
@Article{Mcoh03,
author = {van Hecke, M.},
title = {Coherent and incoherent structures in systems described by the 1{D CGLE}: {Experiments} and identification},
journal = {Physica D},
year = {2003},
volume = {174},
pages = {134--151},
doi = {10.1016/s0167-2789(02)00687-5},
}
@Incollection{ampatt,
author = {van Hecke, M. and P. C. Hohenberg and van Saarloos, W.},
title = {Amplitude equations for pattern forming systems},
booktitle = {Fundamental Problems in Statistical Mechanics, {VIII}},
publisher = {Elsevier},
year = {1994},
editor = {H. van Beijeren and M. H. Ernst},
pages = {245--278},
address = {Amsterdam},
doi = {10.1016/b978-0-444-81591-0.50014-6},
}
@Article{MvHhole01,
Title = {Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex {Ginzburg-Landau} equation},
Author = {van Hecke, M. and M. Howard},
Journal = {Phys. Rev. Lett.},
Year = {2001},
Pages = {2018},
Volume = {86},
Abtract = {Ordered hole-defect dynamics happens when an unstable hole invade a plane wave state and periodically nucleates defects from which new holes are born. The interaction between the holes and a self-disordered background are essential for the occurrence of spatiotemporal chaos in hole-defect states.},
DOI = {10.1103/physrevlett.86.2018}
}
@Article{HeiZha07,
Title = {Nonchaotic and chaotic behavior in three-dimensional quadratic systems: {Five}-one conservative cases},
Author = {J. Heidel and F. Zhang},
Journal = {Int. J. Bifur. Chaos},
Year = {2007},
Pages = {2049--2072},
Volume = {17},
DOI = {10.1142/S021812740701821X}
}
@Article{Heinzl96,
author = {Heinzl, T.},
title = {{Hamiltonian} approach to the {Gribov} problem},
journal = {Nucl. Phys. Proc. Suppl.},
year = {1997},
volume = {54A},
pages = {194--197},
doi = {10.1016/s0920-5632(97)00039-x},
}
@Article{HeLa96,
Title = {A scaling theory for horizontally homogeneous, baroclinically unstable flow on a {Beta} plane},
Author = {Held, I. M. and Larichev, V. D.},
Journal = {J. Atmos. Sci.},
Year = {1996},
Pages = {946--952},
Volume = {53},
DOI = {10.1175/1520-0469(1996)053<0946:ASTFHH>2.0.CO;2}
}
@Article{HePaPi85,
Title = {Stationary external {Rossby} waves in vertical shear},
Author = {Held, I. M. and Panetta, R. L. and Pierrehumbert, R. T.},
Journal = {J. Atmos. Sci.},
Year = {1985},
Pages = {865--883},
Volume = {42},
DOI = {10.1175/1520-0469(1985)042<0865:SERWIV>2.0.CO;2}
}
@Article{HePiPa86,
Title = {Dissipative destabilization of external {Rossby} waves},
Author = {Held, I. M. and Pierrehumbert, R. T. and Panetta, R. L.},
Journal = {J. Atmos. Sci.},
Year = {1986},
Pages = {388--396},
Volume = {43},
DOI = {10.1175/1520-0469(1986)043<0388:DDOERW>2.0.CO;2}
}
@Incollection{Hell79,
author = {R. H. G. Helleman and T. Bountis},
title = {Periodic solutions of arbitrary period, variational methods},
booktitle = {{Stochastic Behavior in Classical and Quantum Hamiltonian Systems}},
publisher = {Springer},
year = {1979},
editor = {Casati, G. and Ford, J.},
pages = {353--375},
address = {Berlin},
doi = {10.1007/BFb0021758},
isbn = {978-3-540-09120-2},
}
@Article{HenCviLip14,
author = {J. M. Heninger and D. Lippolis and P. Cvitanovi\'c},
title = {Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system},
journal = {Phys. Rev. E},
year = {2015},
volume = {92},
pages = {062922},
doi = {10.1103/PhysRevE.92.062922},
}
@Article{HenLipCvi15,
author = {J. M. Heninger and D. Lippolis and P. Cvitanovi\'c},
title = {Perturbation theory for the {Fokker-Planck} operator in chaos},
journal = {Commun. Nonlinear Sci. Numer. Simul.},
year = {2018},
volume = {55},
pages = {16--28},
doi = {10.1016/j.cnsns.2017.06.025},
}
@Article{lattref,
author = {B. I. Henry and S. D. Watt and S. L. Wearne},
title = {A lattice refinement scheme for finding periodic orbits},
journal = {Anziam J.},
year = {2000},
volume = {42},
pages = {C735--C751},
doi = {10.21914/anziamj.v42i0.619},
}
@Article{HerGot10,
author = {S. Hermann and G. A. Gottwald},
title = {The large core limit of spiral waves in excitable media: {A} numerical epproach},
journal = {SIAM J. Appl. Dyn. Sys.},
year = {2010},
volume = {9},
pages = {536--567},
doi = {10.1137/090780055},
}
@Article{HeRuSch08,
author = {Hertsch, A. and Rudolph, G. and Schmidt, M.},
title = {{Gauge Orbit Types for Theories with Classical Compact Gauge Group O(n), SO(n) or Sp(n)}},
journal = {Ann. Henri Poincare},
year = {2011},
volume = {12},
pages = {351--395},
doi = {10.1007/s00023-011-0081-8},
}
@Article{HeMuAlBrHa07,
author = {Heusler, S. and M\"uller, S. and Altland, A. and Braun, P. and Haake, F.},
title = {Periodic-orbit theory of level correlations},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {98},
pages = {044103},
doi = {10.1103/physrevlett.98.044103},
}
@Article{HHKR50yChaos,
Title = {Fifty years of chaos: {Applied} and theoretical},
Author = {T. Hikihara and P. Holmes and T. Kambe and G. Rega},
Journal = {Chaos},
Year = {2012},
Pages = {047501},
Volume = {22},
DOI = {10.1063/1.4769035}
}
@Article{Hilbert93,
Title = {{\"U}ber die vollen {Invariantensysteme}},
Author = {Hilbert, D.},
Journal = {Math. Ann.},
Year = {1893},
Pages = {313--373},
Volume = {42},
DOI = {10.1007/BF01444162}
}
@Book{hille,
Title = {Ordinary Differential Equations in the Complex Domain},
Author = {E. Hille},
Publisher = {Dover},
Year = {1997},
Address = {New York}
}
@Incollection{hindmarsh1983,
Title = {{ODEPACK}, a systematized collection of {ODE} solvers},
Author = {Hindmarsh, A. C.},
Booktitle = {{Scientific Computing}},
Publisher = {North-Holland},
Year = {1983},
Address = {Amsterdam},
Editor = {Stepleman, R. S.},
Pages = {55--64},
Volume = {1},
URL = {https://computation.llnl.gov/casc/nsde/pubs/u88007.pdf}
}
@Article{hislop89,
author = {P. D. Hislop and J. D. Crawford},
title = {Application of spectral deformation to the {Vlasov--Poisson} system. {II. Mathematical} results},
journal = {J. Math. Phys.},
year = {1989},
volume = {30},
pages = {2819--2837},
doi = {10.1063/1.528465},
}
@Article{Hochbruck05,
Title = {Explicit Exponential {Runge--Kutta} Methods for Semilinear Parabolic Problems},
Author = {Hochbruck, M. and Ostermann, A.},
Journal = {SIAM J. Numer. Anal.},
Year = {2005},
Pages = {1069--1090},
Volume = {43},
DOI = {10.1137/040611434}
}
@Article{HoOs10,
Title = {Exponential integrators},
Author = {Hochbruck, M. and Ostermann, A.},
Journal = {Acta Numerica},
Year = {2010},
Pages = {209--286},
Volume = {19},
DOI = {10.1017/S0962492910000048}
}
@Article{HocMey10,
Title = {A characterization of the entropies of multidimensional shifts of finite type},
Author = {Hochman, M. and Meyerovitch, T.},
Journal = {Ann. Math.},
Year = {2010},
Pages = {2011--2038},
Volume = {171},
DOI = {10.4007/annals.2010.171.2011}
}
@Article{science04,
Title = {Experimental observation of nonlinear traveling waves in turbulent pipe flow},
Author = {B. Hof and C. W. H. van Doorne and J. Westerweel and F. T. M. Nieuwstadt and H. Faisst and B. Eckhardt and H. Wedin and R. R. Kerswell and F. Waleffe},
Journal = {Science},
Year = {2004},
Pages = {1594--1598},
Volume = {305},
DOI = {10.1126/science.1100393}
}
@Article{HJM03,
author = {B. Hof and A. Juel and T. Mullin},
title = {Scaling of the turbulence transition threshold in a pipe},
journal = {Phys. Rev. Lett.},
year = {2003},
volume = {91},
pages = {244502},
doi = {10.1103/physrevlett.91.244502},
}
@Article{hof2006flt,
author = {Hof, B. and Westerweel, J. and Schneider, T. M. and Eckhardt, B.},
title = {Finite lifetime of turbulence in shear flows},
journal = {Nature},
year = {2006},
volume = {443},
number = {7107},
pages = {59--62},
doi = {10.1038/nature05089},
}
@Article{HoHoPo87,
Title = {Resolution of {Loschmidt's} paradox: The origin of irreversible behavior in reversible atomistic dynamics},
Author = {Holian, B. L. and Hoover, W. G. and Posch, H. A.},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {10--13},
Volume = {59},
DOI = {10.1103/PhysRevLett.59.10}
}
@Article{Holland94,
Title = {Finite-difference time-domain ({FDTD}) analysis of magnetic diffusion},
Author = {Holland, R.},
Journal = {IEEE Trans. Electromagn. Compat.},
Year = {1994},
Pages = {32--39},
Volume = {36},
DOI = {10.1109/15.265477}
}
@Article{HMR98,
Title = {The {Euler-Poincar\'e} equations and semidirect products with applications to continuum theories},
Author = {Holm, D. D. and J. E. Marsden and Ratiu, T. S.},
Journal = {Adv. Math.},
Year = {1998},
Pages = {1--81},
Volume = {137},
DOI = {10.1006/aima.1998.1721}
}
@Article{HoWi05,
Title = {Baroclinic instabilities of the two-layer quasigeostrophic {Alpha} model},
Author = {Holm, D. D. and Wingate, B. A.},
Journal = {J. Phys. Oceanogr.},
Year = {2005},
Pages = {1287--1296},
Volume = {35},
DOI = {10.1175/JPO2741.1}
}
@Article{Holmes05,
author = {Holmes, P.},
title = {Ninety plus thirty years of nonlinear dynamics: {Less} is more and more is different},
journal = {Int. J. Bifur. Chaos},
year = {2005},
volume = {15},
pages = {2703--2716},
doi = {10.1142/s0218127405013678},
}
@Article{KoHoGu06,
Title = {The dynamics of legged locomotion: {Models}, analyses, and challenges},
Author = {P. Holmes and R. J. Full and D. Koditschek and J. Guckenheimer},
Journal = {SIAM Rev.},
Year = {2006},
Pages = {207--304},
Volume = {48},
DOI = {10.1137/S0036144504445133}
}
@Book{Holmes96,
title = {{Turbulence, Coherent Structures, Dynamical Systems and Symmetry}},
publisher = {Cambridge Univ. Press},
year = {1996},
author = {P. Holmes and J. L. Lumley and G. Berkooz},
address = {Cambridge},
isbn = {9781107008250},
doi = {10.1017/cbo9780511622700},
}
@Article{expholm88,
author = {P. Holmes and J. Marsden and J. Scheurle},
title = {Exponentially small splittings of separatrices with applications to {KAM} theory and degenerate bifurcations},
journal = {Contemp. Math.},
year = {1988},
volume = {81},
pages = {213--244},
doi = {10.1090/conm/081/986267},
}
@Book{Holton79,
Title = {An introduction to dynamic meteorology},
Author = { Holton, J. R. },
Publisher = {Academic},
Year = { 1979 },
Address = {New York}
}
@Article{homann-2007,
author = {Homann, H. and Dreher, J. and Grauer, R.},
title = {Impact of the floating-point precision and interpolation scheme on the results of {DNS} of turbulence by pseudo-spectral codes},
journal = {Comput. Phys. Commun.},
year = {2007},
volume = {177},
pages = {560--565},
doi = {10.1016/j.cpc.2007.05.019},
}
@Article{cpmani,
author = {A. J. Homburg and H. M. Osinga and G. Vegter},
title = {On the computation of invariant manifolds of fixed points},
journal = {Z. Angew. Math. Phys.},
year = {1995},
volume = {46},
pages = {171--187},
doi = {10.1007/bf00944751},
}
@Article{hoopks85,
author = {A. P. Hooper and R. Grimshaw},
title = {Nonlinear instability at the interface between two viscous fluids},
journal = {Phys. Fluids},
year = {1985},
volume = {28},
pages = {37--45},
doi = {10.1063/1.865160},
}
@Article{kshooper88,
Title = {Travelling wave solutions of the {Kuramoto-Sivashinsky} equation},
Author = {A. P. Hooper and R. Grimshaw},
Journal = {Wave Motion},
Year = {1988},
Pages = {405--420},
Volume = {10},
DOI = {10.1016/0165-2125(88)90045-5}
}
@Misc{HooAok16,
Title = {Order and chaos in the one-dimensional {$\phi^4$} model : {N}-dependence and the {Second Law of Thermodynamics}},
Author = {Hoover, W. G. and Aoki, K.},
Year = {2016},
URL = {http://arxiv.org/abs/1605.07721}
}
@Article{HooHoo12,
author = {Hoover, W. G. and Hoover, C. G.},
title = {Local {Gram--Schmidt} and {covariant {Lyapunov} vectors} and exponents for three harmonic oscillator problems},
journal = {Commun. Nonlinear Sci. Numer. Simul.},
year = {2012},
volume = {17},
pages = {1043--1054},
doi = {10.1016/j.cnsns.2011.06.025},
}
@Article{HooHoo13,
author = {Hoover, W. G. and Hoover, C. G.},
title = {Why the instantaneous values of the ''{covariant}'' {Lyapunov} exponents depend upon the chosen state-space norm},
journal = {Computational Methods in Science and Technology},
year = {2014},
volume = {20},
pages = {5-8},
doi = {10.12921/cmst.2014.20.01.5-8},
}
@Article{HPAK02,
Title = {Remarks on non-{Hamiltonian} statistical mechanics: {Lyapunov} exponents and phase-space dimensionality loss},
Author = {W. G. Hoover and H. A. Posch and K. Aoki and D. Kusnezov},
Journal = {Europhys. Lett.},
Year = {2002},
Pages = {337},
Volume = {60},
DOI = {10.1209/epl/i2002-00269-3}
}
@Article{HooPoFoDeZh02,
Title = {{Lyapunov} modes of two-dimensional many-body systems; soft disks, hard disks, and rotors},
Author = {Hoover, W. G. and Posch, H. A. and Forster, C. and Dellago, C. and Zhou, M.},
Journal = {J. Stat. Phys.},
Year = {2002},
Pages = {765--776},
Volume = {109},
DOI = {10.1023/A:1020474901341}
}
@Article{hopf42,
Title = {{Abzweigung einer periodischen L\"{o}sung von einer station\"{a}ren L\"{o}sung eines Differentialsystems}},
Author = {Hopf, E.},
Journal = {Ber. S{\"a}chs. Akad. Wiss. Leipzig, Math.-Phys. Kl.},
Year = {1942},
Pages = {3--22},
Volume = {94}
}
@Article{hopf48,
author = {E. Hopf},
title = {A mathematical example displaying features of turbulence},
journal = {Commun. Pure Appl. Math.},
year = {1948},
volume = {1},
pages = {303--322},
doi = {10.1002/cpa.3160010401},
}
@Article{hopf50,
author = {E. Hopf},
title = {The partial differential equation {$u_t + uu_x = u_{xx}$}},
journal = {Commun. Pure Appl. Math.},
year = {1950},
volume = {3},
pages = {201--230},
doi = {10.1002/cpa.3160030302},
}
@Article{hopf52,
author = {E. Hopf},
title = {Statistical hydromechanics and functional calculus},
journal = {J. Rat. Mech. Anal.},
year = {1952},
volume = {1},
pages = {87--123},
doi = {10.1512/iumj.1952.1.51004},
}
@Book{HoJo90,
title = {Matrix Analysis},
publisher = {Cambridge Univ. Press},
year = {1990},
author = {Horn, R. A. and Johnson, C. R.},
address = {Cambridge},
doi = {10.1017/cbo9781139020411},
}
@Article{Horton07,
Title = {Ihara zeta functions of digraphs},
Author = {M. D. Horton},
Journal = {Linear Algebra Appl.},
Year = {2007},
Pages = {130--142},
Volume = {425},
DOI = {10.1016/j.laa.2007.03.013}
}
@Book{hoyll06,
title = {{Pattern Formation: An Introduction to Methods}},
publisher = {Cambridge Univ. Press},
year = {2006},
author = {R. Hoyle},
address = {Cambridge},
isbn = {9780521817509},
doi = {10.1017/cbo9780511616051},
}
@Article{Hsu76,
Title = {Existence of periodic solutions for the {Belousov-Zaikin-Zhabotinskii} reaction by a theorem of {Hopf}},
Author = {I.-D. Hsu},
Journal = {J. Diff. Equ.},
Year = {1976},
Pages = {399--403},
Volume = {20},
DOI = {10.1016/0022-0396(76)90116-9}
}
@Article{HJLW01,
Title = {General initial value form of the semiclassical propagator},
Author = {Hu, B. and Jie, Q. and Li, B. and Wang, S.},
Journal = {Phys. Rev. A},
Year = {2001},
Pages = {044102},
Volume = {63},
DOI = {10.1103/PhysRevA.63.044102}
}
@Article{HuLiZh00,
Title = {Heat conduction in one-dimensional nonintegrable systems},
Author = {Hu, B. and Li, B. and Zhao, H.},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {3828--3831},
Volume = {61},
DOI = {10.1103/PhysRevE.61.3828}
}
@Article{HuLin11,
Title = {Nonemptiness problems of plane square tiling with two colors},
Author = {Hu, W.-G. and Lin, S.-S.},
Journal = {Proc. Amer. Math. Soc.},
Year = {2011},
Pages = {1045--1059},
Volume = {139},
DOI = {10.1090/S0002-9939-2010-10518-X}
}
@Article{HuLin16,
Title = {On spatial entropy of multi-dimensional symbolic dynamical systems},
Author = {W.-G. Hu and S.-S. Lin},
Journal = {Discrete Continuous Dyn. Syst. Ser. A},
Year = {2016},
Pages = {3705--3717},
Volume = {36},
DOI = {10.3934/dcds.2016.36.3705}
}
@Article{HuKoYa11,
author = {Huber, G. and Koehler, S. A. and Yang, J.},
title = {Micro-swimmers with hydrodynamic interactions},
journal = {Math. Computer Modelling},
year = {2011},
volume = {53},
pages = {1518--1526},
doi = {10.1016/j.mcm.2010.04.002},
}
@Article{Hult07,
Title = {A fourth-order {Runge-Kutta} in the interaction picture method for simulating supercontinuum generation in optical fibers},
Author = {J. Hult},
Journal = {J. Lightwave Technol.},
Year = {2007},
Pages = {3770--3775},
Volume = {25},
DOI = {10.1109/JLT.2007.909373}
}
@Article{Hunt96,
author = {B. R. Hunt},
title = {Maximum local {Lyapunov} dimension bounds the box dimension of chaotic attractors},
journal = {Nonlinearity},
year = {1996},
volume = {9},
pages = {845--852},
doi = {10.1088/0951-7715/9/4/001},
}
@Article{optp1,
author = {B. R. Hunt and E. Ott},
title = {Optimal periodic orbits of chaotic systems},
journal = {Phys. Rev. Lett.},
year = {1996},
volume = {76},
pages = {2254},
doi = {10.1103/physrevlett.76.2254},
}
@Article{HunTod03,
Title = {On the {Arnold} cat map and periodic boundary conditions for planar elongational flow},
Author = {T. A. Hunt and B. D. Todd},
Journal = {Molec. Phys},
Year = {2003},
Pages = {3445--3454},
Volume = {101},
DOI = {10.1080/00268970310001648726}
}
@Article{Hunter2007,
author = {Hunter, J. D.},
title = {Matplotlib: A {2D} graphics environment},
journal = {Comput. Sci. Eng.},
year = {2007},
volume = {9},
pages = {90--95},
abstract = {Matplotlib is a 2D graphics package used for Python
for application development, interactive scripting, and
publication-quality image generation across user
interfaces and operating systems.},
doi = {10.1109/mcse.2007.55},
}
@Article{HurGre60,
Title = {New solution of the {Ising} problem for a rectangular lattice},
Author = {Hurst, C. A. and Green, H. S.},
Journal = {J. Chem. Phys.},
Year = {1960},
Pages = {1059--1062},
Volume = {33},
DOI = {10.1063/1.1731333}
}
@Book{Husemoller1993,
Title = {Fibre Bundles},
Author = {D. Husemoller},
Publisher = {Springer},
Year = {1993},
Address = {New York}
}
@Article{Hutchinson81,
Title = {Fractals and self-similarity},
Author = {J. Hutchinson},
Journal = {Indiana Univ. Math. J.},
Year = {1981},
Pages = {713--747},
Volume = {30},
DOI = {10.1512/iumj.1981.30.30055},
URL = {http://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf}
}
@Book{Huyg1673,
Title = {{L'Horloge \`a Pendule}},
Author = {C. Huygens},
Publisher = {Swets \& Zeitlinger},
Year = {1673},
Address = {Amsterdam}
}
@Article{HydMan11,
Title = {Extensions of {Noether's Second Theorem}: from continuous to discrete systems},
Author = {Hydon, P. E. and Mansfield, E. L.},
Journal = {Proc. R. Soc. London A},
Year = {2011},
Pages = {3206--3221},
Volume = {467},
DOI = {10.1098/rspa.2011.0158},
ISSN = {1364-5021}
}
@Article{HNks86,
Title = {The {Kuramoto-Sivashinsky} equation: a bridge between {PDE}'s and dynamical systems},
Author = {J. M. Hyman and B. Nicolaenko},
Journal = {Physica D},
Year = {1986},
Pages = {113--126},
Volume = {18},
DOI = {10.1016/0167-2789(86)90166-1}
}
@Article{HNZks86,
author = {J. M. Hyman and B. Nicolaenko and S. Zaleski},
title = {Order and complexity in the {Kuramoto-Sivashinsky} model of weakly turbulent interfaces},
journal = {Physica D},
year = {1986},
volume = {23},
pages = {265--292},
abstract = {The properties of the KSe is discussed in even larger domains. Still
the dynamical behavior is dominated by the skeleton of low dimensional
vector fields. More complex dynamics happens in large domain where
intermittency is accurately identified only by high-precision numerical
method. The presence of strange fixed points overrun the cellular
fixed points in large scales which generates complex spatial structure
to the solutions. The Large scale statistical behavior of the system
is computed.},
doi = {10.1016/0167-2789(86)90136-3},
}
@Article{Ihara66,
Title = {On discrete subgroups of the two by two projective linear group over p-adic fields},
Author = {Y. Ihara},
Journal = {J. Math. Society of Japan},
Year = {1966},
Number = {3},
Pages = {219--235},
Volume = {18},
DOI = {10.2969/jmsj/01830219}
}
@Article{IkeSak13,
author = {Ikegami, T. and Sakurai, T.},
title = {Contour integral eigensolver for non-{Hermitian} systems: {A {Rayleigh}-Ritz}-type approach},
journal = {Taiwanese J. Math.},
year = {2010},
volume = {14},
pages = {825--837},
doi = {10.11650/twjm/1500405869},
}
@Article{Ilyash92,
author = {Il'yashenko, Yu. S.},
title = {Global analysis of the phase portrait for the {Kuramoto-Sivashinsky} equation},
journal = {J. Dynam. Diff. Eq.},
year = {1992},
volume = {4},
pages = {585--615},
doi = {10.1007/bf01048261},
}
@Book{ince,
title = {Ordinary Differential Equations},
publisher = {Dover},
year = {1956},
author = {E. L. Ince},
address = {New York},
}
@Techreport{Inubushi13,
Title = {Covariant {Lyapunov} analysis of {Navier-Stokes} turbulence},
Author = {Inubushi, M.},
Institution = {Kyoto Univ.},
Year = {2013},
Address = {Kyoto},
Number = {RIMS Preprint 1770},
URL = {http://www.kurims.kyoto-u.ac.jp/preprint/}
}
@Article{InKoTaYa12,
Title = {Covariant {Lyapunov} analysis of chaotic {Kolmogorov} flows},
Author = {Inubushi, M. and Kobayashi, M. U. and Takehiro, S.-i. and Yamada, M.},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {016331},
Volume = {85},
DOI = {10.1103/PhysRevE.85.016331}
}
@Article{InKoTaYa12a,
author = {Inubushi, M. and Kobayashi, M. U. and Takehiro, S.-i. and Yamada, M.},
title = {Covariant {Lyapunov} analysis of chaotic {Kolmogorov} flows and time-correlation function},
journal = {Procedia IUTAM},
year = {2012},
volume = {5},
pages = {244--248},
note = {IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical},
doi = {10.1016/j.piutam.2012.06.033},
}
@Book{IooAde98,
title = {{Topics in Bifurcation Theory and Applications}},
publisher = {World Scientific},
year = {1998},
author = {Iooss, G. and Adelmeyer, M.},
isbn = {978-981-02-3728-8},
address = {Singapore},
doi = {10.1142/1690},
}
@Book{isham99,
title = {Modern Differential Geometry for Physicists},
publisher = {World Scientific},
year = {1999},
author = {C. J. Isham},
address = {Singapore},
doi = {10.1142/3867},
}
@Article{Ish97,
Title = {Towards a kneading theory for {Lozi mappings}. {I}. {A} solution of the pruning front conjecture and the first tangency problem},
Author = {Ishii, Y.},
Journal = {Nonlinearity},
Year = {1997},
Pages = {731--747},
Volume = {10},
DOI = {10.1088/0951-7715/10/3/008}
}
@Article{Ishii97a,
Title = {Towards a kneading theory for {Lozi mappings}. {II}: {Monotonicity} of the topological entropy and {Hausdorff} dimension of attractors},
Author = {Ishii, Y.},
Journal = {Commun. Math. Phys.},
Year = {1997},
Pages = {375--394},
Volume = {190},
DOI = {10.1007/s002200050245}
}
@Article{IshSa98,
Title = {{Monotonicity of the {Lozi} family near the tent-maps}},
Author = {Ishii, Y. and Sands, D.},
Journal = {Commun. Math. Phys.},
Year = {1998},
Pages = {397--406},
Volume = {198},
DOI = {10.1007/s002200050482}
}
@Article{Ishimura02,
Title = {Remarks on third-order {ODEs} relevant to the {Kuramoto-Sivashinsky} equation},
Author = {N. Ishimura},
Journal = {J. Diff. Eqn.},
Year = {2002},
Pages = {466--477},
Volume = {178},
DOI = {10.1006/jdeq.2001.4018}
}
@Article{IshNak00,
Title = {Nonexistence of monotonic solutions of some third-order ode relevant to the {Kuramoto-Sivashinsky} equation},
Author = {Ishimura, N. and Nakamura, M.},
Journal = {Taiwanese J. Math.},
Year = {2000},
Pages = {621--625},
Volume = {4},
URL = {http://journal.tms.org.tw/index.php/TJM/article/view/1296}
}
@Article{Isola90,
Title = {{$\zeta$}-functions and distribution of periodic orbits of toral automorphisms},
Author = {S. Isola},
Journal = {Europhys. Lett.},
Year = {1990},
Pages = {517--522},
Volume = {11},
DOI = {10.1209/0295-5075/11/6/006}
}
@Article{IPRT90,
Title = {{Lyapunov} spectra of coupled map lattices},
Author = {S. Isola and A. Politi and S. Ruffo and A. Torcini},
Journal = {Phys. Lett. A},
Year = {1990},
Pages = {365--368},
Volume = {143},
DOI = {10.1016/0375-9601(90)90373-V}
}
@Article{IT01,
author = {T. Itano and S. Toh},
title = {The dynamics of bursting process in wall turbulence},
journal = {J. Phys. Soc. Japan},
year = {2001},
volume = {70},
pages = {703--716},
doi = {10.1143/jpsj.70.703},
}
@Article{itoh82,
Title = {Analysis of the phase unwrapping algorithm},
Author = {K. Itoh},
Journal = {Appl. Phys.},
Year = {1982},
Pages = {2470},
Volume = {21},
DOI = {10.1364/AO.21.002470}
}
@Article{SeoSan12,
Title = {New developments in classical chaotic scattering},
Author = {J. M. Seoane, M. A. F. Sanju\'an},
Journal = {Rep. Prog. Phys.},
Year = {2013},
Pages = {016001},
Volume = {76},
DOI = {10.1088/0034-4885/76/1/016001}
}
@Article{Jacobi1841,
Title = {De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum},
Author = {Jacobi, C. G. J.},
Journal = {J. Reine Angew. Math. ({Crelle})},
Year = {1841},
Pages = {439--452},
Volume = {22}
}
@Article{Jac46,
Title = {{\"U}ber ein leichtes Verfahren die in der Theorie der S{\"a}cul{\"a}rst{\"o}rungen vorkommenden Gleichungen numerisch aufzul{\"o}sen},
Author = {Jacobi, C. G. J.},
Journal = {J. Reine Angew. Math. ({Crelle})},
Year = {1846},
Pages = {51--94},
Volume = {30}
}
@Book{Jacobi1969,
Title = {Collected Works},
Author = {Jacobi, C. G. J.},
Publisher = {Amer. Math. Soc.},
Year = {1969},
Address = {Providence RI}
}
@Article{jaeger_kantz,
Title = {Homoclinic tangencies and non-normal {Jacobians} - {Effects} of noise in nonhyperbolic chaotic systems},
Author = {L. Jaeger and H. Kantz},
Journal = {Physica D},
Year = {1997},
Pages = {79--96},
Volume = {105},
DOI = {10.1016/S0167-2789(97)00247-9}
}
@Article{Jakobson81,
Title = {Absolutely continuous invariant measures for one-parameter families of one-dimensional maps},
Author = {M. V. Jakobson},
Journal = {Commun. Math. Phys.},
Year = {1981},
Pages = {39--88},
Volume = {81},
DOI = {10.1007/BF01941800}
}
@Book{Jammer66,
title = {The Conceptual Development of Quantum Mechanics},
publisher = {McGraw-Hill},
year = {1966},
author = {M. Jammer},
address = {New York},
doi = {10.1063/1.3034186},
}
@Article{JGB86,
author = {P. S. {Jang} and R. L. {Gran} and D. J. {Benney}},
title = {On the origin of streamwise vortices in a turbulent boundary layer},
journal = {J. Fluid Mech.},
year = {1986},
volume = {169},
pages = {109},
doi = {10.1017/s0022112086000551},
}
@Article{eckcgl,
author = {B. Janiaud and A. Pumir and D. Bensimon and V. Croquette and H. Richter and L. Kramer},
title = {The {Eckhaus} instability for travelling waves},
journal = {Physica D},
year = {1992},
volume = {55},
pages = {269--286},
doi = {10.1016/0167-2789(92)90060-z},
}
@Book{Jee11,
Title = {An Introduction to Tensors and Group Theory for Physicists},
Author = {Jeevanjee, N.},
Publisher = {Birkh\"auser},
Year = {2011},
Address = {Boston},
ISBN = {9780817647148}
}
@Book{jeffb,
title = {Methods of Mathematical Physics},
publisher = {Cambridge Univ. Press},
year = {1999},
author = {H. Jeffreys and B. Jeffreys},
address = {Cambridge},
doi = {10.2307/3610518},
}
@Article{jensen84,
author = {M. H. Jensen and P. Bak and T. Bohr},
title = {Transition to chaos by interaction of resonances in dissipative systems},
journal = {Phys. Rev. A},
year = {1984},
volume = {30},
pages = {1960},
doi = {10.1103/PhysRevA.30.1960},
}
@Article{Jiang95,
Title = {Equilibrium states for lattice models of hyperbolic type},
Author = {M. Jiang},
Journal = {Nonlinearity},
Year = {1995},
Number = {5},
Pages = {631},
Volume = {8},
Abstract = {We study the structural stability of coupled map lattice models of hyperbolic type under certain metrics. We prove the existence of equilibrium states for continuous functions on lattice models under the conditions of weak interaction and translation invariance. We also study the uniqueness and ergodic properties of these equilibrium states for Holder continuous functions.},
URL = {http://stacks.iop.org/0951-7715/8/i=5/a=001}
}
@Article{JKSN05,
author = {J. Jimenez and G. Kawahara and M. P. Simens and M. Nagata},
title = {Characterization of near-wall turbulence in terms of equilibrium and `bursting' solutions},
journal = {Phys. Fluids},
year = {2005},
volume = {17},
pages = {015105},
doi = {10.1063/1.1825451},
}
@Misc{JinZwo14,
Title = {A local trace formula for {Anosov} flows},
Author = {Jin, L. and Zworski, M.},
Year = {2014},
URL = {https://math.berkeley.edu/~zworski/tracea.pdf}
}
@Article{kev01ks,
author = {M. E. Johnson and M. S. Jolly and I. G. Kevrekidis},
title = {The {Oseberg} transition: visualization of global bifurcations for the {Kuramoto-Sivashinsky} equation},
journal = {Int. J. Bifur. Chaos},
year = {2001},
volume = {11},
pages = {1--18},
doi = {10.1142/s0218127401001979},
}
@Unpublished{stevenj,
Title = {Topics in applied mathematics},
Author = {Johnson, S. G.},
Note = {MIT course 18.325},
Year = {2005}
}
@Article{johnston04,
author = {H. Johnston and J.-G. Liu},
title = {Accurate, stable and efficient {Navier-Stokes} solvers based on explicit treatment of the pressure term},
journal = {J. Comput. Phys.},
year = {2004},
volume = {199},
pages = {221--259},
doi = {10.1016/j.jcp.2004.02.009},
}
@Article{jolly_evaluating_2000,
author = {M. Jolly and R. Rosa and R. T{\'e}mam},
title = {Evaluating the dimension of an inertial manifold for the {Kuramoto-Sivashinsky} equation},
journal = {Advances in Differential Equations},
year = {2000},
volume = {5},
pages = {31--66},
url = {http://projecteuclid.org/euclid.ade/1356651378},
}
@Article{JRT01,
author = {M. Jolly and R. Rosa and R. T{\'e}mam},
title = {Accurate computations on inertial manifolds},
journal = {{SIAM} J. Sci. Comp.},
year = {2001},
volume = {22},
pages = {2216--2238},
doi = {10.1137/s1064827599351738},
}
@Article{jolly1990,
Title = {Approximate inertial manifolds for the {Kuramoto-Sivashinsky} equation: {Analysis} and computations},
Author = {M. S. Jolly and I. G. Kevrekidis and E. S. Titi},
Journal = {Physica D},
Year = {1990},
Pages = {38--60},
Volume = {44},
DOI = {10.1016/0167-2789(90)90046-R}
}
@Article{JoPro87,
Title = {Strong spatial resonance and travelling waves in {Benard} convection},
Author = {C. A. Jones and M. R. E. Proctor},
Journal = {Phys. Lett. A},
Year = {1987},
Pages = {224--228},
Volume = {121},
DOI = {10.1016/0375-9601(87)90008-9}
}
@Misc{scipy,
Title = {{SciPy}: {Open} source scientific tools for {Python}},
Author = {E. Jones and T. Oliphant and P. Peterson and others},
Year = {2001},
URL = {http://www.scipy.org}
}
@Article{kstroy92,
Title = {Steady solutions of the {Kuramoto-Sivashinsky} equation for small wave speed},
Author = {J. Jones and W. C. Troy and A. D. MacGillivary},
Journal = {J. Diff. Eqn.},
Year = {1992},
Pages = {28--55},
Volume = {96},
DOI = {10.1016/0022-0396(92)90143-B}
}
@Article{JorTaNuOb07,
Title = {Old and new results on strange nonchaotic attractors},
Author = {{\'{A}} Jorba and J. C. Tatjer and C. N{\'{u}\~{n}ez} and R. Obaya},
Journal = {Int. J. Bifur. Chaos},
Year = {2007},
Pages = {3895--3928},
Volume = {17},
DOI = {10.1142/S0218127407019780},
Eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218127407019780}
}
@Book{JoSa,
title = {Classical Dynamics - A Contemporary Approach},
publisher = {Cambridge Univ. Press},
year = {1998},
author = {J. V. Jos\'e and E. J. Salatan},
address = {Cambridge},
doi = {10.1017/cbo9780511803772},
}
@Article{JosSat72,
Title = {Bifurcating time periodic solutions and their stability},
Author = {Joseph, D. D. and Sattinger, D. H.},
Journal = {Arch. Rational Mech. Anal.},
Year = {1972},
Pages = {79--109},
Volume = {45},
DOI = {10.1007/BF00253039}
}
@Article{JT63,
author = {D. D. Joseph and L. N. Tao},
title = {Transverse velocity components in fully developed unsteady flows},
journal = {J. Appl. Mech.},
year = {1963},
volume = {30},
pages = {147},
doi = {10.1115/1.3630068},
}
@Article{JosSan16,
Title = {Exploring chaos and entanglement in the {H{\'e}non-Heiles} system using squeezed coherent states},
Author = {Joseph, S. K. and Sanju{\'a}n, M.A.F.},
Journal = {Int. J. Bifur. Chaos},
Year = {2016},
Volume = {26},
DOI = {10.1142/S0218127416500528}
}
@Article{Just98,
Title = {Analytical approach for piecewise linear coupled map lattices},
Author = {Just, W.},
Journal = {J. Stat. Phys.},
Year = {1998},
Pages = {727--748},
Volume = {90},
DOI = {10.1023/A:1023272819435}
}
@Article{Just01,
Title = {Equilibrium phase transitions in coupled map lattices: {A} pedestrian approach},
Author = {Just, W.},
Journal = {J. Stat. Phys.},
Year = {2001},
Pages = {133--142},
Volume = {105},
DOI = {10.1023/A:1012230010077}
}
@Article{Koenig97,
Title = {Linearization of vector fields on the orbit space of the action of a compact {Lie} group},
Author = {M. K{\oe}nig},
Journal = {Math. Proc. Cambridge Philos. Soc.},
Year = {1997},
Pages = {401--424},
Volume = {121},
DOI = {10.1017/S0305004196001314}
}
@Article{KarTel97,
author = {K\'{a}roly, G. and T\'{e}l, T.},
title = {Chaotic tracer scattering and fractal basin boundaries in a blinking vortex-sink system},
journal = {Phys. Rep.},
year = {1997},
volume = {290},
pages = {125--147},
abstract = {unphysical and the openness of the flow comes from having sinks and
unbounded trajectories},
doi = {10.1016/s0370-1573(97)00063-x},
}
@Article{KacWar52,
Title = {A combinatorial solution of the two-dimensional {Ising} model},
Author = {Kac, M. and Ward, J. C.},
Journal = {Phys. Rev.},
Year = {1952},
Pages = {1332--1337},
Volume = {88},
DOI = {10.1103/PhysRev.88.1332}
}
@Article{KT84,
Title = {Escape rate from strange repellers},
Author = {L. Kadanoff and C. Tang},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1984},
Pages = {1276--1279},
Volume = {81},
DOI = {10.1073/pnas.81.4.1276}
}
@Article{KaLiMe13,
Title = {The signed loop approach to the {Ising} model: {Foundations and critical} point},
Author = {Kager, W. and Lis, M. and Meester, R.},
Journal = {J. Stat. Phys.},
Year = {2013},
Pages = {353--387},
Volume = {152},
DOI = {10.1007/s10955-013-0767-z}
}
@Article{KaiTom80,
Title = {Statistical mechanics of deterministic chaos},
Author = {T. Kai and K. Tomita},
Journal = {Progr. Theor. Phys.},
Year = {1980},
Pages = {1532--1550},
Volume = {64},
DOI = {10.1143/PTP.64.1532}
}
@InProceedings{KaCoCa02,
Title = {Are bred vectors the same as {Lyapunov} vectors?},
Author = {{Kalnay}, E. and {Corazza}, M. and {Cai}, M.},
Booktitle = {EGS XXVII General Assembly, Nice, 21-26 April 2002},
Year = {2002}
}
@Article{KaHaOh14,
Title = {On relations among the entropic chaos degree, the {Kolmogorov-Sinai} entropy and the {Lyapunov} exponent},
Author = {Kamizawa, T. and Hara, T. and Ohya, M.},
Journal = {J. Math. Phys.},
Year = {2014},
Volume = {55},
DOI = {10.1063/1.4868217}
}
@Article{Kaneko83,
Title = {Transition from torus to chaos accompanied by frequency lockings with symmetry breaking: {In} connection with the coupled-logistic map},
Author = {Kaneko, K.},
Journal = {Prog. Theor. Phys.},
Year = {1983},
Pages = {1427--1442},
Volume = {69},
DOI = {10.1143/PTP.69.1427},
Eprint = {http://ptp.oxfordjournals.org/content/69/5/1427.full.pdf+html}
}
@Article{Kaneko84,
Title = {Period-doubling of kink-antikink patterns, quasiperiodicity in antiferro-like structures and spatial intermittency in coupled logistic lattice: {Towards} a prelude of a ``field theory of chaos''},
Author = {Kaneko, K.},
Journal = {Prog. Theor. Phys.},
Year = {1984},
Pages = {480--486},
Volume = {72},
DOI = {10.1143/PTP.72.480}
}
@Article{kantzg,
Title = {Repellers, semi-attractors, and long-lived chaotic transients},
Author = {H. Kantz and P. Grassberger},
Journal = {Physica D},
Year = {1985},
Pages = {75--86},
Volume = {17},
DOI = {10.1016/0167-2789(85)90135-6}
}
@Article{KanGra87,
Title = {Chaos in low-dimensional {Hamiltonian} maps},
Author = {H. Kantz and P. Grassberger},
Journal = {Phys. Let. A},
Year = {1987},
Pages = {437--443},
Volume = {123},
DOI = {10.1016/0375-9601(87)90342-2}
}
@Article{KaGrPrLaSi02,
author = {Kantz, H. and Grebogi, C. and Prasad, A. and Lai, Y.-C. and Sinde, E.},
title = {Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors},
journal = {Phys. Rev. E},
year = {2002},
volume = {65},
pages = {026209},
doi = {10.1103/physreve.65.026209},
}
@Article{KaRaYa13,
author = {H. Kantz and G. Radons and H.-l. Yang},
title = {The problem of spurious {Lyapunov} exponents in time series analysis and its solution by covariant {Lyapunov} vectors},
journal = {J. Phys. A},
year = {2013},
volume = {46},
pages = {254009},
doi = {10.1088/1751-8113/46/25/254009},
}
@Article{KaMaPaa96,
Title = {Spatial dynamics of time-periodic solutions for the {Ginzburg-Landau} equation},
Author = {T. Kapitula and S. Maier-Paape},
Journal = {Z. Angew. Math. Phys.},
Year = {1996},
Pages = {265--305},
Volume = {47},
DOI = {10.1007/BF00916827}
}
@Incollection{KapYor79a,
Title = {Chaotic behavior of multidimensional difference equations},
Author = {Kaplan, J. L. and Yorke, J. A.},
Booktitle = {Functional Differential Equations and Approximation of Fixed Points},
Publisher = {Springer},
Year = {1979},
Address = {Berlin},
Editor = {Peitgen, H.-O. and Walther, H.-O.},
Pages = {204--227},
Series = {Lect. Notes Math.},
Volume = {730},
DOI = {10.1007/BFb0064320}
}
@Incollection{KapYor79,
Title = {Numerical solution of a generalized eigenvalue problem for even mappings},
Author = {Kaplan, J. L. and Yorke, J. A.},
Booktitle = {Functional Differential Equations and Approximation of Fixed Points},
Publisher = {Springer},
Year = {1979},
Address = {New York},
Editor = {Peitgen, H.-O. and Walther, H.-O.},
Pages = {228--237},
DOI = {10.1007/BFb0064320}
}
@Article{Karma1994,
Title = {Electrical alternans and spiral wave breakup in cardiac tissue},
Author = {A. Karma},
Journal = {Chaos},
Year = {1994},
Pages = {461--472},
Volume = {4},
DOI = {10.1063/1.166024}
}
@Techreport{Kassam03,
Title = {Solving reaction-diffusion equations 10 times faster},
Author = {A.-K. Kassam and L. N. Trefethen},
Institution = {Oxford University},
Year = {2003},
Number = {1192},
Type = {Numerical Analysis Group Research Report}
}
@Article{ks05com,
Title = {Fourth-order time-stepping for stiff {PDE}s},
Author = {A.-K. Kassam and L. N. Trefethen},
Journal = {SIAM J. Sci. Comput.},
Year = {2005},
Pages = {1214--1233},
Volume = {26},
DOI = {10.1137/S1064827502410633}
}
@Article{Kasteleyn61,
author = {P. W. Kasteleyn},
title = {The statistics of dimers on a lattice: {I. The} number of dimer arrangements on a quadratic lattice},
journal = {Physica},
year = {1961},
volume = {27},
number = {12},
pages = {1209--1225},
doi = {10.1016/0031-8914(61)90063-5},
}
@Article{Kasteleyn63,
Title = {Dimer statistics and phase transitions},
Author = {Kasteleyn, P. W.},
Journal = {J. Math. Phys.},
Year = {1963},
Pages = {287--293},
Volume = {4},
DOI = {10.1063/1.1703953}
}
@Article{Kato03,
author = {S. Kato and M. Yamada},
title = {Unstable periodic solutions embedded in a shell model turbulence},
journal = {Phys. Rev. E},
year = {2003},
volume = {68},
pages = {025302},
abstract = {A UPO is found in the chaotic region of one shell turbulence model
(GOY). The scaling exponents of the structure function are calculated
to verify that the statistics are well approximated by the UPO.},
doi = {10.1103/physreve.68.025302},
}
@Book{Katok95,
Title = {Introduction to the Modern Theory of Dynamical Systems},
Author = {A. Katok and B. Hasselblatt},
Publisher = {Cambridge Univ. Press},
Year = {1995},
Address = {Cambridge}
}
@Article{KKPW89,
Title = {Differentiability and analyticity of topological entropy for {Anosov} and geodesic flows},
Author = {Katok, A. and Knieper, G. and Pollicott, M. and Weiss, H.},
Journal = {Inv. Math.},
Year = {1989},
Pages = {581--597},
Volume = {98},
DOI = {10.1007/BF01393838}
}
@Article{Kaufman49,
Title = {Crystal statistics. {II. Partition} function evaluated by spinor analysis},
Author = {Kaufman, B.},
Journal = {Phys. Rev.},
Year = {1949},
Pages = {1232--1243},
Volume = {76},
DOI = {10.1103/PhysRev.76.1232},
Issue = {8},
Numpages = {0}
}
@Article{Kaup95,
Title = {The variational principle for nonlinear waves in dissipative systems},
Author = {Kaup, D. J. and Malomed, B. A.},
Journal = {Physica D},
Year = {1995},
Pages = {155--159},
Volume = {87},
DOI = {10.1016/0167-2789(95)00143-R}
}
@Article{kavousanakis_projective_2007,
author = {M. E. Kavousanakis and R. Erban and A. G. Boudouvis and C. W. Gear and I. G. Kevrekidis},
title = {Projective and coarse projective integration for problems with continuous symmetries},
journal = {J. Comput. Phys.},
year = {2007},
volume = {225},
pages = {382--407},
doi = {10.1016/j.jcp.2006.12.003},
}
@Article{kaw1970,
Title = {Relativistic nonlinear propagation of laser beams in cold overdense plasmas},
Author = {Kaw, P. and Dawson, J.},
Journal = {Phys. Fluids},
Year = {1970},
Pages = {472--481},
Volume = {13},
DOI = {10.1063/1.1692942}
}
@Article{KawKida01,
author = {G. Kawahara and S. Kida},
title = {Periodic motion embedded in plane {Couette} turbulence: {Regeneration} cycle and burst},
journal = {J. Fluid Mech.},
year = {2001},
volume = {449},
pages = {291},
doi = {10.1017/s0022112001006243},
}
@InProceedings{KK05,
Title = {Unstable periodic motion in plane {Couette} system: The skeleton of turbulence},
Author = {G. Kawahara and S. Kida and M. Nagata},
Booktitle = {One Hundred Years of Boundary Layer Research},
Year = {2005},
Address = {Dordrecht},
Publisher = {Kluwer}
}
@Article{KaSa05,
author = {Kawasaki, M. and Sasa, S.},
title = {Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom},
journal = {Phys. Rev. E},
year = {2005},
volume = {72},
pages = {037202},
doi = {10.1103/physreve.72.037202},
}
@Article{Kaz83,
Title = {Rydberg atoms in weak magnetic fields},
Author = {Kazantsev, A. P. and Pokrovsky, V. L. and Bergou, J.},
Journal = {Phys. Rev. A},
Year = {1983},
Pages = {3659--3662},
Volume = {28},
DOI = {10.1103/PhysRevA.28.3659}
}
@Unpublished{Kazantsev98a,
Title = {Unstable periodic orbits and attractor of the {Lorenz} model},
Author = {Kazantsev, E.},
Note = {Projet NUMATH, Rapport de recherche n. 3344},
Year = {1998},
Institution = {INRIA Lorraine}
}
@Article{Kazantsev98,
Title = {Unstable periodic orbits and attractor of the barotropic ocean model},
Author = {Kazantsev, E.},
Journal = {Nonlin. Proc. Geophys.},
Year = {1998},
Pages = {193--208},
Volume = {5},
DOI = {10.5194/npg-5-193-1998}
}
@Article{Kazantsev01a,
Title = {Sensitivity of attractor to external influences: {Approach} by unstable periodic orbits},
Author = {Kazantsev, E.},
Journal = {Chaos Solit. Fract.},
Year = {2001},
Pages = {1989--2005},
Volume = {12},
Abstract = {A description of a deterministic chaotic system in terms of unstable
periodic orbits (UPOs) is used to develop a method of an a priori
estimate of the sensitivity of statistical averages of the solution
to small external influences. This method allows us to determine
the forcing perturbation which maximizes the norm of the perturbation
of a statistical moment of the solution on the attractor. The method
was applied to the Lorenz model. The estimates of perturbations of
two statistical moments were compared with directly calculated values.
The comparison shows that some 100 UPOs are sufficient to realize
this approach and get a good accuracy. The linear approach remains
valid up to rather high norms of the forcing perturbation.},
DOI = {10.1016/S0960-0779(00)00154-5}
}
@Article{Kazantsev01,
Title = {Sensitivity of the attractor of the barotropic ocean model to external influences: {Approach} by unstable periodic orbits},
Author = {Kazantsev, E.},
Journal = {Nonlin. Proc. Geophys.},
Year = {2001},
Pages = {281--300},
Volume = {8},
DOI = {10.5194/npg-8-281-2001}
}
@Incollection{Keating97,
Title = {Resummation and the turning points of zeta functions},
Author = {Keating, J.P.},
Booktitle = {Classical, Semiclassical and Quantum Dynamics in Atoms},
Publisher = {Springer},
Year = {1997},
Address = {Berlin},
Editor = {B. Eckhardt and H. Friedrich},
Pages = {83--93},
DOI = {10.1007/BFb0105970}
}
@Article{Keating91a,
Title = {Asymptotic properties of the periodic orbits of the cat maps},
Author = {J. P. Keating},
Journal = {Nonlinearity},
Year = {1991},
Pages = {277},
Volume = {4},
DOI = {10.1088/0951-7715/4/2/005}
}
@Article{Keating91,
Title = {The cat maps: quantum mechanics and classical motion},
Author = {J. P. Keating},
Journal = {Nonlinearity},
Year = {1991},
Pages = {309--341},
Volume = {4},
DOI = {10.1088/0951-7715/4/2/006}
}
@Article{KeaMez00,
Title = {Pseudo-symmetries of {Anosov} maps and spectral statistics},
Author = {J. P. Keating and F. Mezzadri},
Journal = {Nonlinearity},
Year = {2000},
Pages = {747--775},
Volume = {13},
DOI = {10.1088/0951-7715/13/3/313}
}
@Article{KeMeRo99,
Title = {Quantum boundary conditions for torus maps},
Author = {J. P. Keating and F. Mezzadri and J. M. Robbins},
Journal = {Nonlinearity},
Year = {1999},
Pages = {579},
Volume = {12},
DOI = {10.1088/0951-7715/12/3/010}
}
@Article{Keefe85,
Title = {Dynamics of perturbed wavetrain solutions to the {Ginzburg-Landau} equation},
Author = {Keefe, L. R.},
Journal = {Stud. Appl. Math.},
Year = {1985},
Pages = {91--153},
Volume = {73},
DOI = {10.1002/sapm198573291}
}
@Article{KellerEpsLogEps,
Title = {Continuity properties of transport coefficients in simple maps},
Author = {G. Keller and P. J. Howard and Klages, R.},
Journal = {Nonlinearity},
Year = {2008},
Pages = {1719},
Volume = {21},
DOI = {10.1088/0951-7715/21/8/003}
}
@InProceedings{Keller77,
Title = {Numerical solution of bifurcation and nonlinear eigenvalue problems},
Author = {H. B. Keller},
Booktitle = {Applications of Bifurcation Theory},
Year = {1977},
Address = {New York},
Editor = {P. H. Rabinowitz},
Pages = {359--384},
Publisher = {Academic}
}
@InProceedings{Keller79,
author = {H. B. Keller},
title = {Global homotopies and {Newton} methods},
booktitle = {Recent Advances in Numerical Analysis},
year = {1979},
editor = {C. de Boor and G. H. Golub},
pages = {73--94},
address = {New York},
publisher = {Academic},
doi = {10.1016/b978-0-12-208360-0.50009-7},
}
@Book{kellbv,
Title = {Numerical Methods for Two-Point Boundary-Value Problems},
Author = {H. B. Keller},
Publisher = {Dover},
Year = {1992},
Address = {New York}
}
@Article{KellerEBK,
Title = {Corrected {Bohr-Sommerfeld} quantum conditions for nonseparable systems},
Author = {J. B. Keller},
Journal = {Ann. Phys.},
Year = {1958},
Pages = {180--188},
Volume = {4},
DOI = {10.1016/0003-4916(58)90032-0}
}
@Article{Kengne04,
Title = {{Ginzburg-Landau} system of complex modulation equations for a distributed nonlinear-dispersive transmission line},
Author = {E. Kengne},
Journal = {J. Phys. A},
Year = {2004},
Pages = {6053},
Volume = {37},
DOI = {10.1088/0305-4470/37/23/007}
}
@Article{BuKe03,
author = {{Kennel}, M.~B. and {Buhl}, M.},
title = {Estimating good discrete partitions from observed data: {Symbolic} false nearest neighbors},
journal = {Phys. Rev. Lett.},
year = {2003},
volume = {91},
pages = {084102},
doi = {10.1063/1.1612266},
}
@Article{kskent92,
author = {P. Kent and J. Elgin},
title = {Travelling-waves of the {Kuramoto-Sivashinsky} equation: {Period-multiplying} bifurcations},
journal = {Nonlinearity},
year = {1992},
volume = {5},
pages = {899--919},
abstract = {Some properties of the KSe are discussed. A unified argument about
the connections and periodic orbits is given. In particular, the
K-bifurcation of the system is conjectured to arises in the 1:n resonances
of a fixed point.},
doi = {10.1088/0951-7715/5/4/004},
}
@Article{Kerswell05,
Title = {Recent progress in understanding the transition to turbulence in a pipe},
Author = {R. R. Kerswell},
Journal = {Nonlinearity},
Year = {2005},
Pages = {R17--R44},
Volume = {18},
DOI = {10.1088/0951-7715/18/6/R01}
}
@Misc{Kerswell12,
Title = {Misunderstanding the turbulence in a pipe},
Author = {R. R. Kerswell},
Note = {In preparation},
Year = {2012}
}
@Article{KeTu06,
author = {Kerswell, R. R. and Tutty, O.R.},
title = {Recurrence of travelling waves in transitional pipe flow},
journal = {J. Fluid Mech.},
year = {2007},
volume = {584},
pages = {69--102},
doi = {10.1017/s0022112007006301},
abstract = { We find that travelling waves with low wall shear stresses (lower
branch solutions) are on a surface which separates initial conditions
which uneventfully relaminarise and those which lead to a turbulent
evolution. Evidence for recurrent travelling wave visits is found
in both 5D and 10D long periodic pipes but only for those travelling
waves with low-to-intermediate wall shear stress and for less than
about 10\%\ of the time in turbulent flow. Dynamical structures such
as periodic orbits need to be isolated and included in any such expansion.},
}
@Article{KNSks90,
Title = {Back in the saddle again: a computer assisted study of the {Kuramoto-Sivashinsky} equation},
Author = {I. G. Kevrekidis and B. Nicolaenko and J. C. Scovel},
Journal = {SIAM J. Appl. Math.},
Year = {1990},
Pages = {760--790},
Volume = {50},
DOI = {10.1137/0150045}
}
@Article{Kim87,
Title = {Turbulence statistics in fully developed channel flow at low {R}eynolds number},
Author = {J. Kim and P. Moin and R. Moser},
Journal = {J. Fluid Mech.},
Year = {1987},
Pages = {133--166},
Volume = {177},
DOI = {10.1017/s0022112087000892}
}
@Article{Kimball01,
Title = {Chaotic properties of the soft-disk {Lorentz} gas},
Author = {Kimball, J. C.},
Journal = {Phys. Rev. E},
Year = {2001},
Pages = {066216},
Volume = {63},
DOI = {10.1103/PhysRevE.63.066216}
}
@Article{kirby_reconstructing_1992,
Title = {Reconstructing phase space from {PDE} simulations},
Author = {M. Kirby and D. Armbruster},
Journal = {Z. Angew. Math. Phys.},
Year = {1992},
Pages = {999--1022},
Volume = {43},
DOI = {10.1007/BF00916425}
}
@Book{KirWil10,
Title = {{A Window Into Zeta and Modular Physics}},
Author = {Kirsten, K. and Williams, F. L.},
Publisher = {Cambridge Univ. Press},
Year = {2010},
ISBN = {9780521199308}
}
@Article{Kirwan88,
Title = {The topology of reduced phase spaces of the motion of vortices on a sphere},
Author = {Kirwan, F.},
Journal = {Physica D},
Year = {1988},
Pages = {99--123},
Volume = {30},
DOI = {10.1016/0167-2789(88)90100-5}
}
@Article{Kiselev98,
Title = {Symmetry breaking and bifurcations in complex {Lorenz} model},
Author = {Kiselev, A. D.},
Journal = {J. Phys. Studies},
Year = {1998},
Pages = {30--37},
Volume = {2},
URL = {https://www.researchgate.net/profile/Alexei_Kiselev2/publication/252760787_Symmetry_breaking_and_bifurcations_in_complex_Lorenz_model_(in_English)/links/00b7d52ebbf6c2aa32000000.pdf}
}
@Article{KlBo011,
Title = {Convergence analysis of {Davidchack and Lai's} algorithm for finding periodic orbits},
Author = {A. Klebanoff and E. Bollt},
Journal = {Chaos Solit. Fract.},
Year = {2001},
Pages = {1305--1322},
Volume = {12},
DOI = {10.1016/S0960-0779(00)00099-0}
}
@Article{KlPe86,
Title = {A numerical study of baroclinic instability at large super-criticality},
Author = {Klein, P. and Pedlosky, J.},
Journal = {J. Atmos. Sci.},
Year = {1986},
Pages = {1243--1262},
Volume = {43},
DOI = {10.1175/1520-0469(1986)043<1263:ANSOBI>2.0.CO;2}
}
@Article{KlPe92,
Title = {The role of dissipation mechanisms in the nonlinear dynamics of unstable baroclinic waves},
Author = {Klein, P. and Pedlosky, J.},
Journal = {J. Atmos. Sci.},
Year = {1992},
Pages = {29--48},
Volume = {49},
DOI = {10.1175/1520-0469(1992)049<0029:TRODMI>2.0.CO;2}
}
@InProceedings{Kleiser80,
author = {L. Kleiser and U. Schuman},
title = {Treatment of incompressibility and boundary conditions in 3-{D} numerical spectral simulations of plane channel flows},
booktitle = {Proc. 3. GAMM Conf. Numerical Methods in Fluid Mechanics},
year = {1980},
editor = {E. Hirschel},
pages = {165--173},
address = {Viewweg, Braunschweig},
organization = {GAMM},
doi = {10.1007/978-3-322-86146-7_17},
}
@Article{KRSR67,
author = {S. J. Kline and W. C. Reynolds and F. A. Schraub and P. W. Rundstadler},
title = {The structure of turbulent boundary layers},
journal = {J. Fluid Mech.},
year = {1967},
volume = {30},
pages = {741--773},
doi = {10.1017/s0022112067001740},
}
@Article{KniKla11a,
Title = {Capturing correlations in chaotic diffusion by approximation methods},
Author = {Knight, G. and Klages, R.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {041135},
Volume = {84},
DOI = {10.1103/PhysRevE.84.041135}
}
@Article{KniKla11b,
author = {Knight, G. and Klages, R.},
title = {Linear and fractal diffusion coefficients in a family of one-dimensional chaotic maps},
journal = {Nonlinearity},
year = {2011},
volume = {24},
pages = {227},
doi = {10.1088/0951-7715/24/1/011},
}
@Article{KnoWei81,
Title = {Bifurcations in a model of double-diffusive convection},
Author = {E. Knobloch and N.O. Weiss},
Journal = {Phys. Let. A},
Year = {1981},
Pages = {127--130},
Volume = {85},
DOI = {10.1016/0375-9601(81)90882-3}
}
@Incollection{knobloch_hopf_1994,
author = {Knobloch, J. and Vanderbauwhede, A.},
title = {Hopf bifurcation at k-fold resonances in equivariant reversible systems},
booktitle = {{Dynamics, Bifurcation and Symmetry, New Trends and New Tools}},
publisher = {Springer},
year = {1994},
editor = {P. Chossat},
pages = {167--179},
address = {Berlin},
doi = {10.1007/978-94-011-0956-7_15},
}
@Article{knobloch_general_1996,
Title = {A general reduction method for periodic solutions in conservative and reversible systems},
Author = {Knobloch, J. and Vanderbauwhede, A.},
Journal = {J. Diff. Eqn.},
Year = {1996},
Pages = {71},
Volume = {8}
}
@Article{knobloch_hopf_1996,
author = {Knobloch, J. and Vanderbauwhede, A.},
title = {Hopf bifurcation at k-fold resonances in conservative systems},
journal = {Progr. Nonlinear Differential Equations Appl.},
year = {1996},
volume = {19},
pages = {155--170},
doi = {10.1007/978-3-0348-7518-9_8},
}
@Article{Knyazev02,
Title = {Principal angles between subspaces in an {A-based} scalar product: {Algorithms} and perturbation estimates},
Author = {A. V. Knyazev and M. E. Argentati},
Journal = {SIAM J. Sci. Comput.},
Year = {2002},
Pages = {2008--2040},
Volume = {23},
DOI = {10.1137/S1064827500377332}
}
@Article{KoSa11,
author = {Kobayashi, M. U. and Saiki, Y.},
title = {Manifold structures of unstable periodic orbits and the appearance of periodic windows in chaotic systems},
journal = {Phys. Rev. E},
year = {2014},
volume = {89},
pages = {022904},
doi = {10.1103/PhysRevE.89.022904},
}
@Article{Koch2013,
Title = {{Embedded exponential operator splitting methods for the time integration of nonlinear evolution equations}},
Author = {Koch, O. and Neuhauser, Ch. and Thalhammer, M.},
Journal = {Appl. Numer. Math.},
Year = {2013},
Pages = {14--24},
Volume = {63},
DOI = {10.1016/j.apnum.2012.09.002}
}
@Article{KohTak07,
Title = {Finding periodic orbits of higher-dimensional flows by including tangential components of trajectory motion},
Author = {Koh, Y. W. and Takatsuka, K.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {066205},
Volume = {76},
DOI = {10.1103/PhysRevE.76.066205}
}
@Article{KoEhlMo96,
Title = {Problems and progress in microswimming},
Author = {Koiller, J. and Ehlers, K. and Montgomery, R.},
Journal = {J. Nonlin. Sci.},
Year = {1996},
Pages = {507--541},
Volume = {6},
DOI = {10.1007/BF02434055}
}
@Book{Koks06,
Title = {Explorations in Mathematical Physics: The Concepts Behind an Elegant Language},
Author = {Koks, D.},
Publisher = {Springer},
Year = {2006},
Address = {New York}
}
@Article{Kolmogorov58,
Title = {A new metric invariant of transient dynamical systems and automorphisms in {Lebesgue} spaces},
Author = {A. N. Kolmogorov},
Journal = {Dokl. Akad. Nauk SSSR},
Year = {1958},
Number = {861-864},
Volume = {119}
}
@Article{kolm91,
Title = {The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers},
Author = {A. N. Kolmogorov},
Journal = {Proc. R. Soc. Lond. A},
Year = {1991},
Number = {1890},
Pages = {9--13},
Volume = {434},
Abstract = {Study the distribution of velocity difference of neighboring points
based on the locally homogeneous and locally isotropic hypothesized
poperties of turbulence motion. Two more similarity hypothesis suggested
the existence of a universal distribution for different viscosity
and energy dissipation rate. The large distance asymptotic behavior
of the distribution is also deduced.}
}
@Article{kooknewt,
author = {H-T Kook and J. D. Meiss},
title = {Application of {Newton}'s method to {Lagrangian} mappings},
journal = {Physica D},
year = {1989},
volume = {36},
pages = {317--326},
abstract = {An algorithm of {Newton}'s method is presented to find periodic orbits
for {Lagrangian} mappings. The method is based on block-diagonalization
of the Hessian Matrix of the action function.},
doi = {10.1016/0167-2789(89)90087-0},
}
@Article{kook89,
author = {H-T. Kook and J. D. Meiss},
title = {Periodic orbits for reversible symplectic mappings},
journal = {Physica D},
year = {1989},
volume = {35},
pages = {65--86},
abstract = {By constructing a 2N-dimensional symplectic map for a Langrangian
system, the orbit structure of the phase space is discussed for a
time-reversible system. Periodic orbits are classfied according to
the rotation number, symmetry, and morse index. Unstable orbits repel
other periodic orbits to form resonances where a orbit can be trapped
for long with the same rotation number. The chain of resonances with
the same commensurability forms channel which provides the communication
bridge between different resonances. The connection of the orbit
structure with the continued fraction representation of real numbers
is discussed.},
doi = {10.1016/0167-2789(89)90096-1},
}
@Article{K31,
Title = {Hamiltonian systems and transformations in {Hilbert} space},
Author = {B. O. Koopman},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1931},
Pages = {315--318},
Volume = {17},
DOI = {10.1073/pnas.17.5.315}
}
@Book{SpectralPDE,
Title = {Implementing Spectral Methods for Partial Differential Equations},
Author = {D. A. Kopriva},
Publisher = {Springer},
Year = {2009},
Address = {New York}
}
@Article{KKCSG07,
Title = {Fractal properties of anomalous diffusion in intermittent maps},
Author = {Korabel, N. and Klages, R. and Chechkin, A. V. and Sokolov, I. M. and Gonchar, V. Yu.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {036213},
Volume = {75},
DOI = {10.1103/PhysRevE.75.036213}
}
@Article{kostelich97,
author = {E. J. Kostelich and I. Kan and C. Grebogi and E. Ott and J. A. Yorke},
title = {Unstable dimension variability: a source of nonhyperbolicity in chaotic systems},
journal = {Physica D},
year = {1997},
volume = {109},
pages = {81--90},
doi = {10.1016/s0167-2789(97)00161-9},
}
@Article{Kowa97,
author = {Kowalski, K.},
title = {Nonlinear dynamical systems and classical orthogonal polynomials},
journal = {J. Math. Phys.},
year = {1997},
volume = {38},
pages = {2483--2505},
doi = {10.1063/1.531990},
}
@Article{KoRe96,
author = {Kowalski, K. and Rembielinski, J.},
title = {Groups and nonlinear dynamical systems. {Dynamics} on the {SU(2)} group},
journal = {Physica D},
year = {1996},
volume = {99},
pages = {237--251},
doi = {10.1016/s0167-2789(96)00137-6},
}
@Article{KoRe98,
author = {K. Kowalski and J. Rembielinski},
title = {Groups and nonlinear dynamical systems. {Chaotic} dynamics on the {SU(2)xSU(2)} group},
journal = {Chaos Solit. Fract.},
year = {1998},
volume = {9},
pages = {437--448},
doi = {10.1016/s0960-0779(97)00113-6},
}
@Article{KrWaHaDa12,
Title = {Sensitivity analysis of limit cycle oscillations},
Author = {J. A. Krakos and Q. Wang and S. R. Hall and D. L. Darmofal},
Journal = {J. Comput. Phys.},
Year = {2012},
Pages = {3228--3245},
Volume = {231},
DOI = {10.1016/j.jcp.2012.01.001}
}
@Article{KraWan41,
Title = {Statistics of the two-dimensional ferromagnet. {Part I}},
Author = {Kramers, H. A. and Wannier, G. H.},
Journal = {Phys. Rev.},
Year = {1941},
Pages = {252--262},
Volume = {60},
DOI = {10.1103/PhysRev.60.252}
}
@Article{Kras04,
Title = {Growing random sequences},
Author = {I. Krasikov and G. J. Rodgers and C. E. Tripp},
Journal = {J. Phys. A},
Year = {2004},
Pages = {2365--2370},
Volume = {37},
Abstract = {The random sequence has been generalized both in the form of addition
and in the probability distributions. Critical parameter values are
discovered around which the system has very different behavior.}
}
@Article{krauskopf_survey_2005,
author = {B. Krauskopf and H. M. Osinga and E. J. Doedel and M. E. Henderson and J. Guckenheimer and A. Vladimirsky and M. Dellnitz and O. Junge},
title = {A survey of methods for computing (un)stable manifolds of vector fields},
journal = {Int. J. Bifur. Chaos},
year = {2005},
volume = {15},
pages = {763--791},
doi = {10.1142/s0218127405012533},
}
@Article{KreEck12,
author = {T. Kreilos and B. Eckhardt},
title = {Periodic orbits near onset of chaos in plane {Couette} flow},
journal = {Chaos},
year = {2012},
volume = {22},
pages = {047505},
doi = {10.1063/1.4757227},
}
@Misc{KreEck13,
author = {T. Kreilos and B. Eckhardt},
title = {Symmetry related dynamics in parallel shear flows},
year = {2013},
note = {published as \refref{KrZaEc14}},
url = {http://arXiv.org/abs/1309.4590},
}
@Article{KLH94,
Title = {Bounds for threshold amplitudes in subcritical shear flows},
Author = {G. Kreiss and A. Lundbladh and D.~S. Henningson},
Journal = {J. Fluid Mech.},
Year = {1994},
Pages = {175--198},
Volume = {270}
}
@Article{Kressner2006,
Title = {A periodic {Krylov-Schur} algorithm for large matrix products},
Author = {D. Kressner},
Journal = {Numer. Math.},
Year = {2006},
Pages = {461--483},
Volume = {103},
DOI = {10.1007/s00211-006-0682-1}
}
@Article{Krogstad2005,
Title = {Generalized integrating factor methods for stiff {PDEs}},
Author = {Krogstad, S.},
Journal = {J. Comput. Phys.},
Year = {2005},
Pages = {72--88},
Volume = {203},
DOI = {10.1016/j.jcp.2004.08.006}
}
@Article{Krupa90,
Title = {Bifurcations of relative equilibria},
Author = {M. Krupa},
Journal = {{SIAM} J. Math. Anal.},
Year = {1990},
Pages = {1453--1486},
Volume = {21},
DOI = {10.1137/0521081}
}
@Article{KrupaRobHetCyc97,
Title = {Robust Heteroclinic Cycles},
Author = {M. Krupa},
Journal = {J. Nonlin. Sci.},
Year = {1997},
Pages = {129--176},
Volume = {7},
Abstract = {Examines the theoretical and applied research of robust cycles. Formation
of heteroclinic cycles in higher codimension; Stability of robust
cycles; Concept of heteroclinic cycles.}
}
@Article{kruskal62,
Title = {Asymptotic theory of {H}amiltonian and other systems with all solutons nearly periodic},
Author = {M. Kruskal},
Journal = {J. Math. Phys.},
Year = {1962},
Number = {4},
Pages = {806},
Volume = {3},
Abstract = {Asymptotic expansion to all orders. A systematic way to construct
the adiabatic invariants.}
}
@Book{KryBog47,
Title = {{Introduction to Nonlinear Mechanics}},
Author = {Krylov, N. M. and Bogoliubov, N. N.},
Publisher = {Princeton Univ. Press},
Year = {1947},
Address = {Princeton NJ}
}
@Article{Kudry08,
author = {Kudryashov, N. A.},
title = {Solitary and periodic solutions of the generalized {Kuramoto-Sivashinsky} equation},
journal = {Regul. Chaotic Dyn.},
year = {2008},
volume = {13},
pages = {234--238},
doi = {10.1134/S1560354708030088},
}
@Article{Kudry08a,
Title = {Nonlinear evolution equations for description of perturbations in a viscoelastic tube},
Author = {N. A. Kudryashov and D. I. Sinelschikov and I. L. Chernyavsky},
Journal = {Nelin. Dinam.},
Year = {2008},
Pages = {69--86},
Volume = {4},
URL = {\mathnet{http://mi.mathnet.ru/nd221}}
}
@Book{Kuehn15,
Title = {{Multiple Time Scale Dynamics}},
Author = {Kuehn, C.},
Publisher = {Springer},
Year = {2015},
Address = {Berlin},
ISBN = {9783319123165}
}
@Book{kundu08,
Title = {Fluid Mechanics},
Author = {P. K. Kundu and I.M. Cohen},
Publisher = {Academic},
Year = {2008},
Address = {San Diego, CA}
}
@Article{KMOSTY10,
Title = {Chaotic behavior in classical {Yang-Mills} dynamics},
Author = {Kunihiro, T. and M\"uller, B. and Ohnishi, A. and Sch\"afer, A. and Takahashi, T. T. and Yamamoto, A.},
Journal = {Phys. Rev. D},
Year = {2010},
Pages = {114015},
Volume = {82},
DOI = {10.1103/PhysRevD.82.114015}
}
@Article{Kuptsov12,
Title = {Fast numerical test of hyperbolic chaos},
Author = {Kuptsov, P. V.},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {015203},
Volume = {85},
DOI = {10.1103/PhysRevE.85.015203}
}
@Article{Kuptsov13,
Title = {Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors},
Author = {Kuptsov, P. V.},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254016},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254016}
}
@Article{KuPa09,
Title = {Strict and fussy modes splitting in the tangent space of the {Ginzburg-Landau} equation},
Author = {Kuptsov, P. V. and Parlitz, U.},
Journal = {Phys. Rev. E},
Year = {2010},
Addendum = {\arXiv{0912.2261}},
Pages = {036214},
Volume = {81},
DOI = {10.1103/PhysRevE.81.036214}
}
@Article{KuPa12,
author = {Kuptsov, P. V. and Parlitz, U.},
title = {Theory and computation of covariant {Lyapunov} vectors},
journal = {J. Nonlinear Sci.},
year = {2012},
volume = {22},
pages = {727--762},
doi = {10.1007/s00332-012-9126-5},
}
@Article{kuramitsu2012,
Title = {Laboratory investigations on the origins of cosmic rays},
Author = {Kuramitsu, Y. and Sakawa, Y. and Morita, T. and Ide, T. and Nishio, K. and Tanji, H. and Aoki, H. and Dono, S. and Gregory, C. D. and Waugh, J. N. and Woolsey, N. and Dizi?re, A. and Pelka, A. and Ravasio, A. and Loupias, B. and Koenig, M. and Pikuz, S. A. and Li, Y. T. and Zhang, Y. and Liu, X. and Zhong, J. Y. and Zhang, J. and Gregori, G. and Nakanii, N. and Kondo, K. and Mori, Y. and Miura, E. and Kodama, R. and Kitagawa, Y. and Mima, K. and Tanaka, K. A. and Azechi, H. and Moritaka, T. and Matsumoto, Y. and Sano, T. and Mizuta, A. and Ohnishi, N. and Hoshino, M. and Takabe, H.},
Journal = {Plasma Phys. Control. Fusion},
Year = {2012},
Pages = {124049},
Volume = {54},
DOI = {10.1088/0741-3335/54/12/124049}
}
@Article{kuturb78,
author = {Y. Kuramoto},
title = {Diffusion-induced chaos in reaction systems},
journal = {Suppl. Progr. Theor. Phys.},
year = {1978},
volume = {64},
pages = {346--367},
abstract = {Phase turbulence and amplitude turbulence are named and distinguished
from a dynamical systems point of view. The prototyped equations
are derived.},
doi = {10.1143/ptps.64.346},
}
@Book{kura84tur,
Title = {Chemical Oscillations, Waves and Turbulence},
Author = {Y. Kuramoto},
Publisher = {Springer},
Year = {1984},
Address = {New York}
}
@Article{KurTsu75,
Title = {On the formation of dissipative structures in reaction--diffusion systems},
Author = {Kuramoto, Y. and Tsuzuki, T.},
Journal = {Progr. Theor. Phys.},
Year = {1975},
Pages = {687--699},
Volume = {54},
DOI = {10.1143/PTP.54.687}
}
@Article{KurTsu76,
Title = {Persistent propagation of concentration waves in dissipative media far from thermal equilibrium},
Author = {Y. Kuramoto and T. Tsuzuki},
Journal = {Progr. Theor. Phys.},
Year = {1976},
Pages = {356--369},
Volume = {55},
Abstract = {The KSe is derived through the CGLe near the
bifurcation point. Some scaling argument is used to
sort out the dominant terms.},
DOI = {10.1143/PTP.55.356}
}
@Article{KurRud00,
Title = {Hecke theory and equidistribution for the quantization of linear maps of the torus},
Author = {Kurlberg, P. and Rudnick, Z.},
Journal = {Duke Math. J.},
Year = {2000},
Pages = {47--77},
Volume = {103},
DOI = {10.1215/S0012-7094-00-10314-6}
}
@Article{Kuznetsov16,
author = {N. V. Kuznetsov},
title = {The {Lyapunov} dimension and its estimation via the {Leonov} method},
journal = {Phys. Let. A},
year = {2016},
pages = {-},
doi = {10.1016/j.physleta.2016.04.036},
}
@Article{KuAlLe16,
author = {Kuznetsov, N. V. and Alexeeva, T. A. and Leonov, G. A.},
title = {Invariance of {Lyapunov} exponents and {Lyapunov} dimension for regular and irregular linearizations},
journal = {Nonlinear Dyn.},
year = {2016},
pages = {1--7},
doi = {10.1007/s11071-016-2678-4},
}
@Article{KuMoVa14,
Title = {Numerical justification of {Leonov} conjecture on {Lyapunov} dimension of {Rossler} attractor},
Author = {N. V. Kuznetsov and T. N. Mokaev and P. A. Vasilyev},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2014},
Pages = {1027--1034},
Volume = {19},
DOI = {10.1016/j.cnsns.2013.07.026}
}
@InProceedings{KuKuSa05,
Title = {Review and examples of non-{Feigenbaum} critical situations associated with period-doubling},
Author = {Kuznetsov, S. P. and Kuznetsov, A. P. and Sataev, I .R.},
Booktitle = {Physics and Control, 2005 International Conference Proceedings},
Year = {2005},
Pages = {610--615},
Abstract = {We review several critical situations, linked with period-doubling
transition to chaos, which require using at least two-dimensional
maps as models representing the universality classes. Each of them
corresponds to a saddle solution of the two-dimensional generalization
of Feigenbaum-Cvitanovic equation and is characterized by a set of
distinct universal constants analogous to Feigenbaum's alpha; and
delta;. We present a number of examples (driven self-oscillators,
coupled Henon-like maps, coupled driven oscillators, coupled chaotic
self-oscillators), which manifest these types of behavior.},
DOI = {10.1109/PHYCON.2005.1514057}
}
@Book{Kuzn04,
title = {Elements of Applied Bifurcation Theory},
publisher = {Springer},
year = {2004},
author = {Y. A. Kuznetsov},
address = {New York},
doi = {10.1007/978-1-4757-3978-7},
}
@Misc{lopezLink,
author = {Vanessa L{\'o}pez},
note = {private communication},
}
@Article{lop05rel,
author = {V. L{\'o}pez and P. Boyland and M. T. Heath and R. D. Moser},
title = {Relative periodic solutions of the complex {Ginzburg-Landau} equation},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2006},
volume = {4},
pages = {1042--1075},
abstract = {Define relative periodic orbits and use Fourier modes to find them.},
doi = {10.1137/040618977},
}
@Misc{Lopez2015,
author = {V. L{\'o}pez},
title = {Numerical continuation of invariant solutions of the complex {Ginzburg--Landau} equation},
year = {2015},
url = {https://arxiv.org/abs/1502.03862},
}
@Article{LaNgKuTa13,
Title = {Large deviations of {Lyapunov} exponents},
Author = {Laffargue, T. and Nguyen Thu Lam, K.-D. and Kurchan, J. and Tailleur, J.},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254002},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254002}
}
@Article{LaMi99,
author = {Lahme, B. and Miranda, R.},
title = {{Karhunen-Loeve} decomposition in the presence of symmetry. {I}},
journal = {IEEE Trans. Image Processing},
year = {1999},
volume = {8},
pages = {1183--1190},
doi = {10.1109/83.784431},
}
@Article{Lai97,
author = {Y.-C. Lai},
title = {Characterization of the natural measure by unstable periodic orbits in nonhyperbolic chaotic systems},
journal = {Phys. Rev. E},
year = {1997},
volume = {56},
pages = {6531--6539},
doi = {10.1103/PhysRevE.56.6531},
}
@Article{lamb_bifurcationperiodic_2003,
author = {Lamb, J. S. W. and Melbourne, I. and Wulff, C.},
title = {General bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions},
journal = {J. Diff. Eqn.},
year = {2003},
volume = {191},
pages = {377--407},
doi = {10.1016/S0022-0396(03)00019-6},
}
@Article{LaMeWu06,
Title = {Hopf bifurcation from relative periodic solutions; secondary bifurcations from meandering spirals},
Author = {Lamb, J. S. W. and Melbourne, I. and Wulff, C. },
Journal = {J. Difference Eqn. and Appl.},
Year = {2006},
Pages = {1127--1145},
Volume = {12},
Abstract = { We consider nonresonant and weakly resonant Hopf
bifurcation from periodic solutions and relative periodic solutions
in dynamical systems with symmetry. In particular, we analyse
phase-locking and irrational torus flows on the bifurcating relative
tori. Results are obtained for systems with compact and noncompact
symmetry groups. In the noncompact case, we distinguish between
bounded and unbounded dynamics. Applications of our results include
secondary Hopf bifurcation from meandering multi-armed spirals. },
DOI = {10.1080/10236190601045747}
}
@Article{lamb98,
Title = {Time reversal symmetry in dynamical systems: {A} survey},
Author = {J. S. W. Lamb and J. A. G. Roberts},
Journal = {Physica D},
Year = {1998},
Pages = {1--39},
Volume = {112},
DOI = {10.1016/S0167-2789(97)00199-1}
}
@Article{LaWu02,
Title = {Reversible relative periodic orbits},
Author = {Lamb, J. S. W. and Wulff, C.},
Journal = {J. Diff. Eqn.},
Year = {2002},
Pages = {60--100},
Volume = {178},
DOI = {10.1006/jdeq.2001.4004}
}
@Book{Lambert1991,
title = {Numerical Methods for Ordinary Differential Systems: The Initial Value Problem},
publisher = {Wiley},
year = {1991},
author = {Lambert, J. D.},
address = {New York},
isbn = {0-471-92990-5},
doi = {10.2307/2153266},
}
@Phdthesis{LanThesis,
Title = {Dynamical Systems Approach to {$1-d$} Spatiotemporal Chaos -- {A} Cyclist's View},
Author = {Y. Lan},
School = {School of Physics, Georgia Inst. of Technology},
Year = {2004},
Address = {Atlanta},
URL = {http://ChaosBook.org/projects/theses.html}
}
@Article{Lan10,
Title = {Cycle expansions: {From} maps to turbulence},
Author = {Y. Lan},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2010},
Pages = {502--526},
Volume = {15},
DOI = {10.1016/j.cnsns.2009.04.022}
}
@Article{Lan11,
Title = {Novel computation of the growth rate of generalized random {Fibonacci} sequences},
Author = {Lan, Y.},
Journal = {J. Stat. Phys.},
Year = {2011},
Pages = {847--861},
Volume = {142},
DOI = {10.1007/s10955-011-0132-z}
}
@Article{LCC06,
Title = {Variational method for locating invariant tori},
Author = {Y. Lan and C. Chandre and P. Cvitanovi{\'c}},
Journal = {Phys. Rev. E},
Year = {2006},
Pages = {046206},
Volume = {74},
DOI = {10.1103/PhysRevE.74.046206}
}
@Article{lanVar1,
author = {Y. Lan and P. Cvitanovi{\'c}},
title = {Variational method for finding periodic orbits in a general flow},
journal = {Phys. Rev. E},
year = {2004},
volume = {69},
pages = {016217},
doi = {10.1103/PhysRevE.69.016217},
}
@Article{lanCvit07,
author = {Lan, Y. and Cvitanovi{\'c}, P.},
title = {Unstable recurrent patterns in {Kuramoto-Siva\-shin\-sky} dynamics},
journal = {Phys. Rev. E},
year = {2008},
volume = {78},
pages = {026208},
doi = {10.1103/PhysRevE.78.026208},
}
@Article{lanmaw03,
Title = {Stationary modulated-amplitude waves in the 1{D} complex {Ginzburg-Landau} equation},
Author = {Y. Lan and N. Garnier and P. Cvitanovi{\'c}},
Journal = {Physica D},
Year = {2004},
Pages = {193--212},
Volume = {188},
DOI = {10.1016/S0167-2789(03)00289-6}
}
@Article{landau44,
author = {L. D. Landau},
title = {On the problem of turbulence},
journal = {Dokl. Akad. Nauk SSSR},
year = {1944},
volume = {44},
pages = {339},
doi = {10.1016/b978-0-08-010586-4.50057-2},
}
@Book{Landau59a,
Title = {Fluid Mechanics},
Author = {L. D. Landau and E. M. Lifshitz},
Publisher = {Pergamon Press},
Year = {1959},
Address = {Oxford}
}
@Article{LROBK13,
Title = {Global structure of regular tori in a generic {4D} symplectic map},
Author = {Lange, S. and Richter, M. and Onken, F. and B{\"a}cker, A. and Ketzmerick, R.},
Journal = {Chaos},
Year = {2014},
Volume = {24},
DOI = {10.1063/1.4882163}
}
@Book{langford_normal_1995,
Title = {Normal Forms and Homoclinic Chaos},
Author = {W. F. Langford and W. Nagata},
Publisher = {AMS},
Year = {1995},
Pages = {294}
}
@Article{LanThi11,
author = {Lanneau, E. and Thiffeault, J.-L.},
title = {On the minimum dilatation of pseudo-{Anosov} homeomorphisms on surfaces of small genus},
journal = {Ann. Inst. Fourier},
year = {2011},
volume = {61},
pages = {105--144},
doi = {10.5802/aif.2599},
}
@Article{laquey74,
author = {R. E. LaQuey and S. M. Mahajan and P. H. Rutherford and W. M. Tang},
title = {Nonlinear saturation of the trapped-ion mode},
journal = {Phys. Rev. Lett.},
year = {1974},
volume = {34},
pages = {391--394},
doi = {10.2172/4202869},
}
@Book{LM94,
Title = {Chaos, Fractals, and Noise; Stochastic Aspects of Dynamics},
Author = {A. Lasota and M. MacKey},
Publisher = {Springer},
Year = {1994},
Address = {New York}
}
@Article{LaKo89,
author = {D. P. Lathrop and E. J. Kostelich},
title = {Characterization of an experimental strange attractor by periodic orbits},
journal = {Phys. Rev. A},
year = {1989},
volume = {40},
pages = {4028--4031},
doi = {10.1103/physreva.40.4028},
}
@Article{LaChWu82,
Title = {A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems},
Author = {Lau, S. L. and Cheung, Y. K. and Wu, S. Y.},
Journal = {J. Appl. Mechanics},
Year = {1982},
Pages = {849--853},
Volume = {49},
DOI = {10.1115/1.3162626}
}
@Article{lau92,
Title = {The cocoon bifurcations in three-dimensional systems with two fixed points},
Author = {Lau, Y.-T.},
Journal = {Int. J. Bifur. Chaos},
Year = {1992},
Pages = {543--558},
Volume = {2},
DOI = {10.1142/S0218127492000690}
}
@Misc{LauOrl12,
author = {Laufer, M. and Orland, P.},
title = {The geometry of {Yang-Mills} orbit space on the lattice},
year = {2012},
url = {http://arXiv.org/abs/1203.5134},
}
@Article{Laurent-Polz04,
author = {F. Laurent-Polz},
title = {Relative periodic orbits in point vortex systems},
journal = {Nonlinearity},
year = {2004},
volume = {17},
pages = {1989--2013},
doi = {10.1088/0951-7715/17/6/001},
}
@Article{Laur91,
author = {B. Lauritzen},
title = {Discrete symmetries and the periodic-orbit expansions},
journal = {Phys. Rev. A},
year = {1991},
volume = {43},
pages = {603--606},
doi = {10.1103/physreva.43.603},
}
@Article{LaSa97,
Title = {Bifurcation analysis for spherically symmetric systems using invariant theory},
Author = {R. Lauterbach and J. A. Sanders},
Journal = {J. Dynam. Diff. Eq.},
Year = {1997},
Pages = {535--560},
Volume = {9},
DOI = {10.1007/BF02219397}
}
@Book{Lau05,
Title = {{Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World}},
Author = {Lautrup, B.},
Publisher = {CRC Press},
Year = {2011},
Address = {Boca Raton, FL}
}
@Incollection{lauw86,
Title = {One-dimensional iterative maps},
Author = {H. A. Lauwerier},
Booktitle = {Chaos},
Publisher = {Princeton Univ. Press},
Year = {1986},
Address = {Princeton NJ},
Editor = {Holden, A. V.},
Pages = {39},
DOI = {10.1515/9781400858156},
ISBN = {9781400858156}
}
@Book{ellip,
title = {{Elliptic Functions and Applications}},
publisher = {Springer},
year = {1989},
author = {D. F. Lawden},
address = {New York},
doi = {10.1007/978-1-4757-3980-0},
}
@Article{Lawson67,
Title = {Generalized {Runge-Kutta} Processes for Stable Systems with Large {Lipschitz} Constants},
Author = {J. D. Lawson},
Journal = {SIAM J. Numer. Anal.},
Year = {1967},
Pages = {372--380},
Volume = {4},
DOI = {10.1137/0704033}
}
@Article{LeAllHa00,
Title = {Sensitivity analysis of the climate of a chaotic system},
Author = {Lea, D. J. and Allen, M. R. and Haine, T. W. N.},
Journal = {Tellus A},
Year = {2000},
Pages = {523--532},
Volume = {52},
Abstract = {This paper addresses some fundamental methodological issues concerning
the sensitivity analysis of chaotic geophysical systems. We show,
using the Lorenz system as an example, that a naive approach to variational
(``adjoint'') sensitivity analysis is of limited utility. Applied
to trajectories which are long relative to the predictability time
scales of the system, cumulative error growth means that adjoint
results diverge exponentially from the ``macroscopic climate sensitivity''(that
is, the sensitivity of time-averaged properties of the system to
finite-amplitude perturbations). This problem occurs even for time-averaged
quantities and given infinite computing resources. Alternatively,
applied to very short trajectories, the adjoint provides an incorrect
estimate of the sensitivity, even if averaged over large numbers
of initial conditions, because a finite time scale is required for
the model climate to respond fully to certain perturbations. In the
Lorenz (1963) system, an intermediate time scale is found on which
an ensemble of adjoint gradients can give a reasonably accurate (O(10%))
estimate of the macroscopic climate sensitivity. While this ensemble-adjoint
approach is unlikely to be reliable for more complex systems, it
may provide useful guidance in identifying important parameter-combinations
to be explored further through direct finite-amplitude perturbations.},
DOI = {10.1034/j.1600-0870.2000.01137.x}
}
@Article{LeBlanc00,
author = {LeBlanc, V. G. and Wulff, C.},
title = {Translational symmetry-breaking for spiral waves},
journal = {J. Nonlin. Sci.},
year = {2000},
volume = {10},
pages = {569--601},
doi = {10.1007/s003320010005},
}
@Article{Leboeuf04,
author = {Leboeuf, P.},
title = {Periodic orbit spectrum in terms of {Ruelle-Pollicott} resonances},
journal = {Phys. Rev. E},
year = {2004},
volume = {69},
pages = {026204},
doi = {10.1103/PhysRevE.69.026204},
}
@Article{Lega:holes,
Title = {Traveling hole solutions of the complex {Ginzburg-Landau} equation: a review},
Author = {J. Lega},
Journal = {Physica D},
Year = {2001},
Pages = {269--287},
Volume = {269},
DOI = {10.1016/s0167-2789(01)00174-9}
}
@Article{Lehoucq1996,
Title = {{Deflation Techniques for an Implicitly Restarted Arnoldi Iteration}},
Author = {Lehoucq, R. B. and Sorensen, D. C.},
Journal = {SIAM J. Matrix Anal. Appl.},
Year = {1996},
Pages = {789--821},
Volume = {17},
DOI = {10.1137/S0895479895281484}
}
@Book{Arpack98,
title = {{ARPACK Users Guide: Solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods}},
publisher = {SIAM},
year = {1998},
author = {R. B. Lehoucq and D. C. Sorensen and C. Yang},
doi = {10.1137/1.9780898719628},
}
@Article{Leis97,
Title = {Hopf-bifurcation in systems with spherical symmetry. {I: Invariant} tori},
Author = {Leis, C.},
Journal = {Doc. Math.},
Year = {1997},
Pages = {61--113},
Volume = {2},
URL = {http://www.emis.ams.org/journals/DMJDMV/vol-02/04.pdf}
}
@Article{LPKDS09,
Title = {Evolutionary phase space in driven elliptical billiards},
Author = {F. Lenz and C. Petri and F. N. R. Koch and F. K. Diakonos and P. Schmelcher},
Journal = {New J. Phys.},
Year = {2009},
Pages = {083035},
Volume = {11},
DOI = {10.1088/1367-2630/11/8/083035}
}
@Misc{LeoKuz15,
Title = {A short survey on {Lyapunov} dimension for finite dimensional dynamical systems in {Euclidean} space},
Author = {{Leonov}, G. A. and {Kuznetsov}, N. V.},
Year = {2015},
URL = {http://arXiv.org/abs/1510.03835}
}
@Article{LePoTo96,
Title = {Chronotopic {Lyapunov} analysis. {I. A} detailed characterization of {1D} systems},
Author = {S. Lepri and A. Politi and A. Torcini},
Journal = {J. Stat. Phys.},
Year = {1996},
Pages = {1429--1452},
Volume = {82},
DOI = {10.1007/BF02183390}
}
@Article{LePoTo97,
Title = {Chronotopic {Lyapunov} analysis. {II. Towards} a unified approach},
Author = {S. Lepri and A. Politi and A. Torcini},
Journal = {J. Stat. Phys.},
Year = {1997},
Pages = {31--45},
Volume = {88},
DOI = {10.1007/BF02508463}
}
@Article{LePoTo97a,
Title = {Entropy potential and {Lyapunov} exponents},
Author = {Lepri, S. and Politi, A. and Torcini, A.},
Journal = {Chaos},
Year = {1997},
Pages = {701-709},
Volume = {7},
DOI = {10.1063/1.166268}
}
@Article{Lesne07,
Title = {The discrete versus continuous controversy in physics},
Author = {A. Lesne},
Journal = {Math. Struct. Computer Sci.},
Year = {2007},
Pages = {185--223},
Volume = {17},
DOI = {10.1017/S0960129507005944}
}
@Article{Letellier03,
Title = {Modding out a continuous rotation symmetry for disentangling a laser dynamics},
Author = {C. Letellier},
Journal = {Int. J. Bifur. Chaos},
Year = {2003},
Pages = {1573--1577},
Volume = {13},
DOI = {10.1142/s0218127403007424}
}
@Article{GL-Let01,
Title = {Covering dynamical systems: {T}wo-fold covers},
Author = {C. Letellier and R. Gilmore},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {016206},
Volume = {63},
DOI = {10.1103/physreve.63.016206}
}
@Article{levenberg44,
Title = {A method for the solution of certain non-linear problems in least squares},
Author = {Levenberg, K},
Journal = {Quart. Appl. Math.},
Year = {1944},
Pages = {164--168},
Volume = {2},
DOI = {10.1090/qam/10666}
}
@Misc{LevnMezi08,
Title = {Ergodic theory and visualization {I}: {Visualization} of ergodic partition and invariant sets},
Author = {Levnaji\'c, Z. and Mezi\'c, I.},
Year = {2008},
URL = {http://arXiv.org/abs/0805.4221}
}
@Article{LiDaLi07,
Title = {Long time behaviour for generalized complex {Ginzburg--Landau} equation},
Author = {D. Li and Z. Dai and X. Liu},
Journal = {J. Math. Anal. Appl.},
Year = {2007},
Pages = {934--948},
Volume = {330},
DOI = {10.1016/j.jmaa.2006.07.095}
}
@Article{LY75,
author = {T. Li and J. A. Yorke},
title = {Period 3 implies chaos},
journal = {Amer. Math. Monthly},
year = {1975},
volume = {82},
pages = {985--992},
url = {http://www.jstor.org/stable/2318254},
}
@Article{LXSH08,
Title = {{Lyapunov} spectra of coupled chaotic maps},
Author = {X. Li and Y. Xue and P. Shi and G. Hu},
Journal = {Int. J. Bifur. Chaos},
Year = {2008},
Pages = {3759--3770},
Volume = {18},
DOI = {10.1142/S0218127408022718}
}
@Article{GLEM07,
author = {{Li}, Y. and {Chevillard}, L. and {Eyink}, G.and {Meneveau}, C.},
title = {Matrix exponential-based closures forthe turbulent subgrid-scale stress tensor},
journal = {Phys. Rev. E},
year = {2009},
volume = {79},
pages = {016305},
doi = {10.1103/physreve.79.016305},
}
@Article{Liao09,
author = {Liao, S. J.},
title = {On the reliability of computed chaotic solutions of non-linear differential equations},
journal = {Tellus A},
year = {2009},
volume = {61},
pages = {550--564},
doi = {10.3402/tellusa.v61i4.15610},
}
@Misc{Liao11,
Title = {Chaos: a bridge from microscopic uncertainty to macroscopic randomness},
Author = {Liao, S. J.},
Year = {2011},
URL = {http://arXiv.org/abs/1108.4472}
}
@Misc{Liao11a,
Title = {On the numerical simulation of propagation of micro-level uncertainty for chaotic dynamic systems},
Author = {Liao, S. J.},
Year = {2011},
URL = {http://arXiv.org/abs/1109.0130}
}
@Book{Lichtenberg92,
Title = {{Regular and Chaotic Dynamics}},
Author = { A. J. Lichtenberg and M. A. Lieberman},
Publisher = {Springer},
Year = {2013},
Address = {New York},
Edition = {2},
ISBN = {9781475721843}
}
@Article{Lichtner2007,
author = {M. Lichtner and M. Radziunas and L. Recke},
title = {Well-posedness, smooth dependence and center manifold reduction for a semilinear hyperbolic system from laser dynamics},
journal = {Math. Methods Appl. Sci.},
year = {2007},
volume = {30},
pages = {931--960},
doi = {10.1002/mma.816},
}
@Article{LinKS74,
author = {Lin, S. P.},
title = {Finite-amplitude side-band stability of a viscous film},
journal = {J. Fluid Mech.},
year = {1974},
volume = {63},
number = {Apr29},
pages = {417--429},
doi = {10.1017/s0022112074001704},
}
@Article{LiMaFeCh10,
Title = {Locating unstable periodic orbits: {When} adaptation integrates into delayed feedback control},
Author = {Lin, W. and Ma, H. and Feng, J. and Chen, G.},
Journal = {Phys. Rev. E},
Year = {2010},
Pages = {046214},
Volume = {82},
DOI = {10.1103/PhysRevE.82.046214}
}
@Incollection{Lind96,
Title = {A zeta function for {$Z^d$}-actions},
Author = {D. A. Lind},
Booktitle = {Ergodic Theory of {$Z^d$} Actions},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Editor = {M. Pollicott and K. Schmidt},
Pages = {433--450},
DOI = {10.1017/CBO9780511662812.019},
ISBN = {9780511662812}
}
@Book{LindMar95,
Title = {{An Introduction to Symbolic Dynamics and Coding}},
Author = {D.A. Lind and B. Marcus},
Publisher = {Cambridge Univ. Press},
Year = {1995},
Address = {Cambridge},
ISBN = {9780521559003}
}
@Article{LiWu87,
Title = {Fast {Galerkin} method and its application to determine periodic solutions of non-linear oscillators},
Author = {F. H. Ling and X. X. Wu},
Journal = {Int. J. Non-Linear Mechanics},
Year = {1987},
Pages = {89 --98},
Volume = {22},
DOI = {10.1016/0020-7462(87)90012-6}
}
@Book{Lipkin66,
Title = {Lie Groups for Pedestrians},
Author = {Lipkin , H. J.},
Publisher = {North-Holland},
Year = {1966},
Address = {Amsterdam}
}
@Phdthesis{LippolisThesis,
author = {Lippolis, D.},
title = {How well can one resolve the state space of a chaotic map?},
school = {School of Physics, Georgia Inst. of Technology},
year = {2010},
address = {Atlanta},
url = {http://ChaosBook.org/projects/theses.html},
}
@Article{LipCvi08,
author = {D. Lippolis and P. Cvitanovi\'c},
title = {How well can one resolve the state space of a chaotic map?},
journal = {Phys. Rev. Lett.},
year = {2010},
volume = {104},
pages = {014101},
doi = {10.1103/PhysRevLett.104.014101},
}
@Unpublished{LipCvi07,
Title = {Optimal resolution of the state space of a chaotic flow in presence of noise},
Author = {D. Lippolis and P. Cvitanovi\'c},
Note = {In preparation},
Year = {2012}
}
@Article{Lis15,
author = {Lis, M.},
title = {A short proof of the {Kac-Ward} formula},
journal = {Annales de l'Institut Henri Poincar{\'{e}} D},
year = {2016},
volume = {3},
pages = {45--53},
doi = {10.4171/aihpd/24},
}
@Article{LiRe97,
Title = {Gauge fields in the separation of rotations and internal motions in the {$n$}-body problem},
Author = {R. G. Littlejohn and M. Reinsch},
Journal = {Rev. Mod. Phys.},
Year = {1997},
Pages = {213--275},
Volume = {69},
DOI = {10.1103/RevModPhys.69.213}
}
@Misc{liuliupego05,
author = {J.-G. Liu and J. Liu and R. L. Pego},
title = {Divorcing pressure from viscosity in incompressible {Navier-Stokes} dynamics},
year = {2005},
url = {http://arXiv.org/abs/math.AP/0502549},
}
@Article{LiMaRu90,
Title = {Periodic orbits and long transients in coupled map lattices},
Author = {R. Livi and G. Mart{\'i}nez-Mekler and S. Ruffo},
Journal = {Physica D},
Year = {1990},
Pages = {452--460},
Volume = {45},
DOI = {10.1016/0167-2789(90)90202-Z}
}
@Article{Llave09,
Title = {A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities},
Author = {de la Llave, R.},
Journal = {J. Dynam. Differential Equations},
Year = {2009},
Pages = {371--415},
Volume = {21},
DOI = {10.1007/s10884-009-9140-y}
}
@Article{LlaMir16,
Title = {Connecting orbits for compact infinite dimensional maps: {Computer} assisted proofs of existence},
Author = {de la Llave, R. and Mireles James, J. D.},
Journal = {SIAM J. Appl. Dyn. Sys.},
Year = {2016},
Pages = {1268--1323},
Volume = {15},
DOI = {10.1137/15M1053608}
}
@Incollection{Llibre15,
Title = {The averaging theory for computing periodic orbits},
Author = {Llibre, J.},
Booktitle = {{Central Configurations, Periodic Orbits, and Hamiltonian Systems}},
Publisher = {Springer},
Year = {2015},
Address = {Basel},
Pages = {1--104},
Series = {Advanced Courses in Mathematics - CRM Barcelona},
DOI = {10.1007/978-3-0348-0933-7_1},
ISBN = {978-3-0348-0932-0}
}
@Article{LoeSom15,
Title = {Discrete {Dirac} operators, critical embeddings and {Ihara-Selberg} functions},
Author = {Loebl, M. and Somberg, P.},
Journal = {Electron. J. Combin.},
Year = {2015},
Pages = {P1--10},
Volume = {22},
URL = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p10}
}
@Article{LoCaCoPeGo11,
Title = {Growth and instability of a laminar plume in a strongly stratified environment},
Author = {Lombardi, M. and Caulfield, C.P. and Cossu, C. and Pesci, A.I. and Goldstein, R.E.},
Journal = {J. Fluid Mech.},
Year = {2011},
Pages = {184--206},
Volume = {671},
DOI = {10.1017/S0022112010005574}
}
@Article{LoTh10,
author = {G. J. Lord and V. Th\"{u}mmler},
title = {Computing stochastic travelling waves},
journal = {SIAM J. Sci. Comput.},
year = {2012},
volume = {34},
pages = {B24--B43},
doi = {10.1137/100784734},
}
@Article{Lorentz1905,
Title = {The motion of electrons in metallic bodies},
Author = {Lorentz, H. A.},
Journal = {K. Ned. Akad. van Wet. B},
Year = {1905},
Pages = {438--453},
Volume = {7},
URL = {http://www.dwc.knaw.nl/DL/publications/PU00013989.pdf}
}
@Article{Lorenz60,
author = {E. N. Lorenz},
title = {Maximum simplification of the dynamics equations},
journal = {Quart. J. Geophys.},
year = {1960},
volume = {12},
pages = {243--254},
doi = {10.1111/j.2153-3490.1960.tb01307.x},
}
@Article{lorenz,
author = {E. N. Lorenz},
title = {Deterministic nonperiodic flow},
journal = {J. Atmos. Sci.},
year = {1963},
volume = {20},
pages = {130--141},
doi = {10.1007/978-0-387-21830-4_2},
}
@Article{Lorenz63a,
Title = {The Mechanics of vacillation},
Author = {E. N. Lorenz},
Journal = {J. Meteorology},
Year = {1963},
Pages = {448--465},
Volume = {20},
DOI = {10.1175/1520-0469(1963)020<0448:TMOV>2.0.CO;2}
}
@Article{Lorenz65,
Title = {A study of the predictability of a 28-variable atmospheric model},
Author = {Lorenz, E. N.},
Journal = {Tellus},
Year = {1965},
Pages = {321--333},
Volume = {17},
Abstract = {A 28-variable model of the atmosphere is constructed by expanding
the equations of a two-level geostrophic model in truncated double-Fourier
series. The model includes the nonlinear interactions among disturbances
of three different wave lengths. Nonperiodic time-dependent solutions
are determined by numerical integration.By comparing separate solutions
with slightly different initial conditions, the growth rate of small
initial errors is studied. The time required for errors comparable
to observational errors in the atmosphere to grow to intolerable
errors is strongly dependent upon the current circulation pattern,
and varies from a few days to a few weeks.Some statistical predictability
of certain quantities seems to be present even after errors in the
complete circulation pattern are no longer small. The feasibility
of performing similar studies with much larger atmospheric models
is considered.},
DOI = {10.1111/j.2153-3490.1965.tb01424.x}
}
@Article{lorenz69,
author = {E. N. Lorenz},
title = {The predictability of a flow which possessesmany scales of motion},
journal = {Tellus},
year = {1969},
volume = {21},
pages = {289--307},
doi = {10.1111/j.2153-3490.1969.tb00444.x},
}
@Article{Lorenz84,
Title = {Irregularity: a fundamental property of the atmosphere},
Author = {Lorenz, E. N.},
Journal = {Tellus A},
Year = {1984},
Pages = {98--110},
Volume = {36},
Abstract = {Some early ideas concerning the general circulation of the atmosphere
are reviewed. A model of the general circulation, consisting of three
ordinary differential equations, is introduced. For different intensities
of the axially symmetric and asymmetric thermal forcing, the equations
may possess one or two stable steady-state solutions, one or two
stable periodic solutions, or irregular (aperiodic) solutions. Qualitative
reasoning which has been applied to the real atmosphere may sometimes
be applied to the model, and checked for soundness by comparing the
conclusions with numerical solutions. The implications of irregularity
for the atmosphere and for atmospheric science are discussed.},
DOI = {10.1111/j.1600-0870.1984.tb00230.x}
}
@Article{Low58,
author = {F. E. Low},
title = {A {{Lagrangian}} formulation of the {{Boltzmann-Vlasov}} equation for plasmas},
journal = {Proc. R. Soc. London A},
year = {1958},
volume = {248},
pages = {282--287},
doi = {10.1098/rspa.1958.0244},
}
@Article{deLMeAvHo12,
author = {de Lozar, A. and Mellibovsky, F. and Avila, M. and Hof, B.},
title = {Edge state in pipe flow experiments},
journal = {Phys. Rev. Lett.},
year = {2012},
volume = {108},
pages = {214502},
doi = {10.1103/PhysRevLett.108.214502},
}
@Article{lozi2,
Title = {Un attracteur {\'e}trange (?) du type attracteur de {H\'enon}},
Author = {R. Lozi},
Journal = {J. Phys. (Paris) Colloq.},
Year = {1978},
Pages = {C5--9},
Volume = {39},
DOI = {10.1051/jphyscol:1978505}
}
@Article{LuOs13,
Title = {Exponential {B}-series: {The} stiff case},
Author = {V. T. Luan and A. Ostermann},
Journal = {SIAM J. Numer. Anal.},
Year = {2013},
Pages = {3431--3445i},
Volume = {51},
DOI = {10.1137/130920204}
}
@Article{LuanOster2014,
Title = {Explicit exponential {Runge--Kutta} methods of high order for parabolic problems},
Author = {Luan, V. T. and Ostermann, A.},
Journal = {J. Comput. Appl. Math.},
Year = {2014},
Pages = {168--179},
Volume = {256},
DOI = {10.1016/j.cam.2013.07.027}
}
@Article{Luan2014,
Title = {Exponential {Rosenbrock} methods of order five --- construction, analysis and numerical comparisons},
Author = {Luan, V. T. and Ostermann, A.},
Journal = {J. Comput. Appl. Math.},
Year = {2014},
Pages = {417--431},
Volume = {255},
DOI = {10.1016/j.cam.2013.04.041}
}
@Incollection{LuanOster2014_2,
author = {Luan, V. T. and Ostermann, A.},
title = {Stiff Order Conditions for Exponential {Runge--Kutta} Methods of Order Five},
booktitle = {{Modeling, Simulation and Optimization of Complex Processes - HPSC 2012: Proceedings of the Fifth International Conference on High Performance Scientific Computing, March 5-9, 2012, Hanoi, Vietnam }},
publisher = {Springer},
year = {2014},
editor = {Bock, G. H. and Hoang, P. X. and Rannacher, R. and Schl{\"o}der, P. J.},
pages = {133--143},
address = {Cham},
doi = {10.1007/978-3-319-09063-4_11},
}
@Article{Luce95,
Title = {Homoclinic explosions in the complex {Ginzburg-Landau} equation},
Author = {B. P. Luce},
Journal = {Physica D},
Year = {1995},
Pages = {553--581},
Volume = {84},
DOI = {10.1016/0167-2789(95)00047-8}
}
@Article{LucDoe1993,
Title = {Scaling of turbulent spike amplitudes in the complex {Ginzburg-Landau} equation},
Author = {{Luce}, B. P. and {Doering}, C. R.},
Journal = {Phys. Lett. A},
Year = {1993},
Pages = {92--98},
Volume = {178},
DOI = {10.1016/0375-9601(93)90733-g}
}
@Article{LundJohan91,
Title = {Direct simulation of turbulent spots in plane {Couette} flow},
Author = {A. Lundbladh and A. Johansson},
Journal = {J. Fluid Mech.},
Year = {1991},
Pages = {499--516},
Volume = {229}
}
@Book{LuoGuo12,
Title = {Vibro-impact Dynamics},
Author = {Luo, A.C.J. and Guo, Y.},
Publisher = {Wiley},
Year = {2012},
Address = {New York}
}
@Article{Lust01,
Title = {Improved numerical {Floquet} multipliers},
Author = {K. Lust},
Journal = {Int. J. Bifur. Chaos},
Year = {2001},
Pages = {2389--2410},
Volume = {11},
DOI = {10.1142/S0218127401003486}
}
@Article{NP,
author = {K. Lust and D. Roose},
title = {An adaptive {Newton-Picard} algorithm with subspace iteration for computing periodic solutions},
journal = {SIAM J. Sci. Comput.},
year = {1998},
volume = {19},
pages = {1188--1209},
doi = {10.1137/s1064827594277673},
}
@Article{Lyap1892,
Title = {Probl\`eme g\'en\'eral de la stabilit\'e du mouvement},
Author = {A. Lyapunov},
Journal = {Ann. Math. Studies},
Year = {1977},
Note = {Russian original Kharkow, 1892},
Volume = {17}
}
@Article{MuHeBrHaAl04,
Title = {Semiclassical foundation of universality in quantum chaos},
Author = {M{\"u}ller, S. and Heusler, S. and Braun, P. and Haake, F. and Altland, A.},
Journal = {Phys. Rev. Lett.},
Year = {2004},
Pages = {014103},
Volume = {93},
DOI = {10.1103/PhysRevLett.93.014103}
}
@Article{Maas11se,
author = {Maas, A.},
title = {Describing gauge bosons at zero and finite temperature},
journal = {Phys. Lett.},
year = {2013},
volume = {524},
pages = {203--300},
doi = {10.1016/j.physrep.2012.11.002},
}
@Article{macchi2013,
Title = {Ion acceleration by superintense laser-plasma interaction},
Author = {Macchi, A. and Borghesi, M. and Passoni, M.},
Journal = {Rev. Mod. Phys.},
Year = {2013},
Pages = {751--793},
Volume = {85},
Abstract = {Ion acceleration driven by superintense laser pulses is attracting
an impressive and steadily increasing effort. Motivations can be
found in the applicative potential and in the perspective to investigate
novel regimes as available laser intensities will be increasing.
Experiments have demonstrated, over a wide range of laser and target
parameters, the generation of multi-{MeV} proton and ion beams with
unique properties such as ultrashort duration, high brilliance, and
low emittance. An overview is given of the state of the art of ion
acceleration by laser pulses as well as an outlook on its future
development and perspectives. The main features observed in the experiments,
the observed scaling with laser and plasma parameters, and the main
models used both to interpret experimental data and to suggest new
research directions are described.},
DOI = {10.1103/RevModPhys.85.751}
}
@Article{MacZwa83,
Title = {Diffusion in a periodic {Lorentz} gas},
Author = {Machta, J. and Zwanzig, R.},
Journal = {Phys. Rev. Lett.},
Year = {1983},
Pages = {1959--1962},
Volume = {50},
DOI = {10.1103/PhysRevLett.50.1959}
}
@Article{MacKay84,
Title = {Equivariant universality classes},
Author = {R. S. MacKay},
Journal = {Phys. Lett. A},
Year = {1984},
Pages = {99--100},
Volume = {106},
DOI = {10.1016/0375-9601(84)90897-1}
}
@Book{Bmack93,
title = {{Renormalisation in Area-preserving Maps}},
publisher = {World Scientific},
year = {1993},
author = {MacKay, R. S.},
address = {Singapore},
doi = {10.1142/9789814354462},
}
@Article{MacMei83,
Title = {Linear stability of periodic orbits in {Lagrangian} systems},
Author = {R. S. Mackay and J. D. Meiss},
Journal = {Phys. Lett. A},
Year = {1983},
Pages = {92--94},
Volume = {98},
DOI = {10.1016/0375-9601(83)90735-1}
}
@Article{mackmeiss84,
author = {MacKay, R. S. and Meiss, J. D. and I. C. Percival},
title = {Transport in {Hamiltonian} systems},
journal = {Physica D},
year = {1984},
volume = {13},
pages = {55--81},
doi = {10.1016/0167-2789(84)90270-7},
}
@Article{mackmeiss87,
author = {MacKay, R. S. and Meiss, J. D. and I. C. Percival},
title = {Resonances in area preserving maps},
journal = {Physica D},
year = {1987},
volume = {27},
pages = {1--20},
doi = {10.1016/0167-2789(87)90002-9},
}
@Article{MacSch12,
Title = {Measuring shape with topology},
Author = {R. MacPherson and B. Schweinhart},
Journal = {J. Math. Phys.},
Year = {2012},
Pages = {073516},
Volume = {53},
DOI = {10.1063/1.4737391}
}
@Article{deMaere10,
Title = {Phase transition and correlation decay in coupled map lattices},
Author = {de Maere, A.},
Journal = {Commun. Math. Phys.},
Year = {2010},
Pages = {229--264},
Volume = {297},
DOI = {10.1007/s00220-010-1041-8}
}
@Article{MaScha94,
Title = {Landau gauge within the Gribov horizon},
Author = {Maggiore, N. and Schaden, M.},
Journal = {Phys. Rev. D},
Year = {1994},
Pages = {6616--6625},
Volume = {50},
DOI = {10.1103/PhysRevD.50.6616}
}
@Article{mahmoud08a,
Title = {Analysis of hyperchaotic complex {Lorenz} systems},
Author = {Mahmoud, G. M. and Ahmed, M. E. and Mahmoud, E. E.},
Journal = {Int. J. Modern Phys. C},
Year = {2008},
Pages = {1477--1494},
Volume = {19}
}
@Article{mahmoud08b,
Title = {Chaotic and hyperchaotic attractors of a complex nonlinear system},
Author = {Mahmoud, G.l M. and Al-Kashif, M. A. and Farghaly, A. A.},
Journal = {J. Phys. A},
Year = {2008},
Volume = {41}
}
@Article{mahmoud09,
author = {Mahmoud, G. M. and Bountis, T. and Al-Kashif, M. A. and Aly, S. A.},
title = {Dynamical properties and synchronization of complex non-linear equations for detuned lasers},
journal = {Dyn. Sys.},
year = {2009},
volume = {24},
pages = {63--79},
doi = {10.1080/14689360802438298},
}
@Article{Mainieri92a,
Title = {Thermodynamic zeta functions for {Ising} models with long-range interactions},
Author = {R. Mainieri},
Journal = {Phys. Rev. A},
Year = {1992},
Pages = {3580--3591},
Volume = {45}
}
@Article{Mainieri92b,
Title = {Zeta-Function for the {Lyapunov} exponent of a product of random matrices},
Author = {R. Mainieri},
Journal = {Phys. Rev. Lett.},
Year = {1992},
Pages = {1965--1968},
Volume = {68}
}
@Misc{Mainieri04,
author = {R. Mainieri},
title = {Can averaged orbits be used to extract scaling functions?},
year = {1993},
url = {http://arXiv.org/abs/chao-dyn/9302004},
}
@Book{Majda03,
title = {Introduction to PDEs and Waves for the Atmosphere and Ocean},
publisher = {American Mathematical Society},
year = {2003},
author = {A. Majda},
address = {New York},
doi = {10.1090/cln/009},
}
@Article{MajSte11,
Title = {Nonlinear dynamics and regional variations in the {MJO} skeleton},
Author = {Majda, A. J. and Stechmann, S. N.},
Journal = {J. Atmos. Sci.},
Year = {2011},
Pages = {3053--3071},
Volume = {68},
DOI = {10.1175/JAS-D-11-053.1}
}
@Article{Mak87,
Title = {Dissipative structure of a nonlinear baroclinic system: {Effect} of asymmetric friction},
Author = {Mak, M.},
Journal = {J. Atmos. Sci.},
Year = {1987},
Pages = {2613--2627},
Volume = {44},
DOI = {10.1175/1520-0469(1987)044<2613:DSOANB>2.0.CO;2}
}
@Article{MaRoLa02,
Title = {Partial reduction in the {N}-body planetary problem using the angular momentum integral},
Author = {Malige, F. and Robutel, P. and Laskar, J.},
Journal = {Celest. Mech. Dynam. Astronom.},
Year = {2002},
Pages = {283--316},
Volume = {84}
}
@Article{ChoMal95a,
Title = {Pattern formation and spatial chaos in lattice dynamical systems. {I}},
Author = {J. Mallet-Paret and S. N. Chow},
Journal = {IEEE Trans. Circuits Systems I Fund. Theory Appl.},
Year = {1995},
Pages = {746--751},
Volume = {42},
DOI = {10.1109/81.473583}
}
@Article{ChoMal95b,
Title = {Pattern formation and spatial chaos in lattice dynamical systems. {II}},
Author = {J. Mallet-Paret and S. N. Chow},
Journal = {IEEE Trans. Circuits Systems I Fund. Theory Appl.},
Year = {1995},
Pages = {752--756},
Volume = {42},
DOI = {10.1109/81.473584}
}
@Article{NLSmal91,
Title = {Modulational instabilities and soliton solutions of a generalized nonlinear Schr{\"{o}}dinger equation},
Author = {B. A. Malomed and L. Stenflo},
Journal = {J. Phys. A},
Year = {1991},
Pages = {L1149--L1153},
Volume = {24},
Abtract = {A {Hamiltonian} equation is proposed for the generalized nonlinear Schr{\"{o}}dinger equation. Soliton solutions are found and the stability of the plane waves is investigated.}
}
@Article{ManCho09b,
Title = {Snake solitons in the cubic--quintic {Ginzburg--Landau} equation},
Author = {Mancas, S. C. and Choudhury, R. S.},
Journal = {Math. and Comput. Simul.},
Year = {2009},
Pages = {73--82},
Volume = {80},
DOI = {10.1016/j.matcom.2009.06.017}
}
@Article{ManCho06,
Title = {Bifurcations and competing coherent structures in the cubic-quintic {Ginzburg--Landau} equation {I: Plane} wave {({CW})} solutions},
Author = {S. C. Mancas and S. R. Choudhury},
Journal = {Chaos Solit. Fract.},
Year = {2006},
Pages = {1256--1271},
Volume = {27},
DOI = {10.1016/j.chaos.2005.04.098}
}
@Article{ManCho06a,
Title = {Traveling wavetrains in the complex cubic-quintic {Ginzburg--Landau} equation},
Author = {S. C. Mancas and S. R. Choudhury},
Journal = {Chaos Solit. Fract.},
Year = {2006},
Pages = {834--843},
Volume = {28},
DOI = {10.1016/j.chaos.2005.08.080}
}
@Article{ManCho07a,
Title = {A novel variational approach to pulsating solitons in the cubic-quintic {Ginzburg--Landau} equation},
Author = {Mancas, S. C. and Choudhury, S. R.},
Journal = {Theoret. Math. Phys.},
Year = {2007},
Pages = {1160--1172},
Volume = {152},
DOI = {10.1007/s11232-007-0099-8}
}
@Article{ManCho07,
Title = {Bifurcations of plane wave {({CW})} solutions in the complex cubic-quintic {Ginzburg--Landau} equation},
Author = {S. C. Mancas and S. R. Choudhury},
Journal = {Math. Comput. Simul.},
Year = {2007},
Pages = {266 --280},
Volume = {74},
DOI = {10.1016/j.matcom.2006.10.009}
}
@Article{ManCho07b,
Title = {The complex cubic-quintic {Ginzburg--Landau} equation: {Hopf} bifurcations yielding traveling waves},
Author = {S. C. Mancas and S. R. Choudhury},
Journal = {Math. Comput. Simul.},
Year = {2007},
Pages = {281--291},
Volume = {74},
DOI = {10.1016/j.matcom.2006.10.022}
}
@Article{ManCho09,
Title = {Spatiotemporal structure of pulsating solitons in the cubic-quintic {Ginzburg--Landau} equation; a novel variational formulation},
Author = {S. C. Mancas and S. R. Choudhury},
Journal = {Chaos Solit. Fract.},
Year = {2009},
Pages = {91--105},
Volume = {40},
DOI = {10.1016/j.chaos.2007.07.046}
}
@Article{ManCho15,
Title = {Pulses and snakes in {Ginzburg--Landau} equation},
Author = {S. C. Mancas and S. R. Choudhury},
Journal = {Nonlinear Dyn.},
Year = {2015},
Pages = {549--571},
Volume = {79},
DOI = {10.1007/s11071-014-1686-5}
}
@Misc{ManKha13,
author = {S. C. Mancas and H. Khanal},
title = {Numerical simulations of snake dissipative solitons in complex cubic-quintic {Ginzburg--Landau} equation},
year = {2013},
url = {http://arxiv.org/abs/1305.1192},
}
@Book{mandel,
Title = {The Fractal Geometry of Nature},
Author = {B. B. Mandelbrot},
Publisher = {WH Freeman Co.},
Year = {1982},
Address = {New York},
ISBN = {9780716711865}
}
@Article{mangles04,
Title = {Monoenergetic beams of relativistic electrons from intense laser-plasma interactions},
Author = {Mangles, S. P. D. and Murphy, C. D. and Najmudin, Z. and Thomas, A. G. R. and Collier, J. L. and Dangor, A. E. and Divall, E. J. and Foster, P. S. and Gallacher, J. G. and Hooker, C. J. and Jaroszynski, D. A. and Langley, A. J. and Mori, W. B. and Norreys, P. A. and Tsung, F. S. and Viskup, R. and Walton, B. R. and Krushelnick, K.},
Journal = {Nature},
Year = {2004},
Pages = {535--538},
Volume = {431},
DOI = {10.1038/nature02939}
}
@Book{man90b,
Title = {Dissipative Structures and Weak Turbulence},
Author = {Manneville, P.},
Publisher = {Academic},
Year = {1990},
Address = {New York}
}
@Book{manneville_instabilities_2004,
title = {Instabilities, Chaos and Turbulence: An Introduction to Nonlinear Dynamics and Complex Systems},
publisher = {Imperial College Press},
year = {2004},
author = {Manneville, P.},
address = {London},
doi = {10.1142/p349},
}
@Article{Mann04,
Title = {Spots and turbulent domains in a model of transitional plane {Couette} flow},
Author = {P. {Manneville}},
Journal = {Theor. Comp. Fluid Dyn.},
Year = {2004},
Pages = {169--181},
Volume = {18},
DOI = {10.1007/s00162-004-0142-4}
}
@Article{MC96pha,
Title = {Phase turbulence in the two-dimensional complex {Ginzburg-Landau} equation},
Author = {Manneville, P. and Chat\'{e}, H.},
Journal = {Physica D},
Year = {1996},
Pages = {30--46},
Volume = {96},
Abtract = {instability of plane waves},
DOI = {10.1016/0167-2789(96)00045-0}
}
@Article{manning,
Title = {{Axiom A} diffeomorphisms have rational zeta function},
Author = {A. Manning},
Journal = {Bull. London Math. Soc.},
Year = {1971},
Pages = {215--220},
Volume = {3},
DOI = {10.1112/blms/3.2.215}
}
@Misc{MaSkAn11,
author = {{Manos}, T. and {Skokos}, C. and {Antonopoulos}, C.},
title = {Probing the local dynamics of periodic orbits by the generalized alignment index {(GALI)} method},
year = {2011},
url = {http://arXiv.org/abs/1103.0700},
}
@InProceedings{Mansfield06,
Title = {Noether's theorem for smooth, difference and finite element schemes},
Author = {E. L. Mansfield},
Booktitle = {Foundations of Computational Mathematics, Santander 2005},
Year = {2006},
Pages = {230--254},
Publisher = {Cambridge Univ. Press},
Series = {London Math. Soc. Lect. Notes},
Volume = {331},
URL = {https://www.kent.ac.uk/smsas/personal/elm2/liz/papers/focm.pdf}
}
@Book{Mansfield10,
title = {A practical guide to the invariant calculus},
publisher = {Cambridge Univ. Press},
year = {2010},
author = {Mansfield, E. L.},
address = {Cambridge},
doi = {10.1017/cbo9780511844621},
}
@Article{Marion1989,
author = {Marion, M. and T{\'e}mam, R.},
title = {Nonlinear {Galerkin} methods},
journal = {SIAM J. Numer. Anal.},
year = {1989},
volume = {26},
pages = {1139--1157},
doi = {10.1137/0726063},
}
@Article{Marques90,
Title = {On boundary conditions for velocity potentials in confined flows: {Application} to {Couette} flow},
Author = {Marqu\'es, F.},
Journal = {Phys. Fluids A},
Year = {1990},
Pages = {729--737},
Volume = {2},
DOI = {10.1063/1.857726}
}
@Article{Marquardt63,
Title = {An algorithm for least-squares estimation of nonlinear parameters},
Author = {Marquardt, D. M.},
Journal = {J. Soc. Indust. Appl. Math.},
Year = {1963},
Pages = {431--441},
Volume = {11},
DOI = {10.1137/0111030}
}
@Article{MarLopBla04,
Title = {Bifurcations in systems with {Z2} spatio-temporal and {O(2)} spatial symmetry},
Author = {F. Marques and J. M. Lopez and H. M. Blackburn},
Journal = {Physica D},
Year = {2004},
Pages = {247--276},
Volume = {189},
DOI = {10.1016/j.physd.2003.09.041}
}
@Book{Marsd92,
title = {Lectures on Mechanics},
publisher = {Cambridge Univ. Press},
year = {1992},
author = {Marsden, J. E.},
address = {Cambridge},
doi = {10.1017/cbo9780511624001},
}
@Book{marsdenbb,
title = {The {Hopf} Bifurcation and its Applications},
publisher = {Springer},
year = {1976},
author = {J. E. Marsden and M. McCracken},
address = {New York},
doi = {10.1007/978-1-4612-6374-6},
}
@Book{marsden_hamiltonian_2007,
Title = {Hamiltonian Reduction by Stages},
Author = {Marsden, J. E. and G. Misiolek and {J.-P.} Ortega and M. Perlmutter and T. S. Ratiu},
Publisher = {Springer},
Year = {1964},
Address = {New York}
}
@Book{MarRat99,
title = {{Introduction to Mechanics and Symmetry}},
publisher = {Springer},
year = {1999},
author = {Marsden, J. E. and Ratiu, T. S.},
address = {New York},
doi = {10.1007/978-0-387-21792-5},
}
@Article{MaWe74,
Title = {Reduction of symplectic manifolds with symmetry},
Author = {Marsden, J. E. and Weinstein, A.},
Journal = {Rep. Math. Phys.},
Year = {1974},
Pages = {121--30},
Volume = {5},
DOI = {10.1016/0034-4877(74)90021-4}
}
@Article{mart87lfa,
author = {C. C. Martens and M. J. Davis and G. S. Ezra},
title = {Local Frequency analysis of chaotic motion in multidimensional systems: energy transport and bottlenecks in planar {OCS}},
journal = {Chem. Phys. Lett.},
year = {1987},
volume = {142},
pages = {519--528},
doi = {10.1016/0009-2614(87)80655-3},
}
@Article{MaWaRe89,
Title = {Classical, semiclassical, and quantum mechanics of a globally chaotic system: Integrability in the adiabatic approximation},
Author = {C. C. Martens and R. L. Waterland and W. P. Reinhardt},
Journal = {J. Chem. Phys.},
Year = {1989},
Pages = {2328},
Volume = {90},
DOI = {10.1063/1.455974}
}
@Article{Martin06,
author = {P. A. Martin},
title = {Discrete scattering theory: {Green}'s function for a square lattice},
journal = {Wave Motion},
year = {2006},
volume = {43},
pages = {619--629},
doi = {10.1016/j.wavemoti.2006.05.006},
}
@Article{MaSiRo73,
author = {P. C. Martin and E. D. Siggia and H. A. Rose},
title = {Statistical dynamics of classical systems},
journal = {Phys. Rev. A},
year = {1973},
volume = {8},
pages = {423--437},
doi = {10.1103/PhysRevA.8.423},
publisher = {American Physical Society ({APS})},
}
@Article{nongal89,
author = {M. Martine and R. T{\'e}mam},
title = {Nonlinear {G{\"a}lerkin} methods},
journal = {SIAM J. Numer. Anal.},
year = {1989},
volume = {26},
number = {5},
pages = {1139--1157},
doi = {10.1137/0726063},
abstract = {nonlinear {G}{\"{a}}lerkin methods},
}
@Article{Marw08,
Title = {A historical review of recurrence plots},
Author = {N. Marwan},
Journal = {Eur. Phys. J.},
Year = {2008},
Pages = {3--12},
Volume = {164},
DOI = {10.1140/epjst/e2008-00829-1}
}
@Article{MRTK07,
Title = {Recurrence plots for the analysis of complex systems},
Author = {Marwan, N. and Romano, M. C. and Thiel, M. and Kurths, J.},
Journal = {Phys. Rep.},
Year = {2007},
Pages = {237},
Volume = {438},
DOI = {10.1016/j.physrep.2006.11.001}
}
@Article{M86,
Title = {Critical layers in shear flows},
Author = {S. A. Maslowe},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1986},
Pages = {405--432},
Volume = {18},
DOI = {10.1146/annurev.fluid.18.1.405}
}
@Article{MaSaTAS81,
author = {S. G. Matanyan and G. K. Savvidy and N. G. Ter-Arutyunyan-Savvidy},
title = {Classical {Yang-Mills} mechanics. {Nonlinear} color oscillations},
journal = {Sov. Phys. JETP},
year = {1981},
volume = {53},
pages = {830--838},
url = {http://www.jetp.ac.ru/cgi-bin/dn/e_053_03_0421.pdf},
}
@Article{Mat82,
Title = {Existence of quasiperiodic orbits for twist homeomorphisms of the annulus},
Author = {Mather, J. N.},
Journal = {Topology},
Year = {1982},
Pages = {457--467},
Volume = {21},
Annote = {Original paper abour Aubry-Mather sets},
DOI = {10.1016/0040-9383(82)90023-4}
}
@Article{Mather91,
Title = {Variational construction of orbits of twist difeomorphisms},
Author = {J. N. Mather},
Journal = {J. Am. Math. Soc.},
Year = {1991},
Pages = {207--263},
Volume = {4},
DOI = {10.2307/2939275}
}
@Book{MathWalk73,
title = {Mathematical Methods of Physics},
publisher = {Addison-Wesley},
year = {1973},
author = {J. Mathews and R. L. Walker},
address = {Reading, MA},
doi = {10.2307/2316002},
}
@Article{MHPRS07,
author = {Mathur, M. and Haller, G. and Peacock, T. and Ruppert-Felsot, J. E. and Swinney, H. L.},
title = {Uncovering the {Lagrangian} skeleton of turbulence},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {98},
pages = {144502},
doi = {10.1103/physrevlett.98.144502},
}
@Article{stabpcgl,
Title = {Stability of plane wave solutions of complex {Ginzburg-Landau} equations},
Author = {B. J. Matkowsky and V. Volpert},
Journal = {Quart. Appl. Math.},
Year = {1993},
Pages = {265--281},
Volume = {51},
DOI = {10.1090/qam/1218368}
}
@Article{maucher2013,
Title = {Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal {Schr\"odinger} equation},
Author = {Maucher, F. and Siminos, E. and Krolikowski, W. and Skupin, S.},
Journal = {New J. Phys.},
Year = {2013},
Pages = {083055},
Volume = {15},
Abstract = {Quasiperiodic oscillations and shape-transformations of
higher-order bright solitons in nonlinear nonlocal media have been
frequently observed numerically in recent years, however, the origin of
these phenomena was never completely elucidated. In this paper, we
perform a linear stability analysis of these higher-order solitons by
solving the Bogoliubov-de Gennes equations. This enables us to understand
the emergence of a new oscillatory state as a growing unstable mode of a
higher-order soliton. Using dynamically important states as a basis, we
provide low-dimensional visualizations of the dynamics and identify
quasiperiodic and homoclinic orbits, linking the latter to
shape-transformations.},
DOI = {10.1088/1367-2630/15/8/083055}
}
@Article{MaRi83,
Title = {Equation of motion for a small rigid sphere in a nonuniform flow},
Author = {{Maxey}, M.~R. and {Riley}, J.~J.},
Journal = {Phys. Fluids},
Year = {1983},
Pages = {883},
Volume = {26},
DOI = {10.1063/1.864230}
}
@Book{Mayer80,
title = {{The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics}},
publisher = {Springer},
year = {1980},
author = {Mayer, D. H.},
address = {Berlin},
isbn = {9783662186497},
doi = {10.1007/bfb0017919},
}
@InProceedings{MMRS05,
Title = {Relative periodic orbits in symmetric {Lagrangian} systems},
Author = {C. Mccord And J. Montaldi And M. Roberts And L. Sbano},
Booktitle = {{EQUADIFF} 2003},
Year = {2005},
Address = {Singapore},
Editor = {Dumortier, F. and Broer, H. W. and Mawhin, J. and Vanderbauwhede, A. and Verduyn Lunel, S.},
Pages = {482--493},
Publisher = {World Scientific},
DOI = {10.1142/9789812702067_0078}
}
@Article{mcord86,
Title = {Uniqueness of connection orbits in the equation {$y^{(3)}=y^2-1$}},
Author = {C. K. McCord},
Journal = {J. Math. Anal. Appl.},
Year = {1986},
Pages = {584--592},
Volume = {114},
DOI = {10.1016/0022-247X(86)90110-1}
}
@Unpublished{McICvi15,
Title = {Periodic orbit theory of linear response},
Author = {B. McInroe and P. Cvitanovi\'c},
Note = {In preparation},
Year = {2015}
}
@Article{McKean74,
Title = {Selberg's trace formula as applied to a compact {Riemann} surface},
Author = {McKean, H. P.},
Journal = {Commun. Pure Appl. Math.},
Year = {1972},
Pages = {225--246},
Volume = {25},
DOI = {10.1002/cpa.3160250302}
}
@Article{McKeon04,
author = {B. J. McKeon and J. Li and W. Jiang and J. F. Morrison and A. J. Smits},
title = {Further observations on the mean velocity distribution in fully developed pipe flow},
journal = {J. Fluid Mech.},
year = {2004},
volume = {501},
pages = {135--147},
doi = {10.1017/S0022112003007304},
}
@Article{McLPerlQui03,
Title = {Lie group foliations: dynamical systems and integrators},
Author = {R.I. McLachlan and M. Perlmutter and G.R.W. Quispel},
Journal = {Future Generation Computer Systems},
Year = {2003},
Pages = {1207--1219},
Volume = {19},
Abstract = {Foliate systems are those which preserve some (possibly singular)
foliation of phase space, such as systems with integrals, systems
with continuous symmetries, and skew product systems. We study numerical
integrators which also preserve the foliation. The case in which
the foliation is given by the orbits of an action of a Lie group
has a particularly nice structure, which we study in detail, giving
conditions under which all foliate vector fields can be written as
the sum of a vector field tangent to the orbits and a vector field
invariant under the group action. This allows the application of
many techniques of geometric integration, including splitting methods
and Lie group integrators.},
DOI = {10.1016/S0167-739X(03)00046-3}
}
@Article{McNMar01,
Title = {Origin of the hydrodynamic {Lyapunov modes}},
Author = {McNamara, S. and Mareschal, M.},
Journal = {Phys. Rev. E},
Year = {2001},
Pages = {051103},
Volume = {64},
DOI = {10.1103/PhysRevE.64.051103}
}
@Misc{MSBF16,
author = {E. S. Medeiros and I. L. Caldas and M. S. Baptista and U. Feudel},
title = {Trapping phenomenon attenuates tipping points for limit cycles},
year = {2016},
url = {https://arxiv.org/abs/1610.01656},
}
@Book{meer_hamiltonian_1994,
title = {Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance},
publisher = {Eindhoven Univ. of Technology, Dept. of Math. and Comp. Sci.},
year = {1994},
author = {J.C. van der Meer and J.A. Sanders and Vanderbauwhede, A.},
series = {Reports on applied and numerical analysis, RANA 94-02},
address = {Eindhoven},
doi = {10.1007/978-94-011-0956-7_19},
}
@Book{Mees81,
Title = {Dynamics of Feedback Systems},
Author = {Mees, A. I.},
Publisher = {Wiley},
Year = {1981},
Address = {New York}
}
@Book{mehta,
Title = {Random Matrices},
Author = {M. L. Mehta},
Publisher = {Academic},
Year = {1991},
Address = {New York}
}
@Article{meis92,
Title = {Symplectic maps, variational principles, and transport},
Author = {Meiss, J. D.},
Journal = {Rev. Mod. Phys.},
Year = {1992},
Pages = {795--848},
Volume = {64},
DOI = {10.1103/revmodphys.64.795}
}
@Book{Meisso7,
title = {Differential Dynamical Systems},
publisher = {SIAM},
year = {2007},
author = {J. D. Meiss},
address = {Philadelphia},
doi = {10.1137/1.9780898718232},
}
@Article{Mei08,
author = {J. D. Meiss},
title = {Visual explorations of dynamics: {The} standard map},
journal = {Pramana, Indian Acad. Sci.},
year = {2008},
volume = {70},
pages = {965--988},
doi = {10.1007/s12043-008-0103-3},
}
@Article{Mel99,
author = {Melbourne, I.},
title = {Steady-state bifurcation with {Euclidean} symmetry},
journal = {Trans. Amer. Math. Soc.},
year = {1999},
volume = {351},
pages = {1575--1603},
doi = {10.1090/S0002-9947-99-02147-9},
}
@Article{mellibovsky11,
Title = {{Takens--Bogdanov} bifurcation of travelling-wave solutions in pipe flow},
Author = {Mellibovsky, F. and Eckhardt, B.},
Journal = {J. Fluid Mech.},
Year = {2011},
Pages = {96--129},
Volume = {670},
DOI = {10.1017/s0022112010005239}
}
@Article{mellibovsky12,
Title = {From travelling waves to mild chaos: {A} supercritical bifurcation cascade in pipe flow},
Author = {F. Mellibovsky and B. Eckhardt},
Journal = {J. Fluid Mech.},
Year = {2012},
Pages = {149--190},
Volume = {709},
DOI = {10.1017/jfm.2012.326}
}
@Article{umb94pat,
author = {F. Melo and P. Umbanhowar and H. L. Swinney},
title = {Transition to parametric wave patterns in a vertically oscillated granular layer},
journal = {Phys. Rev. Lett.},
year = {1994},
volume = {72},
pages = {172--175},
doi = {10.1103/physrevlett.72.172},
}
@Article{Mendoza13,
author = {Mendoza, V.},
title = {Proof of the {Pruning Front Conjecture} for certain {H\'enon} parameters},
journal = {Nonlinearity},
year = {2013},
volume = {26},
pages = {679--690},
doi = {10.1088/0951-7715/26/3/679},
abstract = {The Pruning Front Conjecture is proved for an open set of H\'enon
parameters far from unimodal. More specifically, for an open subset
of H\'enon parameter space, consisting of two connected components
one of which intersects the area-preserving locus, it is shown that
the associated H\'enon maps are prunings of the horseshoe. In particular,
their dynamics is a subshift of the two-sided two-shift.},
}
@Article{MePrKn01,
author = {Mercader, I. and Prat, J. and Knobloch, E.},
title = {The {1:2} mode interaction in {Rayleigh B\'enard} convection with weakly broken midplane symmetry},
journal = {Int. J. Bifur. Chaos},
year = {2001},
volume = {11},
pages = {27--41},
doi = {10.1142/s0218127401002006},
}
@Article{MePrKn02,
Title = {Robust heteroclinic cycles in two-dimensional {Rayleigh-B\'enard} convection without {Boussinesq} symmetry},
Author = {Mercader, I. and Prat, J. and Knobloch, E.},
Journal = {Int. J. Bifur. Chaos},
Year = {2002},
Pages = {2501--2522},
Volume = {12},
DOI = {10.1142/S0218127402006047}
}
@Article{Mermin92,
Title = {The space groups of icosahedral quasicrystals and cubic, orthorhombic, monoclinic, and triclinic crystals},
Author = {Mermin, N. D.},
Journal = {Rev. Mod. Phys.},
Year = {1992},
Pages = {3--49},
Volume = {64},
DOI = {10.1103/RevModPhys.64.3}
}
@Article{Mertz79,
Title = {Speckle imaging, photon by photon},
Author = {L. N. Mertz},
Journal = {Appl. Opt.},
Year = {1979},
Pages = {611--614},
Volume = {18},
Abstract = {A speckle processing prescription is described that
should yield diffraction-limited performance for large telescopes
in spite of atmospheric turbulence and at light levels as low as
100 photons/sec in the picture. The prescription involves
rearranging the spatial frequency components of running glimpses of
the scene according to the complex information (entropy) of those
components. The imaginary part (phase) of the information is
rendered unambiguous by maintaining track of the phase. A 2-D
photon counter furnishes the raw observations. Comparisons and
ramifications of the procedure are discussed.},
DOI = {10.1364/AO.18.000611}
}
@Article{Meseguer03,
Title = {Streak breakdown instability in pipe {Poiseuille} flow},
Author = {A. Meseguer},
Journal = {Phys. Fluids},
Year = {2003},
Pages = {1203--1213},
Volume = {15},
DOI = {10.1063/1.1564093}
}
@Article{MeseguerANM07,
author = {A. Meseguer and F. Mellibovsky},
title = {On a solenoidal {Fourier-Chebyshev} spectral method for stability analysis of the {Hagen--Poiseuille} flow},
journal = {Appl. Numer. Math.},
year = {2007},
volume = {57},
pages = {920--938},
doi = {10.1016/j.apnum.2006.09.002},
}
@Article{MesTre03,
author = {{\'{A}}. Meseguer and L. N. Trefethen},
title = {Linearized pipe flow to {Reynolds} number {$10^7$}},
journal = {J. Comput. Phys.},
year = {2003},
volume = {186},
pages = {178--197},
doi = {10.1016/s0021-9991(03)00029-9},
}
@Article{varcyc,
Title = {{Newton} method for highly unstable orbits},
Author = {B. D. Mestel and I. Percival},
Journal = {Physica D},
Year = {1987},
Pages = {172},
Volume = {24},
DOI = {10.1016/0167-2789(87)90072-8}
}
@Book{Meyer00,
title = {{Matrix Analysis and Applied Linear Algebra}},
publisher = {SIAM},
year = {2000},
author = {Meyer, C.},
address = {Philadelphia},
doi = {10.1137/1.9780898719512},
}
@Book{MeyerHall92,
title = {{Introduction to {Hamiltonian} Dynamical Systems}},
publisher = {Springer},
year = {1992},
author = {K. R. Meyer and G. R. Hall},
address = {New York},
}
@Book{MeyerHall09,
title = {{Introduction to Dynamical Systems and the {N}-body Problem}},
publisher = {Springer},
year = {2009},
author = {K. R. Meyer and G. R. Hall and D. Offin},
address = {New York},
}
@Article{MeWi94,
author = {I. Mezi\'c and S. Wiggins},
title = {On the integrability and perturbation of three-dimensional fluid flows with symmetry},
journal = {J. Nonlin. Sci.},
year = {1994},
volume = {4},
pages = {157--194},
doi = {10.1007/bf02430631},
}
@Article{Mezzadri02,
Title = {On the multiplicativity of quantum cat maps},
Author = {F. Mezzadri},
Journal = {Nonlinearity},
Year = {2002},
Pages = {905--922},
Volume = {15},
DOI = {10.1088/0951-7715/15/3/323}
}
@Article{MicZhi01,
Title = {Symmetry, invariants, topology. Basic tools},
Author = {L. Michel and B.I. Zhilinski\'i},
Journal = {Phys. Lett.},
Year = {2001},
Pages = {11--84},
Volume = {341},
Abstract = {Elementary concepts of group actions: orbits and their
stabilizers, orbit types and their strata are introduced and illustrated
by simple examples. We give the unified description of these notions
which are often used in the different domains of physics under different
names. We also explain some basic facts about rings of invariant
functions and their module structure. This leads to a geometrical study
of the orbit space and of the level surfaces of invariant functions (e.g.
energy levels of Hamiltonians). Combining these tools with Morse theory
we study the extrema of invariant functions. Some physical applications
(not studied in other chapters) are sketched. },
DOI = {10.1016/S0370-1573(00)00088-0}
}
@Article{Mks86,
Title = {Steady solutions of the {Kuramoto-Sivashinsky} equation},
Author = {D. Michelson},
Journal = {Physica D},
Year = {1986},
Pages = {89--111},
Volume = {19},
DOI = {10.1016/0167-2789(86)90055-2}
}
@Article{Michel90,
author = {D. Michelson},
title = {Elementary particles as solutions of the {Sivashinsky} equation},
journal = {Physica D},
year = {1990},
volume = {44},
pages = {502--556},
doi = {10.1016/0167-2789(90)90160-q},
}
@Article{michsiv77,
Title = {Nonlinear analysis of hydrodynamic instability in laminar flames---{II}. {Numerical} experiments},
Author = {D. M. Michelson and G. I. Sivashinsky},
Journal = {Acta Astronaut.},
Year = {1977},
Pages = {1207--1221},
Volume = {4},
DOI = {10.1016/0094-5765(77)90097-2}
}
@Book{Mielke91,
Title = {{Hamiltonian and Lagrangian} Flows on Center Manifolds},
Author = {A. Mielke},
Publisher = {Springer},
Year = {1991},
Address = {New York}
}
@Incollection{Mielke02,
Title = {The {Ginzburg-Landau} equation in its role as a modulation equation},
Author = {A. Mielke},
Booktitle = {Handbook of Dynamical Systems, Vol. 2},
Publisher = {Elsevier},
Year = {2002},
Editor = {B. Fiedler},
Pages = {759--834},
DOI = {10.1016/S1874-575X(02)80036-4}
}
@Incollection{MilThu88,
Title = {Iterated maps of the interval},
Author = {Milnor, J. and Thurston, W.},
Booktitle = {{Dynamical {Systems} ({Maryland} 1986-87)}},
Publisher = {Springer},
Year = {1988},
Address = {New York},
Editor = {A. Dold and B. Eckmann},
Pages = {465--563},
DOI = {10.1007/BFb0082847}
}
@Misc{MiPlSt11,
Title = {On the steady state distributions for turbulence},
Author = {Mini\'c, Dj. and Pleimling, M. and Staples, A. E.},
Year = {2011},
URL = {http://arXiv.org/abs/1105.2941}
}
@Book{Mira87,
Title = {Chaotic dynamics -- {From} one dimensional endomorphism to two dimen\-sional diffeo\-morphism},
Author = {C. Mira},
Publisher = {World Scientific},
Year = {1987},
Address = {Singapore}
}
@Article{GL-Mir93,
Title = {The proto-{Lorenz} system},
Author = {Miranda, R. and Stone, E.},
Journal = {Phys. Lett. A},
Year = {1993},
Pages = {105--113},
Volume = {178},
DOI = {10.1016/0375-9601(93)90735-I}
}
@Article{mislor1,
Title = {Chaos in the {Lorenz} equations: {A} computer assisted proof part {II}: {Details}},
Author = {K. Mischaikow and M. Mrozek},
Journal = {Math. Comput.},
Year = {1998},
Pages = {1023--1047},
Volume = {67},
DOI = {10.1090/s0025-5718-98-00945-4}
}
@Article{misdis,
Title = {Construction of Symbolic Dynamics from Experimental Time Series},
Author = {K. Mischaikow and M. Mrozek and J. Reiss and A. Szymczak},
Journal = {Phys. Rev. Lett.},
Year = {1999},
Number = {6},
Pages = {1144--1147},
Volume = {82},
DOI = {10.1103/physrevlett.82.1144}
}
@Article{MiZg01,
Title = {Topological entropy for multidimensional perturbations of one dimensional maps},
Author = {M. Misiurewicz and P. Zgliczynski},
Journal = {Int. J. Bifur. Chaos},
Year = {2001},
Pages = {1443--1446},
Volume = {11},
DOI = {10.1142/s021812740100281x}
}
@Article{Mitchell12,
Title = {Partitioning two-dimensional mixed phase spaces},
Author = {K. A. Mitchell},
Journal = {Physica D},
Year = {2012},
Pages = {1718--1734},
Volume = {241},
DOI = {10.1016/j.physd.2012.07.004}
}
@Book{MitLop95,
title = {Nonlinear Mechanics, Groups and Symmetry},
publisher = {Kluwer},
year = {1995},
author = {Mitropolsky, Yu. A. and Lopatin, A. K.},
address = {Dordrecht},
doi = {10.1007/978-94-015-8535-4},
}
@Article{MizSat01,
Title = {Zeta functions of digraphs},
Author = {H. Mizuno and I. Sato},
Journal = {Linear Algebra Appl.},
Year = {2001},
Pages = {181--190},
Volume = {336},
DOI = {10.1016/S0024-3795(01)00318-4}
}
@Article{MEF04,
Title = {Fractal lifetimes in the transition to turbulence},
Author = {J. Moehlis and B. Eckhardt and H. Faisst},
Journal = {Chaos},
Year = {2004},
Pages = {S11},
Volume = {14},
DOI = {10.1063/1.1821751}
}
@Article{MFE04,
Title = {A low-dimensional model for turbulent shear flows},
Author = {J. Moehlis and H. Faisst and B. Eckhardt},
Journal = {New J. Phys.},
Year = {2004},
Pages = {56--56},
Volume = {6},
DOI = {10.1088/1367-2630/6/1/056}
}
@Article{MFE04b,
Title = {Periodic orbits and chaotic sets in a low-dimensional model for shear flows},
Author = {J. Moehlis and H. Faisst and B. Eckhardt},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2005},
Pages = {352--376},
Volume = {4},
DOI = {10.1137/040606144}
}
@Article{Mohammedi2014,
Title = {An accurate {Fourier} splitting scheme for solving the cubic-quintic complex {Ginzburg--Landau} equation},
Author = {T. Mohammedi and A. Aissat},
Journal = {Superlattices Microstruct.},
Year = {2014},
Pages = {424--434},
Volume = {75},
DOI = {10.1016/j.spmi.2014.08.007}
}
@Article{MHMwind96,
Title = {Winding number instability in the phase-turbulence regime of the complex {Ginzburg-Landau} equation},
Author = {R. Montagne and E. Hern\'{a}ndez-Garc\'{i}a and M. S. Miguel},
Journal = {Phys. Rev. Lett.},
Year = {1996},
Pages = {267--270},
Volume = {77},
DOI = {10.1103/physrevlett.77.267}
}
@Article{MoPaSp03,
Title = {Real {Floquet} factors of linear time-periodic systems},
Author = {P. Montagnier and C. C. Paige and R. J. Spiteri},
Journal = {Systems {\&} Control Lett.},
Year = {2003},
Pages = {251--262},
Volume = {50},
DOI = {10.1016/S0167-6911(03)00158-0},
URL = {http://www.cs.mcgill.ca/~chris/pub/MonPS03.pdf}
}
@Misc{Montanelli2016,
Title = {Solving stiff {PDE}s in {1D}, {2D} and {3D} with exponential integrators},
Author = {Montanelli, H. and Bootland, N.},
Year = {2016},
URL = {http://arxiv.org/abs/1604.08900}
}
@Article{MoSiSo07,
author = {Montgomery, K. A. and Silber, M. and Solla, S. A.},
title = {Amplification in the auditory periphery: {The} effect of coupling tuning mechanisms},
journal = {Phys. Rev. E},
year = {2007},
volume = {75},
pages = {051924},
doi = {10.1103/PhysRevE.75.051924},
}
@Article{Moore90,
Title = {Unpredictability and undecidability in dynamical systems},
Author = {Moore, C.},
Journal = {Phys. Rev. Lett.},
Year = {1990},
Pages = {2354--2357},
Volume = {64},
DOI = {10.1103/physrevlett.64.2354}
}
@Article{Moore91,
Title = {Generalized shifts: unpredictability and undecidability in dynamical systems},
Author = {Moore, C.},
Journal = {Nonlinearity},
Year = {1991},
Pages = {199--230},
Volume = {4},
DOI = {10.1088/0951-7715/4/2/002}
}
@Article{MS66,
Title = {A thermally excited nonlinear oscillator},
Author = {D. W. Moore and E. A. Spiegel},
Journal = {Astrophys. J.},
Year = {1966},
Pages = {871},
Volume = {143},
DOI = {10.1086/148562}
}
@Techreport{minpack,
Title = {{User Guide for MINPACK-1}},
Author = {Mor\'{e}, J. J. and Garbow, B. S. and Hillstrom, K. E. },
Institution = {Argonne National Laboratory},
Year = {1980},
Number = {ANL-80-74},
URL = {http://www.mcs.anl.gov/\~{}more/ANL8074a.pdf}
}
@Article{MoHoBe87,
Title = {Diffusion in a periodic {Lorentz} gas},
Author = {Moran, B. and Hoover, W. G. and Bestiale, S.},
Journal = {J. Stat. Phys.},
Year = {1987},
Pages = {709--726},
Volume = {48},
DOI = {10.1007/BF01019693}
}
@Article{Morena2014,
Title = {On the potential for entangled states between chaotic systems},
Author = {Morena, M.A. and Short, K.M.},
Journal = {Int. J. Bifur. Chaos},
Year = {2014},
Volume = {24},
Abstract = {We report on the tendency of chaotic systems to be controlled
onto their unstable periodic orbits in such a way that these orbits are
stabilized. The resulting orbits are known as cupolets and collectively
provide a rich source of qualitative information on the associated
chaotic dynamical system. We show that pairs of interacting cupolets may
be induced into a state of mutually sustained stabilization that requires
no external intervention in order to be maintained and is thus considered
bound or entangled. A number of properties of this sort of entanglement
are discussed. For instance, should the interaction be disturbed, then
the chaotic entanglement would be broken. Based on certain properties of
chaotic systems and on examples which we present, there is further
potential for chaotic entanglement to be naturally occurring. A
discussion of this and of the implications of chaotic entanglement in
future research investigations is also presented.},
DOI = {10.1142/S0218127414500771}
}
@Article{pimsimp,
Title = {The {PIM}-simplex method: an extension of the {PIM}-triple method to saddles with an arbitrary number of expanding directions},
Author = {P. Moresco and S. P. Dawson},
Journal = {Physica D},
Year = {1999},
Pages = {38--48},
Volume = {126},
DOI = {10.1016/s0167-2789(98)00234-6}
}
@Article{MFKM10,
Title = {Scytale decodes chaos: {A} method for estimating unstable symmetric solutions},
Author = {Morita, Y. and Fujiwara, N. and Kobayashi, M. U. and Mizuguchi, T.},
Journal = {Chaos},
Year = {2010},
Pages = {013126},
Volume = {20},
DOI = {10.1063/1.3365053}
}
@InProceedings{Morkovin69,
author = {M. V. Morkovin},
title = {On the many faces of transition},
booktitle = {Viscous Drag Reduction},
year = {1969},
editor = {C. S. Wells},
pages = {1--31},
address = {New York},
publisher = {Plenum},
doi = {10.1007/978-1-4899-5579-1_1},
}
@Article{Morrison02,
author = {J. F. Morrison and W. Jiang and B. J. McKeon and A. J. Smits},
title = {Reynolds number dependence of streamwise velocity spectra in turbulent pipe flow},
journal = {Phys. Rev. Lett.},
year = {2002},
volume = {88},
pages = {214501},
doi = {10.1103/physrevlett.88.214501},
}
@Article{Morrison04,
author = {J. F. Morrison and B. J. McKeon and W. Jiang and A. J. Smits},
title = {Scaling of the streamwise velocity component in turbulent pipe flow},
journal = {J. Fluid Mech.},
year = {2004},
volume = {508},
pages = {99--131},
doi = {10.1017/s0022112004008985},
}
@Article{Morr80,
author = {Morrison, P. J.},
title = {The {Maxwell-Vlasov} equations as a continuous {Hamiltonian} system},
journal = {Phys. Lett. A},
year = {1980},
volume = {80},
pages = {383--386},
doi = {10.2172/5017455},
}
@Article{Morr98,
author = {Morrison, P. J.},
title = {Hamiltonian description of the ideal fluid},
journal = {Rev. Mod. Phys.},
year = {1998},
volume = {70},
pages = {467--521},
doi = {10.2172/10128748},
}
@Article{MorrGree80,
author = {Morrison, P. J. and J. M. Greene},
title = {Noncanonical {Hamiltonian} density formulation of hydrodynamics and ideal magnetohydrodynamics},
journal = {Phys. Rev. Lett.},
year = {1980},
volume = {45},
pages = {790--794},
note = {See also Phys. Rev. Lett. 48, 569 (1982)},
doi = {10.1103/PhysRevLett.45.790},
}
@Article{MR94,
author = {G. P. Morriss and L. Rondoni},
title = {Periodic orbit expansions for the Lorentz gas},
journal = {J. Stat. Phys.},
year = {1994},
volume = {75},
pages = {553--584},
doi = {10.1007/BF02186872},
}
@Article{moser96,
Title = {A rapidly converging iteration method and nonlinear partial differential equations {I.}},
Author = {J. Moser},
Journal = {Ann. Scuola Norm. Super. Pisa},
Year = {1966},
Pages = {265--315},
Volume = {20},
URL = {http://www.numdam.org/item?id=ASNSP_1966_3_20_2_265_0}
}
@Article{moser96a,
Title = {A rapidly converging iteration method and nonlinear partial differential equations {II.}},
Author = {J. Moser},
Journal = {Ann. Scuola Norm. Super. Pisa},
Year = {1966},
Pages = {499--535},
Volume = {20},
URL = {http://www.numdam.org/numdam-bin/item?id=ASNSP_1966_3_20_3_499_0}
}
@Book{mosersr,
title = {{Stable and Random Motions in Dynamical Systems}},
publisher = {Princeton Univ. Press},
year = {1973},
author = {J. Moser},
address = {Princeton NJ},
doi = {10.1515/9781400882694},
}
@Article{moser86,
Title = {Minimal solutions of variational problems on a torus},
Author = {J. Moser},
Journal = {Ann. Inst. H. Poincar{\'e} Anal. Non Lin{\'e}aire},
Year = {1986},
Pages = {229--272},
Volume = {3},
URL = {http://www.numdam.org/numdam-bin/item?id=AIHPC_1986__3_3_229_0}
}
@Article{Mo86b,
Title = {Recent developments in the theory of {Hamiltonian} systems},
Author = {Moser, J.},
Journal = {SIAM Rev.},
Year = {1986},
Pages = {459--485},
Volume = {28},
Annote = {overview over KAM theory and Aubry-Mather; stability of fixed points},
DOI = {10.1137/1028153}
}
@Article{Mostow57,
Title = {Equivariant embeddings in {Euclidean} space},
Author = {G. D. Mostow},
Journal = {Ann. Math.},
Year = {1957},
Pages = {432--446},
Volume = {65},
DOI = {10.2307/1970055}
}
@Article{motter03,
Title = {Relativistic chaos is coordinate invariant},
Author = {Motter, A. E.},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Pages = {231101},
Volume = {91},
Abstract = {The noninvariance of Lyapunov exponents in general relativity has
led to the conclusion that chaos depends on the choice of the space-time
coordinates. Strikingly, we uncover the transformation laws of Lyapunov
exponents under general space-time transformations and we find that
chaos, as characterized by positive Lyapunov exponents, is coordinate
invariant. As a result, the previous conclusion regarding the noninvariance
of chaos in cosmology, a major claim about chaos in general relativity,
necessarily involves the violation of hypotheses required for a proper
definition of the Lyapunov exponents.},
DOI = {10.1103/PhysRevLett.91.231101}
}
@Article{Motter09,
author = {Motter, A. E. and Gelfert, K.},
title = {Time-metric equivalence and dimension change under time reparameterizations},
journal = {Phys. Rev. E},
year = {2009},
volume = {79},
pages = {065202},
doi = {10.1103/physreve.79.065202},
}
@Article{motter09-1,
Title = {Relativistic invariance of {Lyapunov} exponents in bounded and unbounded systems},
Author = {Motter, A. E. and Saa, A.},
Journal = {Phys. Rev. Lett.},
Year = {2009},
Month = may,
Number = {18},
Pages = {184101},
Volume = {102},
Abstract = {The study of chaos in relativistic systems has been hampered by the
observer dependence of Lyapunov exponents ({LEs)} and of conditions,
such as orbit boundedness, invoked in the interpretation of {LEs}
as indicators of chaos. Here we establish a general framework that
overcomes both difficulties and apply the resulting approach to address
three fundamental questions: how {LEs} transform under Lorentz and
Rindler transformations and under transformations to uniformly rotating
frames. The answers to the first and third questions show that inertial
and uniformly rotating observers agree on a characterization of chaos
based on {LEs.} The second question, on the other hand, is an ill-posed
problem due to the event horizons inherent to uniformly accelerated
observers.},
DOI = {10.1103/PhysRevLett.102.184101}
}
@Incollection{MuPe06,
author = {T. Mullin and J. Peixinho},
title = {Recent observations of the transition to turbulence in a pipe},
booktitle = {{IUTAM Symposium on Laminar-Turbulent Transition}},
publisher = {Springer},
year = {2006},
editor = {Govindarajan, R.},
volume = {78},
series = {Fluid Mechanics and Its Applications},
pages = {45--55},
address = {New York},
doi = {10.1007/1-4020-4159-4_5},
}
@Article{Mummert08,
author = {P. P. Mummert},
title = {Holomorphic shadowing for {H\'enon} maps},
journal = {Nonlinearity},
year = {2008},
volume = {21},
pages = {2887--2898},
doi = {10.1088/0951-7715/21/12/009},
}
@Article{munoz-almaraz_continuation_2003,
Title = {Continuation of periodic orbits in conservative and {Hamiltonian} systems},
Author = {Munoz-Almaraz, F. J. and Freire, E. and Galan, J. and Doedel, E. J. and Vanderbauwhede, A.},
Journal = {Physica D},
Year = {2003},
Pages = {1--38},
Volume = {181},
DOI = {10.1016/s0167-2789(03)00097-6}
}
@Article{muloz-almaraz_continuation_2007,
Title = {Continuation of normal doubly symmetric orbits in conservative reversible systems},
Author = {Munoz-Almaraz, F. J. and Freire, E. and Galan, J. and Vanderbauwhede, A.},
Journal = {Celest. Mech. Dynam. Astronom.},
Year = {2006},
Pages = {17--47},
Volume = {97},
DOI = {10.1007/s10569-006-9048-3}
}
@Article{MuntheKaas99,
Title = {High order {Runge-Kutta} methods on manifolds},
Author = {H. Munthe-Kaas},
Journal = {Appl. Numer. Math.},
Year = {1999},
Pages = {115--127},
Volume = {29},
DOI = {10.1016/S0168-9274(98)00030-0}
}
@Article{Murat03,
author = {Muratore-Ginanneschi, P.},
title = {Path integration over closed loops and {Gutzwiller}'s trace formula},
journal = {Phys. Rep.},
year = {2002},
volume = {383},
pages = {299--397},
doi = {10.1016/S0370-1573(03)00212-6},
}
@Article{Nachtigal1992,
Title = {How fast are nonsymmetric matrix iterations?},
Author = {Nachtigal, N. M. and Reddy, S. C. and Trefethen, L. N.},
Journal = {SIAM J. Matrix Anal. Appl.},
Year = {1992},
Pages = {778--795},
Volume = {13},
DOI = {10.1137/0613049}
}
@Article{N90,
Title = {Three-dimensional finite-amplitude solutions in plane {Couette} flow: bifurcation from infinity},
Author = {M. Nagata},
Journal = {J. Fluid Mech.},
Year = {1990},
Pages = {519--527},
Volume = {217},
DOI = {10.1017/S0022112090000829}
}
@Article{N97,
author = {Nagata, M.},
title = {Three-dimensional traveling-wave solutions in plane {Couette} flow},
journal = {Phys. Rev. E},
year = {1997},
volume = {55},
pages = {2023--2025},
doi = {10.1103/physreve.55.2023},
}
@Article{NajHav95,
Title = {Derivatives of the matrix exponential and their computation},
Author = {I. Najfeld and T. F. Havel},
Journal = {Adv. Appl. Math.},
Year = {1995},
Pages = {321--375},
Volume = {16},
DOI = {10.1006/aama.1995.1017}
}
@Book{Naka90,
title = {Geometry, Topology and Physics},
publisher = {Inst. of Physics Publ.},
year = {1990},
author = {M. Nakahara},
address = {Bristol},
doi = {10.1887/0750306068},
}
@Article{Nambu73,
Title = {Generalized {Hamiltonian} dynamics},
Author = {Nambu, Y.},
Journal = {Phys. Rev. D},
Year = {1973},
Pages = {2405--2414},
Volume = {7},
DOI = {10.1103/PhysRevD.7.2405}
}
@Article{Neimark59,
Title = {On some cases of periodic motions depending on parameters},
Author = {Neimark, J.},
Journal = {Dokl. Akad. Nauk SSSR},
Year = {1959},
Note = {in Russian},
Pages = {736--739},
Volume = {129}
}
@Article{Neu79a,
Title = {Chemical waves and the diffusive coupling of limit cycle oscillators},
Author = {John C. Neu},
Journal = {SIAM J. Appl. Math.},
Year = {1979},
Pages = {509--515},
Volume = {36},
DOI = {10.1137/0136038}
}
@Article{Neu79,
Title = {Coupled chemical oscillators},
Author = {J. C. Neu},
Journal = {SIAM J. Appl. Math.},
Year = {1979},
Pages = {307--315},
Volume = {37},
DOI = {10.1137/0137022}
}
@Article{neumann,
Title = {{Uber merkw{\"u}rdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen}},
Author = {J. von Neumann and E. P. Wigner},
Journal = {Phys. Zeit.},
Year = {1929},
Pages = {467--470},
Volume = {30},
DOI = {10.1007/978-3-662-02781-3_20}
}
@Article{newenv74,
Title = {Envelope equations},
Author = {A. C. Newell},
Journal = {Lect. Appl. Math.},
Year = {1974},
Pages = {157--163},
Volume = {15}
}
@Article{nhouse74,
Title = {Diffeomorphisms with infinitely many sinks},
Author = {Newhouse, S. E.},
Journal = {Topology },
Year = {1974},
Pages = {9--18},
Volume = {13},
DOI = {10.1016/0040-9383(74)90034-2}
}
@Article{nhouse79,
Title = {The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms},
Author = {Newhouse, S. E.},
Journal = {Publ. Math., Inst. Hautes Etud. Sci.},
Year = {1979},
Pages = {101--152},
Volume = {50},
DOI = {10.1007/BF02684771}
}
@Article{nhouse78,
author = {S. E. Newhouse and D. Ruelle and F. Takens},
title = {Occurrence of strange {Axiom A} attractors near quasi-periodic flows on ${T}^m$ $(m=3$ or more)},
journal = {Commun. Math. Phys.},
year = {1978},
volume = {64},
pages = {35--40},
doi = {10.1007/BF01940759},
}
@Book{Newman12,
Title = {{Computational Physics}},
Author = {Newman, M. E. J.},
Publisher = {Createspace Independent Pub},
Year = {2012},
ISBN = {9781480145511}
}
@Article{NS86,
Title = {Instabilities of {Ginzburg-Landau} equation: {Pt. II, },secondary bifurcation},
Author = {P. K. Newton and L. Sirovich},
Journal = {Quart. Appl. Math.},
Year = {1986},
Pages = {367--374},
Volume = {44},
URL = {http://www.jstor.org/stable/43637380}
}
@Article{NS86a,
Title = {Instabilities of {Ginzburg-Landau} equation: periodic solutions},
Author = {P. K. Newton and L. Sirovich},
Journal = {Quart. Appl. Math.},
Year = {1986},
Pages = {49--58},
Volume = {44},
URL = {http://www.jstor.org/stable/43637346}
}
@Article{Nichkawde13,
Title = {Optimal state-space reconstruction using derivatives on projected manifold},
Author = {Nichkawde, C.},
Journal = {Phys. Rev. E},
Year = {2013},
Pages = {022905},
Volume = {87},
DOI = {10.1103/PhysRevE.87.022905}
}
@Article{Nickel07,
Title = {Travelling wave solutions to the {Kuramoto-Sivashinsky} equation},
Author = {J. Nickel},
Journal = {Chaos Solit. Fract.},
Year = {2007},
Pages = {1376--1382},
Volume = {33},
DOI = {10.1016/j.chaos.2006.01.087}
}
@Article{Nicolaenko86,
Title = {Some mathematical aspects of flame chaos and flame multiplicity},
Author = {B. Nicolaenko},
Journal = {Physica D},
Year = {1986},
Pages = {109--121},
Volume = {20},
DOI = {10.1016/0167-2789(86)90099-0}
}
@Article{NSTks85,
author = {B. Nicolaenko and B. Scheurer and R. T{\'e}mam},
title = {Some global dynamical properties of the {Kuramoto-Sivashinsky} equations: nonlinear stability and attractors},
journal = {Physica D},
year = {1985},
volume = {16},
pages = {155--183},
doi = {10.1016/0167-2789(85)90056-9},
}
@Article{NingHakenCLE90,
author = {Ning, C. Z. and Haken, H.},
title = {Detuned lasers and the complex {Lorenz} equations: {Subcritical} and supercritical {Hopf} bifurcations},
journal = {Phys. Rev.},
year = {1990},
volume = {41},
pages = {3826--3837},
doi = {10.1103/physreva.41.3826},
}
@Article{NiHa91,
author = {Ning, C. Z. and Haken, H.},
title = {Phase anholonomy in dissipative optical-systems with periodic oscillations},
journal = {Phys. Rev. A},
year = {1991},
volume = {43},
pages = {6410--6413},
doi = {10.1103/physreva.43.6410},
}
@Article{NiHa92,
author = {Ning, C. Z. and Haken, H.},
title = {An invariance property of the geometrical phase and its consequence in detuned lasers},
journal = {Z. Phys. B},
year = {1992},
volume = {89},
pages = {261--262},
doi = {10.1007/bf01318153},
}
@Article{NiHa92a,
author = {C. Z. Ning and H. Haken},
title = {Geometrical phase and amplitude accumulations in dissipative systems with cyclic attractors},
journal = {Phys. Rev. Lett.},
year = {1992},
volume = {68},
pages = {2109--2112},
doi = {10.1103/physrevlett.68.2109},
}
@Article{NTOD92,
Title = {Search for regular orbits in the {$x^2 y^2$} potential problem},
Author = {M. L. A. Nip and J. A. Tuszynski and M. Otwinowski and J. M. Dixon},
Journal = {J. Phys. A},
Year = {1992},
Pages = {5553},
Volume = {25},
Abstract = {Analytical and numerical investigation is provided into the motion
of a particle close to unstable straight-interval y=+or-x orbits
in the system H=1/2(p 2 x +p 2 y +x 2 y 2 ). Physical interpretation
is provided which involves a perturbation analysis leading to doubly
periodic solutions for x(t) and y(t). Second-order ordinary differential
equations are derived to describe the trajectory of the particle
in the x-y plane and the functional form of x(t).},
DOI = {10.1088/0305-4470/25/21/014}
}
@Article{Nizette2001,
Title = {Stability and bifurcations of periodically modulated, optically injected laser diodes},
Author = {M. Nizette and T. Erneux and A. Gavrielides and V. Kovanis},
Journal = {Phys. Rev. E},
Year = {2001},
Pages = {026212},
Volume = {63},
DOI = {10.1103/physreve.63.026212}
}
@Article{Noether15,
Title = {{Der Endlichkeitssatz der Invarianten endlicher Gruppen}},
Author = {Noether, E.},
Journal = {Math. Ann.},
Year = {1915},
Pages = {89--92},
Volume = {77},
DOI = {10.1007/BF01456821}
}
@Article{Nonnen03,
Title = {Spectral properties of noisy classical and quantum propagators},
Author = {S. Nonnenmacher},
Journal = {Nonlinearity},
Year = {2003},
Pages = {1685--1713},
Volume = {16},
DOI = {10.1088/0951-7715/16/5/309}
}
@Article{NoTaDauTu04,
Title = {Survey of instability thresholds of flow between exactly counter-rotating disks},
Author = {C. Nore and M. Tartar and O. Daube and L. S. Tuckerman},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {45--65},
Volume = {511},
DOI = {10.1017/S0022112004008559}
}
@Article{NoFre82,
Title = {Transition to chaos in the {Duffing} oscillator},
Author = {S. Novak and R. G. Frehlich},
Journal = {Phys. Rev. A},
Year = {1982},
Pages = {3660--3663},
Volume = {26},
DOI = {10.1103/PhysRevA.26.3660}
}
@Article{bknk83,
Title = {Pattern selection and spatiotemporal transition to chaos in the {Ginzburg-Landau} equation},
Author = {K. Nozaki and N. Bekki},
Journal = {Phys. Rev. Lett.},
Year = {1983},
Pages = {2171--2174},
Volume = {51},
DOI = {10.1103/physrevlett.51.2171}
}
@Article{bknk84,
Title = {Exact solutions of the generalized {Ginzburg-Landau} equation},
Author = {K. Nozaki and N. Bekki},
Journal = {J. Phys. Soc. Japan},
Year = {1984},
Pages = {1581--1582},
Volume = {53},
DOI = {10.1143/jpsj.53.1581}
}
@Article{pimyk,
Title = {A procedure for finding numerical trajectories on chaotic saddles},
Author = {H. E. Nusse and J. A. Yorke},
Journal = {Physica D},
Year = {1989},
Pages = {137--156},
Volume = {36},
DOI = {10.1016/0167-2789(89)90253-4}
}
@Article{OhlRav13,
Title = {Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing},
Author = {M. Ohlberger and S. Rave},
Journal = {Comptes Rendus Mathematique},
Year = {2013},
Pages = {901--906},
Volume = {351},
Abstract = {Abstract We present a new method for the nonlinear
approximation of the solution manifolds of parameterized nonlinear
evolution problems, in particular in hyperbolic regimes with moving
discontinuities. Given the action of a Lie group on the solution space,
the original problem is reformulated as a partial differential algebraic
equation system by decomposing the solution into a group component and a
spatial shape component, imposing appropriate algebraic constraints on
the decomposition. The system is then projected onto a reduced basis
space. We show that efficient online evaluation of the scheme is possible
and study a numerical example showing its strongly improved performance
in comparison to a scheme without freezing. },
DOI = {10.1016/j.crma.2013.10.028}
}
@Article{Olmsted94,
Title = {Rotational invariance and {Goldstone modes} in nematic elastomers and gels},
Author = {Olmsted, P. D.},
Journal = {J. Phys. II France},
Year = {1994},
Pages = {2215--2230},
Volume = {4},
DOI = {10.1051/jp2:1994257}
}
@Book{liede,
Title = {Applications of Lie Groups to Differential Equations},
Author = {P. J. Olver},
Publisher = {Springer},
Year = {1998},
Address = {New York}
}
@Book{OlverInv,
title = {Classical Invariant Theory},
publisher = {Cambridge Univ. Press},
year = {1999},
author = {P. J. Olver},
address = {Cambridge},
isbn = {9780521558211},
doi = {10.1017/cbo9780511623660},
}
@Article{OlVa94,
Title = {A continuation method to study periodic orbits of the {Froeschl\'e} map},
Author = {A. Olvera and C. Vargas},
Journal = {Physica D},
Year = {1994},
Pages = {351--371},
Volume = {72},
Abstract = {The dynamics of many Hamiltonian systems with three degrees of freedom
is represented by the Froeschl\'e map which is symplectic and four-dimensional.
In this paper we study sequences of periodic orbits approaching the
invariant tori in order to obtain information about its stability.
A homotopic method is used to continue the branches of periodic orbits.
We found that the existence of turning points is related to the linear
stability of the periodic orbit and its rotation vector.},
DOI = {10.1016/0167-2789(94)90238-0}
}
@Article{Onsager44,
Title = {Crystal Statistics. {I. A Two}-Dimensional Model with an Order-Disorder Transition},
Author = {Onsager, L.},
Journal = {Phys. Rev.},
Year = {1944},
Pages = {117--149},
Volume = {65},
DOI = {10.1103/PhysRev.65.117}
}
@Article{Onsager53,
Title = {Fluctuations and irreversible processes},
Author = {L. Onsager and S. Machlup},
Journal = {Phys. Rev.},
Year = {1953},
Pages = {1505--1512},
Volume = {91},
DOI = {10.1103/PhysRev.91.1505}
}
@Article{Orszag71,
Title = {Accurate solution of the {Orr-Sommerfeld} stability equation},
Author = {S. A. Orszag},
Journal = {J. Fluid Mech.},
Year = {1971},
Pages = {689},
Volume = {50},
DOI = {10.1017/s0022112071002842}
}
@Article{Orszag1,
Title = {Boundary conditions for incompressible flows},
Author = {S. A. Orszag and M. Israeli and M. Deville},
Journal = {J. Sci. Comput.},
Year = {1986},
Pages = {75--111},
Volume = {1},
DOI = {10.1007/bf01061454}
}
@Incollection{BrCv12,
author = {Ortega Arango, S.},
title = {Towards reducing continuous symmetry of baroclinic flows},
booktitle = {{ChaosBook.org/projects}},
publisher = {Georgia Inst. of Technology},
year = {2012},
chapter = {Towards reducing continuous symmetry of baroclinic flows},
url = {http://ChaosBook.org/projects/index.shtml#Ortega},
}
@Article{OrRa04,
Title = {Symmetry reduction in symplectic and {Poisson} geometry},
Author = {J.-P. Ortega and T. S. Ratiu},
Journal = {Lett. Math. Phys.},
Year = {2004},
Pages = {11--60},
Volume = {69},
DOI = {10.1007/s11005-004-0898-x}
}
@Article{lyaos,
Title = {A multiplicative ergodic theorem. {Liapunov} characteristic numbers for dynamical systems},
Author = {V. I. Oseledec},
Journal = {Trans. Moscow Math. Soc.},
Year = {1968},
Pages = {197--221},
Volume = {19},
Abstract = {The Liapunov characteristic numbers are defined by investigating the
limiting volume of infinitesimal size. Their existence is proved
by construction and application of the ergodic theorem. At a.e. every
point, the tangent space is divided into stable and unstable subspace
corresponding the positive and negative Liapunov numbers. If the
eigenvalues are non-degenerate, the Liapunov vectors are well defined
a.e.},
URL = {http://mi.mathnet.ru/eng/mmo214}
}
@Book{ottbook,
title = {Chaos and Dynamical Systems},
publisher = {Cambridge Univ. Press},
year = {2002},
author = {E. Ott},
address = {Cambridge},
doi = {10.1017/cbo9780511803260},
}
@Article{OttYo08:3503096,
Title = {When {Lyapunov} exponents fail to exist},
Author = {Ott, W. and Yorke, J. A.},
Journal = {Phys. Rev. E},
Year = {2008},
Volume = {78},
DOI = {10.1103/physreve.78.056203}
}
@Book{Botti89,
Title = {The Kinematics of Mixing: Stretching, Chaos and Transport},
Author = {Ottino, J. M.},
Publisher = {Cambridge Univ. Press},
Year = {1989},
Address = {Cambridge},
ISBN = {9780521368780}
}
@Article{OzHaRoBu13,
Title = {Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization},
Author = {Oza, A. U. and Harris, D. M. and Rosales, R. R. and Bush, J. W. M.},
Journal = {J. Fluid Mech.},
Year = {2014},
Pages = {404--429},
Volume = {744},
DOI = {10.1017/jfm.2014.50}
}
@Article{OzRoBu13,
Title = {A trajectory equation for walking droplets: hydrodynamic pilot-wave theory},
Author = {Oza, A. U. and Rosales, R. R. and Bush, J. W. M.},
Journal = {J. Fluid Mech.},
Year = {2013},
Pages = {552--570},
Volume = {737},
DOI = {10.1017/jfm.2013.581}
}
@Book{almeida88,
Title = {Hamiltonian Systems: Chaos and Quantization},
Author = {Ozorio de Almeida, A. M.},
Publisher = {Cambridge Univ. Press},
Year = {1988},
Address = {Cambridge},
ISBN = {9780521386708}
}
@Article{OzoHan84,
Title = {Periodic orbits and a correlation function for the semiclassical density of states},
Author = {Ozorio de Almeida, A. M. and Hannay, J. H.},
Journal = {J. Phys. A},
Year = {1984},
Pages = {3429},
Volume = {17},
DOI = {10.1088/0305-4470/17/18/013}
}
@Article{Ozorio,
Title = {Resonant periodic orbits and the semiclassical energy spectrum},
Author = {Ozorio de Almeida, A. M. and Hannay, J. H.},
Journal = {J. Phys. A},
Year = {1987},
Pages = {5873},
Volume = {20},
DOI = {10.1088/0305-4470/20/17/021}
}
@Article{paskauskas2008,
Title = {Dynamical bottlenecks to intramolecular energy flow},
Author = {R. Pa\v{s}kauskas and C. Chandre and T. Uzer},
Journal = {Phys. Rev. Lett.},
Year = {2008},
Pages = {083001},
Volume = {100},
DOI = {10.1103/PhysRevLett.100.083001}
}
@Article{paskauskas2009a,
Title = {Bottlenecks to vibrational energy flow in {OCS}: {Structures} and mechanisms},
Author = {R. Pa\v{s}kauskas and C. Chandre and T. Uzer},
Journal = {J. Chem. Phys.},
Year = {2009},
Pages = {164105},
Volume = {130},
DOI = {130(16):164105:1-11}
}
@Article{paskauskas09,
author = {Pa{\v{s}}kauskas, R. and De Ninno, G.},
title = {{Lyapunov} stability of {Vlasov} equilibria using {Fourier-Hermite} modes},
journal = {Phys. Rev. E},
year = {2009},
volume = {80},
pages = {036402},
doi = {10.1103/physreve.80.036402},
}
@Article{PaCrFaSh80,
Title = {Geometry from a time series},
Author = {Packard, N. H. and Crutchfield, J. P. and Farmer, J. D. and Shaw, R. S.},
Journal = {Phys. Rev. Lett.},
Year = {1980},
Pages = {712--716},
Volume = {45},
DOI = {10.1103/physrevlett.45.712}
}
@Article{PaiL81,
Title = {A {Schur} decomposition for {Hamiltonian} matrices},
Author = {C.C. Paige and Van Loan, C.},
Journal = {Linear Algebra Appl.},
Year = {1981},
Pages = {11--32},
Volume = {41},
DOI = {10.1016/0024-3795(81)90086-0}
}
@Article{BisPal98,
Title = {Symmetry reduction and semiclassical analysis of axially symmetric systems},
Author = {S. Pal and D. Biswas},
Journal = {Phys. Rev. E},
Year = {1998},
Pages = {1475--1484},
Volume = {57},
DOI = {10.1103/physreve.57.1475}
}
@Article{Pal61,
Title = {On the existence of slices for actions of non-compact {Lie} groups},
Author = {R. S. Palais},
Journal = {Ann. Math.},
Year = {1961},
Pages = {295--323},
Volume = {73},
DOI = {10.2307/1970335}
}
@Article{palaniyappan2012,
Title = {Dynamics of relativistic transparency and optical shuttering in expanding overdense plasmas},
Author = {Palaniyappan, Sasi and Hegelich, B. Manuel and Wu, Hui-Chun and Jung, Daniel and Gautier, Donald C. and Yin, Lin and Albright, Brian J. and Johnson, Randall P. and Shimada, Tsutomu and Letzring, Samuel and Offermann, Dustin T. and Ren, Jun and Huang, Chengkun and H\"orlein, Rainer and Dromey, Brendan and Fernandez, Juan C. and Shah, Rahul C.},
Journal = {Nature Phys.},
Year = {2012},
Pages = {763--769},
Volume = {8},
Abstract = {Overdense plasmas are usually opaque to laser light. However, when
the light is of sufficient intensity to drive electrons in the plasma
to near light speeds, the plasma becomes transparent. This process?known
as relativistic transparency?takes just a tenth of a picosecond.
Yet all studies of relativistic transparency so far have been restricted
to measurements collected over timescales much longer than this,
limiting our understanding of the dynamics of this process. Here
we present time-resolved electric field measurements (with a temporal
resolution of {\textasciitilde} 50 fs) of the light, initially reflected
from, and subsequently transmitted through, an expanding overdense
plasma. Our result provides insight into the dynamics of the transparent-overdense
regime of relativistic plasmas, which should be useful in the development
of laser-driven particle accelerators, X-ray sources and techniques
for controlling the shape and contrast of intense laser pulses.},
DOI = {10.1038/nphys2390}
}
@Inbook{Palmer06,
Title = {Predictability of Weather and Climate},
Author = {T. Palmer},
Chapter = {Predictability of weather and climate: {From} theory to practice},
Editor = {T. Palmer and E. Hagedorn},
Pages = {1--30},
Publisher = {Cambridge U. Press},
Year = {2006}
}
@Article{PalZan13,
Title = {Singular vectors, predictability and ensemble forecasting for weather and climate},
Author = {T. N. Palmer and L. Zanna},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254018},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254018}
}
@Article{Panetta93,
Title = {Zonal jets in wide baroclinically unstable regions: {Persistence} and scale selection},
Author = {Panetta, R. L.},
Journal = {J. Atmos. Sci.},
Year = {1993},
Pages = {2073--2106},
Volume = {50},
DOI = {10.1175/1520-0469(1993)050<2073:ZJIWBU>2.0.CO;2}
}
@Article{PaHe88,
Title = {Baroclinic eddy fluxes in a one-dimensional model of quasi-geostrophic turbulence},
Author = {Panetta, R. L. and Held, I. M.},
Journal = {J. Atmos. Sci.},
Year = {1988},
Pages = {3354--3365},
Volume = {45},
DOI = {10.1175/1520-0469(1988)045<3354:BEFIAO>2.0.CO;2}
}
@Article{PaHePi87,
Title = {External {Rossby} waves in the two-layer model},
Author = {Panetta, R. L. and Held, I. M. and Pierrehumbert, R. T.},
Journal = {J. Atmos. Sci.},
Year = {1987},
Pages = {2924--2933},
Volume = {44},
DOI = {10.1175/1520-0469(1987)044<2924:ERWITT>2.0.CO;2}
}
@Book{ParChu89,
title = {Practical Numerical Algorithms for Chaotic Systems},
publisher = {Springer},
year = {1989},
author = {Parker, T. S. and Chua, L. O.},
address = {New York},
doi = {10.1007/978-1-4612-3486-9},
}
@Article{PP83,
Title = {An analogue of the prime number theorem for closed orbits of {Axiom A} flows},
Author = {W. Parry and M. Pollicott},
Journal = {Ann. Math.},
Year = {1983},
Pages = {573--591},
Volume = {118},
DOI = {10.2307/2006982}
}
@Article{PGER13,
author = {Pausch, M. and Grossmann, F. and Eckhardt, B. and Romanovski, V. G.},
title = {{Gr{\"o}bner} basis methods for stationary solutions of low-dimensional model for a shear flow},
journal = {J. Nonlinear Sci.},
year = {2014},
volume = {24},
pages = {935--948},
doi = {10.1007/s00332-014-9208-7},
}
@Article{PawSchu91,
Title = {Unstable periodic orbits and prediction},
Author = {K. Pawelzik and H. G. Schuster},
Journal = {Phys. Rev. A},
Year = {1991},
Pages = {1808--1812},
Volume = {43},
DOI = {10.1103/PhysRevA.43.1808}
}
@Article{PaLo10,
author = {Paz{\'o}, D. and L{\'o}pez, J. M.},
title = {Characteristic {Lyapunov} vectors in chaotic time-delayed systems},
journal = {Phys. Rev. E},
year = {2010},
volume = {82},
pages = {056201},
doi = {10.1103/physreve.82.056201},
}
@Article{PaLoPo13,
author = {Paz{\'o}, D. and L{\'o}pez, J. M. and Politi, A.},
title = {Universal scaling of {Lyapunov}-exponent fluctuations in space-time chaos},
journal = {Phys. Rev. E},
year = {2013},
volume = {87},
pages = {062909},
doi = {10.1103/physreve.87.062909},
}
@Article{PaSzLoRo09,
Title = {Structure of characteristic {Lyapunov} vectors in spatiotemporal chaos},
Author = {D. Paz{\'o} and I. G. Szendro and J. M. L{\'o}pez and M. A. Rodr{\'i}guez},
Journal = {Phys. Rev. E},
Year = {2008},
Pages = {016209},
Volume = {78},
DOI = {10.1103/PhysRevE.78.016209}
}
@Article{PaLoRo13,
Title = {On the angle between the first and second {Lyapunov} vectors in spatio-temporal chaos},
Author = {D. Paz{\'o} and J. M. L{\'o}pez and M. A. Rodr\'iguez},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254014},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254014}
}
@Article{peckham90,
Title = {The necessity of the {Hopf} bifurcation for periodically forced oscillators},
Author = {Peckham, B. B.},
Journal = {Nonlinearity},
Year = {1990},
Pages = {261--280},
Volume = {3},
DOI = {10.1088/0951-7715/3/2/002}
}
@Article{PSHMR14,
Title = {Cluster synchronization and isolated desynchronization in complex networks with symmetries},
Author = {Pecora, L. M. and Sorrentino, F. and Hagerstrom, A. M. and Murphy, T. E. and Roy, R.},
Journal = {Nature Commun.},
Year = {2014},
Volume = {5},
DOI = {10.1038/ncomms5079}
}
@Article{PeKl91,
Title = {The nonlinear dynamics of slightly supercritical baroclinic jets},
Author = {Pedlosky, J. and Klein, P.},
Journal = {J. Atmos. Sci.},
Year = {1991},
Pages = {1276--1286},
Volume = {48},
DOI = {10.1175/1520-0469(1991)048<1276:TNDOSS>2.0.CO;2}
}
@Article{PePo87,
Title = {Wave-wave interaction of unstable baroclinic waves},
Author = {Pedlosky, J. and Polvani, L. M.},
Journal = {J. Atmos. Sci.},
Year = {1987},
Pages = {631--647},
Volume = {44},
DOI = {10.1175/1520-0469(1987)044<0631:WIOUBW>2.0.CO;2}
}
@Book{Penr04,
Title = {The Road to Reality: A Complete Guide to the Laws of the Universe},
Author = {R. Penrose},
Publisher = {A. A. Knopf},
Year = {2005},
Address = {New York}
}
@Book{PerRich82N,
Title = {Introduction to Dynamics},
Author = {I. Percival and D. Richards},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Address = {Cambridge}
}
@Article{PerViv,
Title = {A linear code for the sawtooth and cat maps},
Author = {I. Percival and F. Vivaldi},
Journal = {Physica D},
Year = {1987},
Pages = {373--386},
Volume = {27},
DOI = {10.1016/0167-2789(87)90037-6}
}
@Article{PerViv87b,
Title = {Arithmetical properties of strongly chaotic motions},
Author = {I. Percival and F. Vivaldi},
Journal = {Physica D},
Year = {1987},
Pages = {105--130},
Volume = {25},
DOI = {10.1016/0167-2789(87)90096-0}
}
@Article{NLSper77,
Title = {Nonlinear Schr{\"{o}}dinger equation including growth and damping},
Author = {N. R. Pereira and L. Stenflo},
Journal = {Phys. Fluids},
Year = {1977},
Number = {10},
Pages = {1733},
Volume = {20},
Abstract = {A nonlinear Schr{\"{o}}dinger equation is found with growth and damping
terms in the weakly nonlinear regime. An exact solitary solution
is found for the equation.},
DOI = {10.1063/1.861773}
}
@Book{perkob,
title = {Differential Equations and Dynamical Systems},
publisher = {Springer},
year = {1991},
author = {L. Perko},
address = {New York},
doi = {10.1007/978-1-4684-0392-3},
}
@Article{Pesin77,
Title = {Characteristic {Lyapunov} exponents and smooth ergodic theory},
Author = {Ya. B. Pesin},
Journal = {Russian Math. Surveys},
Year = {1977},
Pages = {55--114},
Volume = {32},
DOI = {10.1070/RM1977v032n04ABEH001639}
}
@Book{Pesin2004,
Title = {Lectures on partial hyperbolicity and stable ergodicity},
Author = {Pesin, Ya. B.},
Publisher = {European Mathematical Society},
Year = {2004},
Address = {Z\"urich},
DOI = {10.4171/003}
}
@Article{PesSin88,
Title = {Space-time chaos in the system of weakly interacting hyperbolic systems},
Author = {Ya. B. Pesin and Ya. G. Sinai},
Journal = {J. Geom. Phys.},
Year = {1988},
Pages = {483--492},
Volume = {5},
DOI = {10.1016/0393-0440(88)90035-6}
}
@Book{PesSch95,
title = {An Introduction to Quantum Field Theory},
publisher = {Perseus Books},
year = {1995},
author = {Peskin, M. E. and Schroeder, D. V.},
address = {Cambridge, Massachusetts},
doi = {10.1063/1.2807734},
}
@Article{PePaVr08,
Title = {Stochastic optimization for detecting periodic orbits of nonlinear mappings},
Author = {Petalas, Y. G. and Parsopoulos, K. E. and Vrahatis, M. N.},
Journal = {Nonlin. Phenom. Complex Sys.},
Year = {2008},
Pages = {285 -- 291},
Volume = {11}
}
@Article{Peterhof1999,
Title = {All-optical clock recovery using multisection distributed-feedback lasers},
Author = {D. Peterhof and B. Sandstede},
Journal = {J. Nonlin. Sci.},
Year = {1999},
Pages = {575--613},
Volume = {9},
DOI = {10.1007/s003329900079}
}
@Article{PeLiAh11,
Title = {Interpretation of {Floquet} eigenvalues and eigenvectors for periodic systems},
Author = {Peters, D. A. and Lieb, S. M. and Ahaus, L. A.},
Journal = {J. Am. Helicopter Soc.},
Year = {2011},
Pages = {1--11},
Volume = {56},
DOI = {10.4050/JAHS.56.032001}
}
@Article{PetCorBol06,
Title = {Symbolic dynamics of coupled map lattices},
Author = {Pethel, S. D. and Corron, N. J. and Bollt, E.},
Journal = {Phys. Rev. Lett.},
Year = {2006},
Pages = {034105},
Volume = {96},
DOI = {10.1103/PhysRevLett.96.034105}
}
@Article{PetCorBol07,
Title = {Deconstructing spatiotemporal chaos using local symbolic dynamics},
Author = {Pethel, S. D. and Corron, N. J. and Bollt, E.},
Journal = {Phys. Rev. Lett.},
Year = {2007},
Pages = {214101},
Volume = {99},
DOI = {10.1103/PhysRevLett.99.214101}
}
@Book{PetTri09,
title = {Applications of Group Theory in Quantum Mechanics},
publisher = {Dover},
year = {2009},
author = {Petrashen, M. I. and Trifonov, E. D.},
isbn = {9780486472232},
address = {New York},
}
@Article{Petropoulos97,
Title = {Analysis of exponential time-differencing for {FDTD} in lossy dielectrics},
Author = {Petropoulos, P. G.},
Journal = {IEEE Trans. Antennas Propag.},
Year = {1997},
Pages = {1054--1057},
Volume = {45},
DOI = {10.1109/8.585755}
}
@Book{Peyret02,
Title = {Spectral Methods for Incompressible Flows},
Author = {R. Peyret},
Publisher = {Springer},
Year = {2002},
Address = {New York}
}
@Incollection{Pfenninger61,
Title = {Transition in the inlet length of tubes at high Reynolds numbers},
Author = {W. Pfenninger},
Booktitle = {Boundary Layer and Flow Control},
Publisher = {Pergamon},
Year = {1961},
Address = {Oxford, UK},
Editor = {G. V. Lachmann},
Pages = {970--980},
DOI = {10.1016/B978-1-4832-1323-1.50013-0}
}
@Article{phillips51,
Title = {A simple three-dimensional model for the study of large-scale extratropical flow patterns},
Author = {N. A. Phillips},
Journal = {J. Meteorology},
Year = {1951},
Pages = {381--394},
Volume = {8},
DOI = {10.1175/1520-0469(1951)008<0381:astdmf>2.0.co;2}
}
@Article{PikPol98,
Title = {Dynamic localization of {Lyapunov} vectors in spacetime chaos},
Author = {A. Pikovsky and A. Politi},
Journal = {Nonlinearity},
Year = {1998},
Pages = {1049--1062},
Volume = {11},
DOI = {10.1088/0951-7715/11/4/016}
}
@Article{PSD01,
Title = {Detecting unstable periodic orbits in chaotic continuous-time dynamical systems},
Author = {D. Pingel and P. Schmelcher and F. K. Diakonos},
Journal = {Phys. Rev. E},
Year = {2001},
Number = {2},
Pages = {026214},
Volume = {64},
Abstract = {Change the stability of the fixed points on the Poincar\'{e} section
to find periodic orbits.},
DOI = {10.1103/physreve.64.026214}
}
@Article{PSDB00,
author = {D. Pingel and P. Schmelcher and F. K. Diakonos and O. Biham},
title = {Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems},
journal = {Phys. Rev. E},
year = {2000},
volume = {62},
pages = {2119},
doi = {10.1103/physreve.62.2119},
}
@Article{PlaSirFit91,
Title = {An investigation of chaotic {Kolmogorov} flows},
Author = {Platt, N. and Sirovich, L. and Fitzmaurice, N.},
Journal = {Phys. Fluids A},
Year = {1991},
Pages = {681--696},
Volume = {3},
DOI = {10.1063/1.858074}
}
@Book{poinper,
Title = {New Methods in Celestial Mechanics},
Author = {H. Poincar\'{e}},
Publisher = {Springer},
Year = {1992},
Address = {New York}
}
@Article{Poinc1896,
author = {H. Poincar{\'e}},
title = {Sur les solutions p\'eriodiques et le principe de moindre action},
journal = {C. R. Acad. Sci. Paris},
year = {1896},
volume = {123},
pages = {915--918},
}
@Book{poincare,
Title = {Les M\'ethodes Nouvelles de la M\'echanique C\'eleste},
Author = {H. Poincar\'e},
Publisher = {Guthier-Villars},
Year = {1899},
Address = {Paris},
Note = {For a very readable exposition of {Poincar\'e}'s work and the development of the dynamical systems theory up to 1920's see \refreff{JBG97}.}
}
@Article{Poiseuille1844,
Title = {Recherches exp{\'e}rimentales sur le mouvement des liquides dans les tubes de tr{\`e}s-petits diam{\`e}tres},
Author = {J. L. Poiseuille},
Journal = {C. R. Acad. Sci. Paris},
Year = {1840},
Pages = {961},
Volume = {11}
}
@Article{PoGiYaMa06,
Title = {From synchronization to {Lyapunov} exponents and back},
Author = {Politi, A. and Ginelli, F. and Yanchuk, S. and Maistrenko, Y.},
Journal = {Physica D},
Year = {2006},
Pages = {90},
Volume = {224},
DOI = {10.1016/j.physd.2006.09.032}
}
@Article{PolPuc92,
Title = {Invariant measure in coupled maps},
Author = {A. Politi and G. P. Puccioni},
Journal = {Physica D},
Year = {1992},
Pages = {384--391},
Volume = {58},
DOI = {10.1016/0167-2789(92)90124-6}
}
@Article{PolTor92,
Title = {Periodic orbits in coupled {H{\'e}non} maps: {Lyapunov} and multifractal analysis},
Author = {Politi, A. and Torcini, A.},
Journal = {Chaos},
Year = {1992},
Pages = {293--300},
Volume = {2},
DOI = {10.1063/1.165871}
}
@article{PolTor92b,
title = {Towards a statistical mechanics of spatiotemporal chaos},
author = {A. Politi and A. Torcini},
journal = {Phys. Rev. Lett.},
volume = {69},
pages = {3421--3424},
year = {1992},
doi = {10.1103/PhysRevLett.69.3421}
}
@Article{PoToLe98,
Title = {{Lyapunov} exponents from node-counting arguments},
Author = {A. Politi and A. Torcini and S. Lepri},
Journal = {J. Phys. IV},
Year = {1998},
Pages = {263},
Volume = {8},
DOI = {10.1051/jp4:1998636}
}
@Article{Polizzi09,
Title = {Density-matrix-based algorithm for solving eigenvalue problems},
Author = {Polizzi, E.},
Journal = {Phys. Rev. B},
Year = {2009},
Pages = {115112},
Volume = {79},
DOI = {10.1103/PhysRevB.79.115112}
}
@Article{Pollicott91,
Title = {A note on the {Artuso-Aurell-Cvitanovic} approach to the {Feigenbaum} tangent operator},
Author = {Pollicott, M.},
Journal = {J. Stat. Phys.},
Year = {1991},
Pages = {257--267},
Volume = {62},
DOI = {10.1007/BF01020869}
}
@Book{Pollicott93,
title = {Lectures on ergodic theory and Pesin theory on compact manifolds},
publisher = {Cambridge Univ. Press},
year = {1993},
author = {Pollicott, M.},
address = {Cambridge},
isbn = {9780521435932},
doi = {10.1017/cbo9780511752537},
}
@Incollection{Pollicott02,
Title = {Periodic orbits and zeta functions},
Author = {M. Pollicott},
Booktitle = {{Handbook of Dynamical Systems}},
Publisher = {Elsevier},
Year = {2002},
Address = {New York},
Editor = {Hasselblatt, B. and Katok, A.},
Pages = {409--452},
Volume = {1, Part A},
DOI = {10.1016/S1874-575X(02)80007-8}
}
@Book{HasKat02,
Title = {{Handbook of Dynamical Systems}},
Author = {Hasselblatt, B. and Katok, A.},
Publisher = {Elsevier},
Year = {2002},
Address = {New York},
DOI = {10.1016/S1874-575X(02)80007-8}
}
@Article{pomeau80,
Title = {Intermittent transition to turbulence in dissipative dynamical systems},
Author = {Y. Pomeau and Manneville, P.},
Journal = {Commun. Math. Phys.},
Year = {1980},
Pages = {189},
Volume = {74},
DOI = {10.1007/BF01197757}
}
@Article{PoPuPe84,
Title = {Intrinsic stochasticity with many degrees of freedom},
Author = {Pomeau, Y. and Pumir, A. and Pelce, P.},
Journal = {J. Stat. Phys.},
Year = {1984},
Pages = {39--49},
Volume = {37},
DOI = {10.1007/BF01012904}
}
@Book{popebook,
title = {Turbulent Flows},
publisher = {Cambridge Univ. Press},
year = {2000},
author = {S. B. Pope},
address = {Cambridge},
doi = {10.1017/cbo9780511840531},
}
@Article{PoKno05,
Title = {Dynamics in the 1:2~{s}patial resonance with broken reflection symmetry},
Author = {J. Porter and E. Knobloch},
Journal = {Physica D},
Year = {2005},
Pages = {318--344},
Volume = {201},
DOI = {10.1016/j.physd.2005.01.001}
}
@Article{PorCvi04,
Title = {A perturbative analysis of modulated amplitude waves in {Bose-Einstein} condensates},
Author = {Porter, M. A. and Cvitanovi\'c, P.},
Journal = {Chaos},
Year = {2004},
Pages = {739--755},
Volume = {14},
DOI = {10.1063/1.1779991}
}
@Article{porter2004modulated,
author = {Porter, M. A. and Cvitanovi\'c, P.},
title = {Modulated amplitude waves in {Bose-Einstein} condensates},
journal = {Phys. Rev. E},
year = {2004},
volume = {69},
pages = {047201},
doi = {10.1103/physreve.69.047201},
}
@Article{percgl,
Title = {Exact periodic solutions of the complex {Ginzburg-Landau} equation},
Author = {A. V. Porubov and M. G. Velarde},
Journal = {J. Math. Phys.},
Year = {1999},
Pages = {884},
Volume = {40},
DOI = {10.1063/1.532692}
}
@Article{Posch13,
Title = {Symmetry properties of orthogonal and covariant {Lyapunov} vectors and their exponents},
Author = {H. A. Posch},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254006},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254006}
}
@Incollection{PoHi00,
Title = {Simulation of billiards and of hard body fluids},
Author = {Posch, H. A. and Hirschl, R.},
Booktitle = {Hard ball systems and the {Lorentz gas}},
Publisher = {Springer},
Year = {2000},
Address = {Berlin},
Editor = {Sz{\'a}sz, D. and Bunimovich, L. A.},
Pages = {279--314}
}
@Article{Postle09,
author = {Postlethwaite, C. M.},
title = {Stabilization of long-period periodic orbits using time-delayed feedback control},
journal = {SIAM J. Appl. Dyn. Sys.},
year = {2009},
volume = {8},
pages = {21--39},
doi = {10.1137/080721510},
}
@Book{Press96,
title = {{Numerical Recipes in {Fortran} 77}},
publisher = {Cambridge Univ. Press},
year = {1996},
author = {W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling},
isbn = {9780521430647},
address = {Cambridge},
edition = {2},
}
@Book{nr,
Title = {Numerical Recipes in {C}},
Author = {W. H. Press and S. A. Teukolsky and W. T. Vetterling and B. P. Flannery},
Publisher = {Cambridge Univ. Press},
Year = {1992},
Address = {Cambridge}
}
@Article{Pringle2009,
Title = {Highly symmetric travelling waves in pipe flow},
Author = {Pringle, C. C. T. and Duguet, Y. and Kerswell, R.},
Journal = {Philos. Trans. R. Soc. A},
Year = {2009},
Pages = {457--472},
Volume = {367},
DOI = {10.1098/rsta.2008.0236},
Owner = {root}
}
@Article{Pringle07,
Title = {Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow},
Author = {Pringle, C. C. T. and Kerswell, R. R.},
Journal = {Phys. Rev. Lett.},
Year = {2007},
Pages = {074502},
Volume = {99},
DOI = {10.1103/physrevlett.99.074502}
}
@Article{Proctor88,
Title = {Odd symplectic groups},
Author = {Proctor, R. A.},
Journal = {Inv. Math.},
Year = {1988},
Pages = {307--332},
Volume = {92},
DOI = {10.1007/bf01404455}
}
@Article{Proctor93,
Title = {Reflection and algorithm proofs of some more {Lie} group dual pair identities},
Author = {Proctor, R. A.},
Journal = {J. Combin. Theory A},
Year = {1993},
Number = {1},
Pages = {107--127},
Volume = {62},
DOI = {10.1016/0097-3165(93)90074-i}
}
@Book{PuLev86,
title = {{Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging}},
publisher = {Harvard Univ. Press},
year = {1985},
author = {Puccia, C.J. and Levins, R.},
isbn = {9780674741102},
doi = {10.4159/harvard.9780674435070},
}
@Article{pugh67cl,
Title = {An improved closing lemma and a general density theorem},
Author = {C. Pugh},
Journal = {Amer. J. Math.},
Year = {1967},
Pages = {1010},
Volume = {89},
DOI = {10.2307/2373414}
}
@Article{PugShu89,
Title = {Ergodic attractors},
Author = {Pugh, C. and Shub, M.},
Journal = {Trans. Amer. Math. Soc.},
Year = {1989},
Pages = {1--54},
Volume = {312},
DOI = {10.1090/S0002-9947-1989-0983869-1}
}
@Article{PuShSt04,
Title = {Stable ergodicity},
Author = {C. Pugh and M. Shub and A. Starkov},
Journal = {Bull. Amer. Math. Soc},
Year = {2004},
Pages = {1--41},
Volume = {41},
DOI = {10.1090/S0273-0979-03-00998-4}
}
@Article{Enrique03,
Title = {On the dynamics of dominated splitting},
Author = {Pujals, E. R. and Sambarino, M.},
Journal = {Ann. Math.},
Year = {2009},
Pages = {675--740},
Volume = {169},
DOI = {10.4007/annals.2009.169.675}
}
@Phdthesis{PutkaradzeThesis,
Title = {Local structures in extended systems},
Author = {Putkaradze, V.},
School = {Copenhagen Univ.},
Year = {1997},
Address = {Copenhagen},
URL = {http://ChaosBook.org/projects/theses.html}
}
@Article{Pyragas92,
Title = {Continuous control of chaos by self-controlling feedback},
Author = {K. Pyragas},
Journal = {Phys. Lett. A },
Year = {1992},
Pages = {421--428},
Volume = {170},
DOI = {10.1016/0375-9601(92)90745-8}
}
@Article{Qin03,
Title = {Bifurcations of steady states in a class of lattices of nonlinear discrete {Klein-Gordon} type with double-quadratic on-site potential},
Author = {Qin, W.-X.},
Journal = {J. Phys. A},
Year = {2003},
Pages = {9865--9873},
Volume = {36},
DOI = {10.1088/0305-4470/36/38/304}
}
@Article{QuaTro00,
Title = {Subshifts of multi-dimensional shifts of finite type},
Author = {Quas, A. N. and Trow, P. B.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {2000},
Pages = {859--874},
Volume = {20},
DOI = {10.1017/s0143385700000468}
}
@Article{ross,
Title = {An equation for continuous chaos},
Author = {O. E. R\"ossler},
Journal = {Phys. Lett. A},
Year = {1976},
Pages = {397--398},
Volume = {57},
DOI = {10.1016/0375-9601(76)90101-8}
}
@Article{Radziunas2006,
Title = {Numerical bifurcation analysis of the traveling wave model of multisection semiconductor lasers},
Author = {M. Radziunas},
Journal = {Physica D},
Year = {2006},
Pages = {98--112},
Volume = {213},
DOI = {10.1016/j.physd.2005.11.003}
}
@Article{RamSri00,
Title = {A comparative study of computation of {Lyapunov} spectra with different algorithms},
Author = {Ramasubramanian, K. and Sriram, M. S.},
Journal = {Physica D},
Year = {2000},
Pages = {72--86},
Volume = {139},
DOI = {10.1016/S0167-2789(99)00234-1}
}
@Article{transgol,
author = {R. Ramshankar and J. P. Gollub},
title = {Transport by capillary waves, {Part II}: {Scalar} dispersion and the structure of the concentration field},
journal = {Phys. Fluids A},
year = {1991},
volume = {3},
pages = {1344--1350},
doi = {10.1063/1.858063},
}
@Article{Rand82,
Title = {Dynamics and symmetry. {Predictions} for modulated waves in rotating fluids},
Author = {Rand, D.},
Journal = {Arch. Rational Mech. Anal.},
Year = {1982},
Pages = {1--37},
Volume = {79},
DOI = {10.1007/BF02416564}
}
@Article{RasDie08,
Title = {A geometrical method for the approximation of invariant tori},
Author = {B. Rasmussen and L. Dieci},
Journal = {J. Comput. Appl. Math.},
Year = {2008},
Pages = {388--412},
DOI = {10.1016/j.cam.2007.05.025}
}
@Article{RaHaAb96,
Title = {Global stability properties of the complex {Lorenz} model},
Author = {Rauh, A. and Hannibal, L. and Abraham, N. B.},
Journal = {Physica D},
Year = {1996},
Pages = {45--58},
Volume = {99},
DOI = {10.1016/s0167-2789(96)00129-7}
}
@Article{Recke1998a,
Title = {Forced frequency locking of rotating waves},
Author = {L. Recke},
Journal = {Ukrain. Math. J.},
Year = {1998},
Pages = {94--101},
Volume = {50},
DOI = {10.1007/bf02514692}
}
@Article{Recke1998,
Title = {Forced symmetry breaking and forced frequency locking of modulated waves},
Author = {L. Recke and D. Peterhof},
Journal = {J. Diff. Eqn.},
Year = {1998},
Pages = {233--262},
Volume = {144},
DOI = {10.1006/jdeq.1997.3379}
}
@Article{Recke2010,
author = {L. Recke and A. Samoilenko and A. Teplinsky and V. Tkachenko and S. Yanchuk},
title = {Frequency locking of modulated waves},
journal = {Discrete Continuous Dyn. Syst. Ser. A},
year = {2011},
volume = {31},
pages = {847--875},
doi = {10.3934/dcds.2011.31.847},
}
@Misc{ReSaTkYa11,
Title = {Frequency locking by external forcing in systems with rotational symmetry},
Author = {{Recke}, L. and {Samoilenko}, A. and {Tkachenko}, V. and {Yanchuk}, S. },
Year = {2011},
URL = {http://arXiv.org/abs/1108.5990}
}
@Article{RSBH98,
author = {S. C. Reddy and P. J. Schmid and J. S. Baggett and D. S. Henningson},
title = {On stability of streamwise streaks and transition thresholds in plane channel flows},
journal = {J. Fluid Mech.},
year = {1998},
volume = {365},
pages = {269--303},
doi = {10.1017/s0022112098001323},
}
@Article{ReiMos95,
Title = {Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems},
Author = {Reick, C. and Mosekilde, E.},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {1418--1435},
Volume = {52},
DOI = {10.1103/PhysRevE.52.1418}
}
@Article{reimann1,
Title = {Noisy one-dimensional maps near a crisis 1: {Weak {Gauss}ian} white and colored noise},
Author = {P. Reimann},
Journal = {J. Stat. Phys.},
Year = {1996},
Pages = {1467--1501},
Volume = {82},
DOI = {10.1007/bf02183392}
}
@Article{reimann2,
Title = {Noisy one-dimensional maps near a crisis 2: {General} uncorrelated weak noise},
Author = {P. Reimann},
Journal = {J. Stat. Phys.},
Year = {1996},
Pages = {403--425},
Volume = {85},
DOI = {10.1007/bf02174212}
}
@Article{ReCi05,
Title = {Intermittency induced by attractor-merging crisis in the {Kuramoto-Sivashinsky} equation},
Author = {Rempel, E. L. and Chian, A. C.},
Journal = {Phys. Rev. E},
Year = {2005},
Pages = {016203},
Volume = {71},
DOI = {10.1103/PhysRevE.71.016203}
}
@Article{ReCh07,
Title = {Origin of transient and intermittent dynamics in spatiotemporal chaotic systems},
Author = {Rempel, E. L. and Chian, A. C.},
Journal = {Phys. Rev. Lett.},
Year = {2007},
Pages = {014101},
Volume = {98},
DOI = {10.1103/physrevlett.98.014101}
}
@Article{RCMR04,
Title = {Analysis of chaotic saddles in high-dimensional dynamical systems: the {Kuramoto-Sivashinsky} equation},
Author = {Rempel, E. L. and Chian, A. C. and Macau, E. E. and Rosa, R. R.},
Journal = {Chaos},
Year = {2004},
Pages = {545--56},
Volume = {14},
DOI = {10.1063/1.1759297}
}
@Article{ReChMi07,
Title = {Chaotic saddles at the onset of intermittent spatiotemporal chaos},
Author = {Rempel, E. L. and Chian, A. C. and Miranda, R. A.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {056217},
Volume = {76},
DOI = {10.1103/PhysRevE.76.056217}
}
@Article{R1883,
author = {O. Reynolds},
title = {An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels},
journal = {Proc. Roy. Soc. Lond. Ser. A},
year = {1883},
volume = {35},
number = {224-226},
pages = {935--982},
doi = {10.1098/rspl.1883.0018},
}
@Article{R1894,
author = {O. Reynolds},
title = {On the dynamical theory of incompressible viscous flows and the determination of the criterion},
journal = {Proc. Roy. Soc. Lond. Ser. A},
year = {1894},
volume = {56},
pages = {40--45},
doi = {10.1098/rspl.1894.0075},
}
@Book{Richter10,
Title = {Semiclassical Theory of Mesoscopic Quantum Systems},
Author = {Richter, K.},
Publisher = {Springer},
Year = {2000},
Address = {Berlin},
DOI = {10.1007/BFb0109634},
ISBN = {9783662156506},
URL = {http://www.physik.uni-regensburg.de/forschung/richter/richter/pages/research/springer-tracts-161.pdf}
}
@Article{RSW90N,
Title = {A breathing chaos},
Author = {P. H. Richter and H.-J. Scholz and A. Wittek},
Journal = {Nonlinearity},
Year = {1990},
Pages = {45--67},
Volume = {3},
DOI = {10.1088/0951-7715/3/1/004}
}
@Article{Rink200331,
Title = {Symmetric invariant manifolds in the {Fermi-Pasta-Ulam} lattice},
Author = {B. Rink},
Journal = {Physica D},
Year = {2003},
Pages = {31--42},
Volume = {175},
DOI = {10.1016/s0167-2789(02)00694-2}
}
@Book{Risken96,
Title = {The {Fokker-Planck} Equation},
Author = {H. Risken and H. Haken},
Publisher = {Springer},
Year = {1996},
Address = {New York}
}
@Article{Rivas13,
Title = {Semiclassical matrix elements for a chaotic propagator in the scar function basis},
Author = {A. M. F. Rivas},
Journal = {J. Phys. A},
Year = {2013},
Volume = {46},
Abstract = {A semiclassical approximation for the matrix elements of a quantum
chaotic propagator in the scar function basis has been derived. The
obtained expression is solely expressed in terms of canonical invariant
objects. For our purpose, we have used the recently developed, semiclassical
matrix elements of the propagator in coherent states, together with
the linearization of the flux in the neighborhood of a classically
unstable periodic orbit of chaotic two-dimensional systems. The expression
derived here is successfully verified to be exact for a (linear)
cat map, after the theory is adapted to a discrete phase space appropriate
to a quantized torus.},
DOI = {10.1088/1751-8113/46/14/145101}
}
@Article{RiKl97,
Title = {Effects of an asymmetric friction on the nonlinear equilibration of a baroclinic system},
Author = {Rivi\'ere, P. and Klein, P.},
Journal = {J. Atmos. Sci.},
Year = {1997},
Pages = {1610--1627},
Volume = {54},
DOI = {10.1175/1520-0469(1997)054<1610:EOAAFO>2.0.CO;2}
}
@Book{lls,
Title = {Systems of Quasilinear Equations and Their Applications to Gas Dynamics},
Author = {B. L. Ro\v{z}destvenski\v{i} and N. N. Janenko},
Publisher = {AMS},
Year = {1983},
Address = {Providence, RI}
}
@Article{robb,
Title = {Discrete symmetries in periodic-orbit theory},
Author = {Robbins, J. M.},
Journal = {Phys. Rev. A},
Year = {1989},
Pages = {2128--2136},
Volume = {40},
DOI = {10.1103/PhysRevA.40.2128}
}
@Article{RoMo08,
author = {Robinson, D. J. and Morriss, G. P.},
title = {{Lyapunov} mode dynamics in hard-disk systems},
journal = {J. Stat. Phys.},
year = {2008},
volume = {131},
pages = {1--31},
doi = {10.1007/s10955-007-9473-z},
}
@Article{Robinson-PLA1994,
Title = {Inertial manifolds for the {Kuramoto-Sivashinsky} equation},
Author = {Robinson, J. C.},
Journal = {Phys. Lett. A},
Year = {1994},
Pages = {190--193},
Volume = {184},
DOI = {10.1016/0375-9601(94)90775-7}
}
@Article{Robinson1995,
Title = {Finite-dimensional behavior in dissipative partial differential equations},
Author = {Robinson, J. C.},
Journal = {Chaos},
Year = {1995},
Pages = {330--345},
Volume = {5},
DOI = {10.1063/1.166081}
}
@Book{Robinson2001,
title = {Infinite-dimensional dynamical systems: {An} introduction to dissipative parabolic {PDE}s and the theory of global attractors},
publisher = {Cambridge Univ. Press},
year = {2001},
author = {Robinson, J. C},
isbn = {9780521632041},
}
@Article{Robinson91,
Title = {Coherent motions in the turbulent boundary layer},
Author = {S. K. Robinson},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1991},
Pages = {601--639},
Volume = {23},
DOI = {10.1146/annurev.fluid.23.1.601}
}
@Article{Rodriguez1990,
Title = {Global bifurcations into chaos in systems with {SO(2)} symmetry},
Author = {Rodr{\'i}guez, J. D. and Schell, M.},
Journal = {Phys. Lett. A},
Year = {1990},
Pages = {25--31},
Volume = {146},
DOI = {10.1016/0375-9601(90)90024-I}
}
@Article{sirovcgl90,
Title = {Low-dimensional dynamics for the complex {Ginzburg-Landau} equation},
Author = {J. D. Rodriguez and L. Sirovich},
Journal = {Physica D},
Year = {1990},
Pages = {77--86},
Volume = {43},
DOI = {10.1016/0167-2789(90)90017-j}
}
@Article{Ro88,
Title = {Painleve property and constants of the motion of the complex {Lorenz} model},
Author = {Roekaerts, D},
Journal = {J. Phys. A},
Year = {1988},
Pages = {L495--L498},
Volume = {21},
DOI = {10.1088/0305-4470/21/9/003}
}
@Article{Roettger05,
Title = {Periodic points classify a family of Markov shifts },
Author = {C. G. J. Roettger},
Journal = {J. Number Theory },
Year = {2005},
Pages = {69--83},
Volume = {113},
DOI = {10.1016/j.jnt.2004.11.012}
}
@Book{Roman12,
Title = {Fundamentals of Group Theory: An Advanced Approach},
Author = {Roman, S.},
Publisher = {Birkh\"auser},
Year = {2012},
Address = {Boston},
ISBN = {0817683003}
}
@Article{Romanov73,
Title = {Stability of plane-parallel {Couette} flow},
Author = {V. A. Romanov},
Journal = {Funct. Anal. Appl.},
Year = {1973},
Pages = {137--146},
Volume = {7},
DOI = {10.1007/bf01078886},
URL = {http://dx.doi.org/10.1007/bf01078886}
}
@Article{romero-bastida2012,
author = {Romero-Bastida, M. and Paz{\'o}, Diego and L{\'o}pez, Juan M.},
title = {Covariant hydrodynamic {Lyapunov} modes and strong stochasticity threshold in {Hamiltonian} lattices},
journal = {Phys. Rev. E},
year = {2012},
volume = {85},
pages = {026210},
doi = {10.1103/PhysRevE.85.026210},
abstract = {We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov
vectors for capturing hydrodynamic Lyapunov modes ({HLMs)} in one-dimensional
Hamiltonian lattices. We show that, in contrast with previous claims,
{HLMs} do exist for any energy density, so that strong chaos is not
essential for the appearance of genuine (covariant) {HLMs.} In contrast,
Gram-Schmidt Lyapunov vectors lead to misleading results concerning
the existence of {HLMs} in the case of weak chaos.},
}
@Phdthesis{RosenqvThesis,
Title = {Periodic orbit theory beyond semiclassics: convergence, diffraction and {$\hbar$} corrections},
Author = {Rosenqvist, P. E.},
School = {Copenhagen Univ.},
Year = {1995},
Address = {Copenhagen},
URL = {http://ChaosBook.org/projects/theses.html}
}
@Article{RCDL93,
Title = {A practical method for calculating largest {Lyapunov} exponents from small data sets},
Author = {Rosenstein, M. T. and Collins, J. J. and De Luca, C. J.},
Journal = {Physica D},
Year = {1993},
Pages = {117--134},
Volume = {65},
Abstract = {Detecting the presence of chaos in a dynamical system is an important
problem that is solved by measuring the largest Lyapunov exponent.
Lyapunov exponents quantify the exponential divergence of initially
close state-space trajectories and estimate the amount of chaos in
a system. We present a new method for calculating the largest Lyapunov
exponent from an experimental time series. The method follows directly
from the definition of the largest Lyapunov exponent and is accurate
because it takes ...},
DOI = {10.1016/0167-2789(93)90009-p}
}
@Article{roth99,
author = {D. Rothstein and E. Henry and J. P. Gollub},
title = {Persistent patterns in transient chaotic fluid mixing},
journal = {Nature},
year = {1999},
volume = {401},
pages = {770--772},
doi = {10.1038/44529},
}
@Article{Roupas11,
author = {Z. Roupas},
title = {Phase space geometry and chaotic attractors in dissipative {Nambu} mechanics},
journal = {J. Phys. A},
year = {2012},
volume = {45},
pages = {195101},
doi = {10.1088/1751-8113/45/19/195101},
}
@Article{RoCaRe12,
Title = {Dual pairing of symmetry and dynamical groups in physics},
Author = {Rowe, D. J. and Carvalho, M. J. and Repka, J.},
Journal = {Rev. Mod. Phys.},
Year = {2012},
Pages = {711--757},
Volume = {84},
DOI = {10.1103/RevModPhys.84.711}
}
@Article{RoSa00,
Title = {Nonlinear dimensionality reduction by locally linear embedding},
Author = {Roweis, S. T. and Saul, L. K.},
Journal = {Science},
Year = {2000},
Pages = {2323--2326},
Volume = {290},
Abstract = {Many areas of science depend on exploratory data analysis and visualization.
The need to analyze large amounts of multivariate data raises the
fundamental problem of dimensionality reduction: how to discover
compact representations of high-dimensional data. Here, we introduce
locally linear embedding {(LLE),} an unsupervised learning algorithm
that computes low-dimensional, neighborhood-preserving embeddings
of high-dimensional inputs. Unlike clustering methods for local dimensionality
reduction, {LLE} maps its inputs into a single global coordinate
system of lower dimensionality, and its optimizations do not involve
local minima. By exploiting the local symmetries of linear reconstructions,
{LLE} is able to learn the global structure of nonlinear manifolds,
such as those generated by images of faces or documents of text.},
DOI = {10.1126/science.290.5500.2323}
}
@Article{rowley_reduction_2003,
Title = {Reduction and reconstruction for self-similar dynamical systems},
Author = {Rowley, C. W. and Kevrekidis, I. G. and Marsden, J. E. and Lust, K.},
Journal = {Nonlinearity},
Year = {2003},
Pages = {1257--1275},
Volume = {16},
DOI = {10.1088/0951-7715/16/4/304}
}
@Article{rowley_reconstruction_2000,
Title = {Reconstruction equations and the {Karhunen-Lo{\'e}ve} expansion for systems with symmetry},
Author = {Rowley, C. W. and Marsden, J. E.},
Journal = {Physica D},
Year = {2000},
Pages = {1--19},
Volume = {142},
DOI = {10.1016/S0167-2789(00)00042-7}
}
@Article{RoMeBaSchHe09,
Title = {Spectral analysis of nonlinear flows},
Author = {Rowley, C. W. and Mezi\'c, I. and Bagheri, S. and Schlatter, P. and Henningson, D. S.},
Journal = {J. Fluid Mech.},
Year = {2009},
Pages = {115},
Volume = {641},
DOI = {10.1017/s0022112009992059}
}
@Article{rue68,
Title = {Statistical mechanics of a one-dimensional lattice gas},
Author = {D. Ruelle},
Journal = {Commun. Math. Phys.},
Year = {1968},
Pages = {267--288},
Volume = {9},
DOI = {10.1007/BF01654281}
}
@Article{ruell73,
Title = {Bifurcations in presence of a symmetry group},
Author = {D. Ruelle},
Journal = {Arch. Rational Mech. Anal.},
Year = {1973},
Pages = {136--152},
Volume = {51},
DOI = {Bifurcations in presence of a symmetry group}
}
@Article{Ruelle73NY,
Title = {Some comments on chemical oscillations},
Author = {Ruelle, D.},
Journal = {Trans. N. Y. Acad. Sci.},
Year = {1973},
Pages = {66--71},
Volume = {35},
DOI = {10.1111/j.2164-0947.1973.tb01505.x}
}
@Article{Rue76,
Title = {A measure associated with {Axiom-A} attractors},
Author = {D. Ruelle},
Journal = {Amer. J. Math.},
Year = {1976},
Pages = {619--654},
Volume = {98},
DOI = {10.2307/2373810}
}
@Article{Ruelle76a,
author = {Ruelle, D.},
title = {Generalized zeta-functions for {Axiom A} basic sets},
journal = {Bull. Amer. Math. Soc},
year = {1976},
volume = {82},
pages = {153--157},
doi = {10.1090/S0002-9904-1976-14003-7},
}
@Article{Ruelle76,
Title = {Zeta-functions for expanding maps and {Anosov} flows},
Author = {D. Ruelle},
Journal = {Inv. Math.},
Year = {1976},
Pages = {231--242},
Volume = {34},
DOI = {10.1007/BF01403069}
}
@Article{Ruelle78,
Title = {An inequality for the entropy of differentiable maps},
Author = {Ruelle, D.},
Journal = {Bol. Soc. Bras. Mat.},
Year = {1978},
Pages = {83--87},
Volume = {9},
DOI = {10.1007/BF02584795}
}
@Article{ruelle79,
Title = {Ergodic theory of differentiable dynamical systems},
Author = {D. Ruelle},
Journal = {Publ. Math. IHES},
Year = {1979},
Pages = {27--58},
Volume = {50},
DOI = {10.1007/BF02684768}
}
@Article{ruelext,
Title = {Large volume limit of the distribution of characteristic exponents in turbulence},
Author = {D. Ruelle},
Journal = {Commun. Math. Phys.},
Year = {1982},
Pages = {287--302},
Volume = {87},
DOI = {10.1007/BF01218566}
}
@Article{ruelle86,
Title = {Locating resonances for {Axiom A} dynamical systems},
Author = {D. Ruelle},
Journal = {J. Stat. Phys.},
Year = {1986},
Pages = {281--292},
Volume = {44},
DOI = {10.1007/bf01011300}
}
@Article{ruelle86a,
Title = {Resonances of chaotic dynamical systems},
Author = {D. Ruelle},
Journal = {Phys. Rev. Lett.},
Year = {1986},
Pages = {405--407},
Volume = {56},
DOI = {10.1103/physrevlett.56.405}
}
@Article{rue87b,
Title = {One-dimensional {Gibbs} states and {Axiom A} diffeomorphisms},
Author = {D. Ruelle},
Journal = {J. Diff. Geom.},
Year = {1987},
Pages = {117--137},
Volume = {25},
URL = {http://projecteuclid.org/euclid.jdg/1214440727}
}
@Article{rue87a,
Title = {Resonances for {Axiom A} flows},
Author = {D. Ruelle},
Journal = {J. Diff. Geom.},
Year = {1987},
Pages = {99--116},
Volume = {25},
URL = {http://projecteuclid.org/euclid.jdg/1214440726}
}
@Article{ruelle89,
Title = {The thermodynamic formalism for expanding maps},
Author = {D. Ruelle},
Journal = {Commun. Math. Phys.},
Year = {1989},
Pages = {239--262},
Volume = {125},
DOI = {10.1007/bf01217908},
Idoi = {10.1007/BF01217908}
}
@Article{Ruelle90,
Title = {An extension of the theory of {Fredholm} determinants},
Author = {D. Ruelle},
Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
Year = {1990},
Pages = {175--193},
Volume = {72},
DOI = {10.1007/BF02699133}
}
@Article{Ruelle96,
Title = {Differentiation of {SRB} states},
Author = {Ruelle, D.},
Journal = {Commun. Math. Phys.},
Year = {1997},
Pages = {227--241},
Volume = {187},
DOI = {10.1007/s002200050134}
}
@Article{Ruelle98,
Title = {General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium},
Author = {D. Ruelle},
Journal = {Phys. Lett. A },
Year = {1998},
Pages = {220--224},
Volume = {245},
DOI = {10.1016/S0375-9601(98)00419-8}
}
@Article{Ruelle98a,
Title = {Nonequilibrium statistical mechanics near equilibrium: computing higher-order terms},
Author = {D. Ruelle},
Journal = {Nonlinearity},
Year = {1998},
Pages = {5},
Volume = {11-18},
DOI = {10.1088/0951-7715/11/1/002}
}
@Article{Ruelle03,
Title = {Differentiation of {SRB} states: {Correction} and complements},
Author = {D. Ruelle},
Journal = {Commun. Math. Phys.},
Year = {2003},
Pages = {185--190},
Volume = {234},
DOI = {10.1007/s00220-002-0779-z}
}
@Article{rue04ne,
Title = {Conversations on nonequilibrium physics with an extraterrestrial},
Author = {D. Ruelle},
Journal = {Phys. Today},
Year = {2004},
Number = {5},
Pages = {48--53},
Volume = {57},
Abstract = {New ideas of nonequilibrium physics are introduced. Emphasize the
SRB measure approach and energy fluctuation theorem.},
DOI = {10.1063/1.1768674}
}
@Book{ruelle,
Title = {Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics},
Author = {D. Ruelle},
Publisher = {Cambridge Univ. Press},
Year = {2004},
Address = {Cambridge},
Edition = {2\textsuperscript{nd}},
ISBN = {9780521546492}
}
@Article{Ruelle07,
Title = {Nonequilibrium statistical mechanics and entropy production in a classical infinite system of rotators},
Author = {Ruelle, D.},
Journal = {Commun. Math. Phys.},
Year = {2007},
Pages = {233--265},
Volume = {270},
DOI = {10.1007/s00220-006-0126-x}
}
@Article{Ruelle09,
author = {D. Ruelle},
title = {A review of linear response theory for general differentiable dynamical systems},
journal = {Nonlinearity},
year = {2009},
volume = {22},
pages = {855--870},
doi = {10.1088/0951-7715/22/4/009},
}
@Article{Ruelle12,
Title = {A mechanical model for {Fourier's} law of heat conduction},
Author = {Ruelle, D.},
Journal = {Commun. Math. Phys.},
Year = {2012},
Pages = {755--768},
Volume = {311},
DOI = {10.1007/s00220-011-1304-z}
}
@Article{RueSin86,
Title = {From dynamical systems to statistical mechanics and back},
Author = {D. Ruelle and Ya. G. Sinai},
Journal = {Physica A},
Year = {1986},
Pages = {1--8},
Volume = {140},
DOI = {10.1016/0378-4371(86)90199-8}
}
@Article{ruell71,
Title = {On the nature of turbulence},
Author = {D. Ruelle and F. Takens},
Journal = {Commun. Math. Phys.},
Year = {1971},
Pages = {167},
Volume = {20},
DOI = {10.1007/bf01646553}
}
@Article{hhrugh92,
Title = {The correlation spectrum for hyperbolic analytic maps},
Author = {H. H. Rugh},
Journal = {Nonlinearity},
Year = {1992},
Pages = {1237},
Volume = {5},
DOI = {10.1088/0951-7715/5/6/003}
}
@Phdthesis{RughThesis,
Title = {Time Evoluation and Correlations in Chaotic Dynamical Systems},
Author = {Rugh, H. H.},
School = {Univ. of Copenhagen},
Year = {1992},
Address = {Copenhagen}
}
@Article{hhrugh94,
Title = {On the asymptotic form and the reality of spectra of {Perron-Frobenius} operators},
Author = {H. H. Rugh},
Journal = {Nonlinearity},
Year = {1994},
Pages = {1055},
Volume = {7},
Abstract = {We study the eigenvalue spectrum of the generalized Perron-Frobenius
operator for 1-D maps having two expanding branches. We show that
if one branch 'dominates' the other, the dominating branch determines
the asymptotic form of the spectrum. In particular, we obtain sufficient
conditions for the reality of the spectrum of the usual Perron-Frobenius
operator.},
DOI = {10.1088/0951-7715/7/3/015}
}
@Article{Ruhe10,
author = {Ruhe, A.},
title = {Rational {Krylov} for real pencils with complex eigenvalues},
journal = {Taiwanese J. Math.},
year = {2010},
volume = {14},
pages = {795},
url = {http://www.jstor.org/stable/43834817},
}
@Article{Rumb00,
author = {M. Rumberger},
title = {{Lyapunov} exponents on the orbit space},
journal = {Discrete Continuous Dyn. Syst. Ser. A},
year = {2000},
volume = {7},
pages = {91--113},
doi = {10.3934/dcds.2001.7.91},
}
@Article{Rumb01,
Title = {On eigenvalues on the orbit space},
Author = {M. Rumberger},
Journal = {J. Pure Appl. Algebra},
Year = {2001},
Pages = {89--99},
Volume = {158},
DOI = {10.1016/S0022-4049(00)00023-2}
}
@Incollection{RumSch01,
Title = {The orbit space method: {Theory} and application},
Author = {M. Rumberger and J. Scheurle},
Booktitle = {{Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}},
Publisher = {Springer},
Year = {2001},
Address = {New York},
Editor = {B. Fiedler},
URL = {http://dynamics.mi.fu-berlin.de/danse/}
}
@Article{RusHanOtt1980,
Title = {Dimension of strange attractors},
Author = {Russell, D. A. and Hanson, J. D. and Ott, E.},
Journal = {Phys. Rev. Lett.},
Year = {1980},
Pages = {1175--1178},
Volume = {45},
DOI = {10.1103/PhysRevLett.45.1175}
}
@Book{haleinf84,
Title = {{An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory}},
Author = {Rybakowski, K.P. and Hale, J.K. and Magalhaes, L.T. and Oliva, W.M.},
Publisher = {Springer},
Year = {1984},
Address = {New York},
ISBN = {9781475744934}
}
@Article{SanNet10,
Title = {On the multiple shooting continuation of periodic orbits by {Newton-Krylov} methods},
Author = {S{\'a}nchez, J. and Net, M.},
Journal = {Int. J. Bifur. Chaos},
Year = {2010},
Pages = {43--61},
Volume = {20},
DOI = {10.1142/S0218127410025399}
}
@Article{SanNet13,
Title = {A parallel algorithm for the computation of invariant tori in large-scale dissipative systems},
Author = {S{\'a}nchez, J. and M. Net},
Journal = {Physica D},
Year = {2013},
Pages = {22--33},
Volume = {252},
Abstract = {A parallelizable algorithm to compute invariant tori
of high-dimensional dissipative systems, obtained upon discretization of
PDEs is presented. The size of the set of equations to be solved is
only a small multiple of the dimension of the original system. The
sequential and parallel implementations are compared with a previous
method (Sanchez et{~}al. (2010)){~}[11], showing that important savings in
wall-clock time can be achieved. In order to test it, a thermal
convection problem of a binary mixture of fluids has been used. The new
method can also be applied to problems with very low rotation numbers,
for which the previous is not suitable. This is tested in two examples of
two-dimensional maps.},
DOI = {10.1016/j.physd.2013.02.008}
}
@Article{SaNeSi10,
Title = {Computation of invariant tori by {Newton--Krylov} methods in large-scale dissipative systems},
Author = {S{\'a}nchez, J. and Net, M. and Sim{\'o}, C.},
Journal = {Physica D},
Year = {2010},
Pages = {123--133},
Volume = {239},
DOI = {10.1016/j.physd.2009.10.012}
}
@Article{sanchez2016,
author = {S{\'a}nchez-Arriaga, G. and Siminos, E.},
title = {Relativistic quasi-solitons and embedded solitons with circular polarization in cold plasmas},
journal = {J. Phys. A},
year = {2017},
volume = {50},
pages = {185501},
doi = {10.1088/1751-8121/aa65a0},
}
@Article{SSL10-1,
Title = {Relativistic solitary waves modulating long laser pulses in plasmas},
Author = {S{\'a}nchez-Arriaga, G. and Siminos, E. and Lefebvre, E.},
Journal = {Plasma Phys. Control. Fusion},
Year = {2011},
Pages = {045011},
Volume = {53},
Abstract = {This paper discusses the existence of solitary electromagnetic waves
trapped in a self-generated Langmuir wave and embedded in an infinitely
long circularly polarized electromagnetic wave propagating through
a plasma. From a mathematical point of view they are exact solutions
of the one-dimensional relativistic cold fluid plasma model with
nonvanishing boundary conditions. Under the assumption of travelling
wave solutions with velocity V and vector potential frequency ?,
the fluid model is reduced to a Hamiltonian system. The solitary
waves are homoclinic (grey solitons) or heteroclinic (dark solitons)
orbits to fixed points. Using a dynamical systems description of
the Hamiltonian system and a spectral method, we identify a large
variety of solitary waves, including asymmetric ones, discuss their
disappearance for certain parameter values and classify them according
to (i) grey or dark character, (ii) the number of humps of the vector
potential envelope and (iii) their symmetries. The solutions come
in continuous families in the parametric V?? plane and extend up
to velocities that approach the speed of light. The stability of
certain types of grey solitary waves is investigated with the aid
of particle-in-cell simulations that demonstrate their propagation
for a few tens of the inverse of the plasma frequency.},
DOI = {10.1088/0741-3335/53/4/045011},
Language = {en}
}
@Article{SSL10,
Title = {Relativistic solitary waves with phase modulation embedded in long laser pulses in plasmas},
Author = {S{\'a}nchez-Arriaga, G. and Siminos, E. and Lefebvre, E.},
Journal = {Phys. Plasmas},
Year = {2011},
Pages = {082304--082304-10},
Volume = {18},
Abstract = {We investigate the existence of nonlinear phase-modulated relativistic
solitary waves embedded in an infinitely long circularly polarized
electromagnetic wave propagating through a plasma. These states are
exact nonlinear solutions of the 1-dimensional Maxwell-fluid model
for a cold plasma composed of electrons and ions. The solitary wave,
which consists of an electromagnetic wave trapped in a self-generated
Langmuir wave, presents a phase modulation when the group velocity
V and the phase velocity Vph of the long circularly polarized electromagnetic
wave do not match the condition {VVph}?=?c2. The main properties
of the waves as a function of their group velocities, wavevectors,
and frequencies are studied, as well as bifurcations of the dynamical
system that describes the waves when the parameter controlling the
phase modulation changes from zero to a finite value. Such a transition
is illustrated in the limit of small amplitude waves where an analytical
solution for a grey solitary wave exists. The solutions are interpreted
as the stationary state after the collision of a long laser pulse
with an isolated solitary wave.},
DOI = {10.1063/1.3624498}
}
@Article{sanchez2015,
Title = {Relativistic breather-type solitary waves with linear polarization in cold plasmas},
Author = {S\'{a}nchez-Arriaga, G. and Siminos, E. and Saxena, V. and Kourakis, I.},
Journal = {Phys. Rev. E},
Year = {2015},
Pages = {033102},
Volume = {91},
Abstract = {Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. Localized structures, in the form of exact numerical nonlinear solutions of the one-dimensional Maxwell-fluid model for a cold plasma with fixed ions, are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breather-type behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finite-differences scheme allows us to compute a branch of solutions within the frequency range Ωmin{\textless}Ω{\textless}ωpe, where ωpe and Ωmin are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatiotemporal structure of the waves and their main properties as a function of Ω is presented. Small-amplitude oscillations appearing in the tail of the solitary waves, a consequence of the linear polarization and harmonic excitation, are explained with the aid of the Akhiezer-Polovin system. Direct numerical simulations of the Maxwell-fluid model show that these solitary waves propagate without change for a long time.},
DOI = {10.1103/PhysRevE.91.033102}
}
@Article{Saad1986,
Title = {{GMRES}: {A} generalized minimal residual algorithm for solving nonsymmetric linear systems},
Author = {Saad, Y. and Schultz, M. H.},
Journal = {SIAM J. Sci. Stat. Comput.},
Year = {1986},
Pages = {856--869},
Volume = {7},
DOI = {10.1137/0907058}
}
@Article{SHcgl90,
Title = {Pulses and fronts in the complex {Ginzburg-Landau} equation near a subcritical bifurcation},
Author = {van Saarloos, W. and P. C. Hohenberg},
Journal = {Phys. Rev. Lett.},
Year = {1990},
Pages = {749},
Volume = {64},
DOI = {10.1103/physrevlett.64.749}
}
@Article{SHcoh92,
Title = {Fronts, pulses, sources and sinks in generalized complex {Ginzburg-Landau} equations},
Author = {van Saarloos, W. and Hohenberg, P. C.},
Journal = {Physica D},
Year = {1992},
Pages = {303--367},
Volume = {56},
DOI = {10.1016/0167-2789(92)90175-M}
}
@Article{Sacker65,
Title = {A new approach to the perturbation theory of invariant surfaces},
Author = {Sacker, R. J.},
Journal = {Commun. Pure Appl. Math.},
Year = {1965},
Pages = {717--732},
Volume = {18},
DOI = {10.1002/cpa.3160180409}
}
@InProceedings{SadoEfst05,
Title = {No polar coordinates},
Author = {D. A. Sadovski and K. Efstathiou},
Booktitle = {Geometric Mechanics and Symmetry: the Peyresq Lectures},
Year = {2005},
Address = {Cambridge},
Editor = {J. Montaldi and T. Ratiu},
Pages = {211--302},
Publisher = {Cambridge Univ. Press}
}
@Misc{sahai2015,
Title = {A chaotic dynamical system that paints},
Author = {Sahai, T. and Mathew, G. and Surana, A.},
Year = {2015},
URL = {http://arXiv.org/abs/1504.02010}
}
@Article{Saiki07,
Title = {Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors},
Author = {Saiki, Y.},
Journal = {Nonlin. Proc. Geophys.},
Year = {2007},
Pages = {615--620},
Volume = {14},
DOI = {10.5194/npg-14-615-2007}
}
@Article{SaiYam98,
Title = {Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems},
Author = {Y. Saiki and M. Yamada},
Journal = {Nonlin. Proc. Geophys.},
Year = {2008},
Pages = {675--680},
Volume = {15},
DOI = {10.5194/npg-15-675-2008}
}
@Article{SYCMR15,
Title = {Reconstruction of chaotic saddles by classification of unstable periodic orbits: {Kuramoto-Sivashinsky} equation},
Author = {Saiki, Y. and Yamada, M. and Chian, A. C.-L. and Miranda, R. A. and Rempel, E. L.},
Journal = {Chaos},
Year = {2015},
Pages = {103123},
Volume = {25},
DOI = {10.1063/1.4933267}
}
@Article{saka90br,
Title = {Breakdown of the phase dynamics},
Author = {H. Sakaguchi},
Journal = {Progr. Theor. Phys.},
Year = {1990},
Pages = {792--800},
Volume = {84},
DOI = {10.1143/ptp.84.792}
}
@Article{SakWhe03,
Title = {Semiclassical trace formulas for noninteracting identical particles},
Author = {J. Sakhr and N. D. Whelan},
Journal = {Phys. Rev. E},
Year = {2003},
Pages = {066213},
Volume = {67},
DOI = {10.1103/physreve.67.066213}
}
@Article{SakSug03rnold,
Title = {A projection method for generalized eigenvalue problems using numerical integration},
Author = {Sakurai, T. and Sugiura, H.},
Journal = {J. Comput. Appl. Math.},
Year = {2003},
Pages = {119--128},
Volume = {159},
DOI = {10.1016/s0377-0427(03)00565-x}
}
@Article{SalArt15,
Title = {Oseledets' splitting of standard-like maps},
Author = {Sala, M. and Artuso, R.},
Journal = {Chaos},
Year = {2015},
Volume = {25},
DOI = {10.1063/1.4909524}
}
@Incollection{Sald12,
author = {L. E. Saldana},
title = {A survey of spiral wave studies: {Dynamics} and symmetries},
booktitle = {{ChaosBook.org/projects}},
publisher = {Georgia Inst. of Technology},
year = {2012},
chapter = {A survey of spiral wave studies: {Dynamics} and symmetries},
url = {http://ChaosBook.org/projects/index.shtml#Saldana},
}
@Book{Salmon98,
Title = {Lectures on Geophysical Fluid Dynamics},
Author = {Salmon, R.},
Publisher = {Oxford Univ. Press},
Year = {1998},
Address = {Oxford}
}
@Article{saltzman1962,
Title = {Finite amplitude free convection as an initial value problem},
Author = {B. Saltzman},
Journal = {J. Atmos. Sci.},
Year = {1962},
Pages = {329--341},
Volume = {19},
DOI = {10.1175/1520-0469(1962)019<0329:fafcaa>2.0.co;2},
URL = {http://dx.doi.org/10.1175/1520-0469(1962)019<0329:fafcaa>2.0.co;2}
}
@Article{samelson01,
Title = {{Lyapunov}, {Floquet}, and singular vectors for baroclinic waves},
Author = {Samelson, R. M.},
Journal = {Nonlin. Proc. Geophys.},
Year = {2001},
Pages = {439--448},
Volume = {8},
DOI = {10.5194/npg-8-439-2001}
}
@Article{same01,
Title = {Periodic orbits and disturbance growth for baroclinic waves},
Author = {Samelson, R. M.},
Journal = {J. Atmos. Sci.},
Year = {2001},
Pages = {436--450},
Volume = {58},
DOI = {10.1175/1520-0469(2001)058<0436:poadgf>2.0.co;2}
}
@Article{samelson03,
Title = {A nonlinear baroclinic wave-mean oscillation with multiple normal-mode instabilities},
Author = {Samelson, R. M. and Wolfe, C. L.},
Journal = {J. Atmos. Sci.},
Year = {2003},
Pages = {1186--1199},
Volume = {60},
DOI = {10.1175/1520-0469(2003)060<1186:anbwow>2.0.co;2}
}
@Article{Samoilenko2005,
Title = {Conditions for synchronization of one oscillation system},
Author = {A. M. Samoilenko and L. Recke},
Journal = {Ukrain. Math. J.},
Year = {2005},
Pages = {1089--1119},
Volume = {57},
DOI = {10.1007/s11253-005-0250-3}
}
@Article{sand-jensen2007,
Title = {How to write consistently boring scientific literature},
Author = {Sand-Jensen, K.},
Journal = {Oikos},
Year = {2007},
Pages = {723--727},
Volume = {116},
DOI = {10.1111/j.0030-1299.2007.15674.x}
}
@Article{Sandri96,
Title = {Numerical calculation of {Lyapunov} exponents},
Author = {M. Sandri},
Journal = {Mathematica J.},
Year = {1996},
Pages = {78--84},
Volume = {6},
URL = {http://www.mathematica-journal.com/issue/v6i3/article/sandri/contents/63sandri.pdf}
}
@Article{SaScWu97a,
Title = {Center-manifold reduction for spiral waves},
Author = {Sandstede, B. and Scheel, A. and Wulff, C.},
Journal = {C. R. Acad. Sci. Paris, S\'er. I},
Year = {1997},
Pages = {153--158},
Volume = {324},
DOI = {10.1016/s0764-4442(97)80030-4}
}
@Article{SaScWu97,
Title = {Dynamics of spiral waves on unbounded domains using center-manifold reductions},
Author = {Sandstede, B. and Scheel, A. and Wulff, C.},
Journal = {J. Diff. Eqn.},
Year = {1997},
Pages = {122--149},
Volume = {141},
DOI = {10.1006/jdeq.1997.3326}
}
@Article{SaScWu99a,
Title = {Bifurcations and dynamics of spiral waves},
Author = {Sandstede, B. and Scheel, A. and Wulff, C.},
Journal = {J. Nonlin. Sci.},
Year = {1999},
Pages = {439--478},
Volume = {9},
DOI = {10.1007/s003329900076}
}
@Incollection{SaScWu99,
Title = {Dynamical behavior of patterns with {Euclidean} symmetry},
Author = {Sandstede, B. and Scheel, A. and Wulff, C.},
Booktitle = {Pattern Formation in Continuous and Coupled Systems},
Publisher = {Springer},
Year = {1999},
Address = {New York},
Pages = {249--264},
DOI = {10.1007/978-1-4612-1558-5_19}
}
@Article{sanz12,
Title = {Model for ultraintense laser-plasma interaction at normal incidence},
Author = {Sanz, J. and Debayle, A. and Mima, K.},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {046411},
Volume = {85},
Abstract = {An analytical study of the relativistic interaction of a linearly
polarized laser field of ? frequency with highly overdense plasma
is presented. In agreement with one-dimensional particle-in-cell
simulations, the model self-consistently explains the transition
between the sheath inverse bremsstrahlung absorption regime and the
... heating (responsible for the ... electron bunches), as well as
the high harmonic radiations and the mean electron energy.},
DOI = {10.1103/PhysRevE.85.046411}
}
@Article{sarri10,
Title = {Observation of postsoliton expansion following laser propagation through an underdense plasma},
Author = {Sarri, G. and Singh, D. K. and Davies, J. R.},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {175007},
Volume = {105},
DOI = {10.1103/physrevlett.105.175007}
}
@Article{Sartori91,
author = {Sartori, G.},
title = {Geometric invariant theory: a model-independent approach to spontaneous symmetry and/or supersymmetry breaking},
journal = {Rivista Nuovo Cim.},
year = {1991},
volume = {14},
pages = {1--120},
doi = {10.1007/BF02810048},
}
@Article{SarTal98,
Title = {Orbit spaces of compact coregular simple Lie groups with 2, 3 and 4~{b}asic polynomial invariants: {Effective} tools in the analysis of invariant potentials},
Author = {Sartori, G. and Talamini, V.},
Journal = {J. Math. Phys.},
Year = {1998},
Pages = {2367--2401},
Volume = {39},
DOI = {10.1063/1.532294}
}
@Article{SarVal06,
Title = {Orbit spaces of reflection groups with 2, 3 and 4~{b}asic polynomial invariants},
Author = {Sartori, G. and Valente, G.},
Journal = {J. Phys. A},
Year = {1996},
Pages = {193},
Volume = {29},
DOI = {10.1088/0305-4470/29/1/019}
}
@Article{SarVal05b,
Title = {Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata},
Author = {Sartori, G. and Valente, G.},
Journal = {J. Phys. A},
Year = {2003},
Pages = {1913},
Volume = {36},
DOI = {10.1088/0305-4470/36/7/308}
}
@Article{SarVal05,
Title = {Constructive axiomatic approach to the determination of the orbit spaces of coregular compact linear groups},
Author = {Sartori, G. and Valente, G.},
Journal = {Acta Appl. Math.},
Year = {2005},
Pages = {191--228},
Volume = {87},
DOI = {10.1007/s10440-005-1144-y}
}
@Article{SarVal05a,
Title = {The radial problem in gauge field theory models},
Author = {G. Sartori and G. Valente},
Journal = {Ann. Phys.},
Year = {2005},
Pages = {286--325},
Volume = {319},
DOI = {10.1016/j.aop.2005.04.016}
}
@Article{Sartorius1998,
Title = {All-optical clock recovery module based on self-pulsating dfb laser},
Author = {B. Sartorius and C. Bornholdt and O. Brox and H. J. Ehrke and D. Hoffmann and R. Ludwig and M. M{\"o}hrle},
Journal = {Electronics Lett.},
Year = {1998},
Pages = {1664},
Volume = {34},
DOI = {10.1049/el:19981152}
}
@Article{Sato05,
Title = {Bartholdi zeta functions of group coverings of digraphs},
Author = {Sato, I.},
Journal = {Far East J. Math. Sci.},
Year = {2005},
Pages = {321–339},
Volume = {18},
URL = {http://www.pphmj.com/abstract/527.htm}
}
@Article{SaRo02,
author = {Saul, L. K. and Roweis, S. T.},
title = {{Think Globally, Fit Locally: Unsupervised} learning of low dimensional manifolds},
journal = {J. Mach. Learn. Res.},
year = {2003},
volume = {4},
pages = {119--155},
url = {http://www.jmlr.org/papers/v4/saul03a.html},
}
@Article{saxena2013,
Title = {Interaction of spatially overlapping standing electromagnetic solitons in plasmas},
Author = {Saxena, V. and Kourakis, I. and S\'anchez-Arriaga, G. and Siminos, E.},
Journal = {Phys. Lett. A},
Year = {2013},
Pages = {473--477},
Volume = {377},
DOI = {10.1016/j.physleta.2012.12.010}
}
@Article{Scarf67,
Title = {The approximation of fixed points of a continuous mapping},
Author = {H. Scarf},
Journal = {SIAM J. Appl. Math.},
Year = {1967},
Volume = {15},
DOI = {10.1137/0115116}
}
@Article{spercgl,
Title = {Small-amplitude periodic and chaotic solutions of the complex {Ginzburg-Landau} equation for a subcritical bifurcation},
Author = {W. Sch{\"{o}}pf and L. Kramer},
Journal = {Phys. Rev. Lett.},
Year = {1991},
Pages = {2316--2319},
Volume = {66},
DOI = {10.1103/physrevlett.66.2316}
}
@Article{ScFrKa82,
Title = {Diffusive dynamics in systems with translational symmetry: {A} one--dimensional--map model},
Author = {M. Schell and S. Fraser and R. Kapral},
Journal = {Phys. Rev. A},
Year = {1982},
Pages = {504--521},
Volume = {26},
DOI = {10.1103/PhysRevA.26.504}
}
@Article{SMcgl02,
author = {J. Scheuer and B. A. Malomed},
title = {Stable and chaotic solutions of the complex {Ginzburg-Landau} equation with periodic boundary conditions},
journal = {Physica D},
year = {2002},
volume = {161},
pages = {102--115},
doi = {10.1016/s0167-2789(01)00363-3},
}
@Article{SOHV05,
Title = {Continuation of quasi-periodic invariant tori},
Author = {F. Schilder and H. M. Osinga and W. Vogt},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2005},
Pages = {459--488},
Volume = {4},
DOI = {10.1137/040611240}
}
@Article{SchlAvVa11,
Title = {Numerical bifurcation study of superconducting patterns on a square},
Author = {Schl{\"o}mer, N. and Avitabile, D. and Vanroose, W.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2012},
Pages = {447--477},
Volume = {11},
DOI = {10.1137/100807132}
}
@Article{SD98,
Title = {General appoach to the localization of unstable periodic orbits in chaotic dynamical systems},
Author = {P. Schmelcher and F. K. Diakonos},
Journal = {Phys. Rev. E},
Year = {1998},
Pages = {2739--2746},
Volume = {57},
Abstract = {Change stability of maps to locate periodic orbits.},
DOI = {10.1103/physreve.57.2739}
}
@Incollection{Schmidt84,
Title = {Hamilton's principle and the splitting of periodic orbits},
Author = {Schmidt, G.},
Booktitle = {{Statistical Physics and Chaos in Fusion Plasmas}},
Publisher = {John Wiley and Sons},
Year = {1984},
Editor = {Horton Jr., C. W. and Reichl , L. E.},
Pages = {57},
DOI = {10.1016/0167-2789(83)90266-x},
ISBN = {9780471883104}
}
@Phdthesis{Schmi99,
Title = {Transition to Turbulence in Linearly Stable Shear Flows},
Author = {A. Schmiegel},
School = {Philipps-Universit{\"a}t Marburg},
Year = {1999},
URL = {http://archiv.ub.uni-marburg.de/diss/z2000/0062}
}
@Article{SE00,
Title = {Persistent turbulence in annealed plane {Couette} flow},
Author = {A. Schmiegel and B. Eckhardt},
Journal = {Europhys. Lett.},
Year = {2000},
Pages = {395--400},
Volume = {51},
DOI = {10.1209/epl/i2000-00507-2}
}
@Article{Schmitt04,
Title = {Spectral theory for nonanalytic coupled map lattices},
Author = {M. Schmitt},
Journal = {Nonlinearity},
Year = {2004},
Pages = {671},
Volume = {17},
DOI = {10.1088/0951-7715/17/2/018}
}
@Article{Schneider2005,
Title = {Entrainment of modulation frequency: {A} case study},
Author = {K. R. Schneider},
Journal = {Int. J. Bifur. Chaos},
Year = {2005},
Pages = {3579--3588},
Volume = {15},
DOI = {10.1142/s0218127405014234}
}
@Article{SchEckYor07,
Title = {Turbulence, transition, and the edge of chaos in pipe flow},
Author = {T. M. Schneider and B. Eckhardt and J. Yorke},
Journal = {Phys. Rev. Lett.},
Year = {2007},
Pages = {034502},
Volume = {99},
DOI = {10.1103/PhysRevLett.99.034502}
}
@Article{Schuster2000,
Title = {Review of {FDTD} time-stepping schemes for efficient simulation of electric conductive media},
Author = {Schuster, C. and Christ, A. and Fichtner, W.},
Journal = {Microw. Opt. Technol. Lett.},
Year = {2000},
Pages = {16--21},
Volume = {25},
DOI = {10.1002/(SICI)1098-2760(20000405)25:1<16::AID-MOP6>3.0.CO;2-O}
}
@Book{Schutz80,
Title = {Geometrical Methods of Mathematical Physics},
Author = {Schutz, B. F.},
Publisher = {Cambridge Univ. Press},
Year = {1980},
Address = {Cambridge}
}
@Book{Schutz85,
Title = {A First Course in General Relativity},
Author = {Schutz, B. F.},
Publisher = {Cambridge Univ. Press},
Year = {1985},
Address = {Cambridge}
}
@Article{Schwartz62,
Title = {Global cross sections of compact dynamical systems},
Author = {Schwartzman, S.},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {1962},
Pages = {786--791},
Volume = {48},
DOI = {10.1073/pnas.48.5.786}
}
@Article{Schwarz75,
Title = {Smooth functions invariant under the action of a compact {Lie} group},
Author = {G. Schwarz},
Journal = {Topology},
Year = {1975},
Pages = {63--68},
Volume = {14},
DOI = {10.1016/0040-9383(75)90036-1}
}
@Article{Selberg56,
Title = {Harmonic analysis and discontinuous groups in weakly symmetric {Riemannian} spaces with applications to {Dirichlet} series},
Author = {Selberg, A.},
Journal = {J. Indian Math. Soc. (N.S.)},
Year = {1956},
Pages = {47--87},
Volume = {20}
}
@Article{SelBran04,
Title = {Preferred regime transition routes and evidence for an unstable periodic orbit in a baroclinic model},
Author = {F. M. Selten and G. Branstator},
Journal = {J. Atmos. Sci.},
Year = {2004},
Pages = {2267--2282},
Volume = {61},
DOI = {10.1175/1520-0469(2004)061<2267:PRTRAE>2.0.CO;2}
}
@Article{condisfam1,
Title = {Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators},
Author = {J.-A. Sepulchre and R. Mackay},
Journal = {Nonlinearity},
Year = {1997},
Pages = {679--713},
Volume = {10},
DOI = {10.1088/0951-7715/10/3/006}
}
@Article{Shabanov00,
author = {Shabanov, S. V.},
title = {Geometry of the physical phase space in quantum gauge systems},
journal = {Phys. Lett.},
year = {2000},
volume = {326},
pages = {1--163},
doi = {10.1016/S0370-1573(99)00085-X},
}
@Article{SZN98,
Title = {Direct numerical simulation of transition in pipe flow under the influence of wall disturbances},
Author = {H. Shan and Z. Zhang and F.T.M Nieuwstadt},
Journal = {Int. J. Heat Fluid Flow},
Year = {1998},
Pages = {320--325},
Volume = {19},
DOI = {10.1016/S0142-727X(98)10008-5}
}
@Article{ShSi82,
Title = {Irregular flow of a liquid film down a vertical column},
Author = {T. Shlang and G. I. Sivashinsky},
Journal = {J. Physique},
Year = {1982},
Pages = {459--466},
Volume = {43},
DOI = {10.1051/jphys:01982004303045900}
}
@Article{ShWi87,
Title = {Self-propulsion at low {Reynolds} number},
Author = {Shapere, A. and Wilczek, F.},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {2051--2054},
Volume = {58},
DOI = {10.1103/physrevlett.58.2051}
}
@Article{ShWi89,
Title = {Efficiencies of self-propulsion at low {Reynolds} number},
Author = {Shapere, A. and Wilczek, F.},
Journal = {J. Fluid Mech.},
Year = {1989},
Pages = {587--599},
Volume = {198},
DOI = {10.1017/s0022112089000261}
}
@Article{ShWi89a,
Title = {Gauge kinematics of deformable bodies},
Author = {Shapere, A. and Wilczek, F.},
Journal = {Amer. J. Physics},
Year = {1989},
Pages = {514--518},
Volume = {57},
DOI = {10.1119/1.15986}
}
@Article{ShWi06,
Title = {Geometry of self-propulsion at low {Reynolds} number},
Author = {Shapere, A. and Wilczek, F.},
Journal = {J. Fluid Mech.},
Year = {1989},
Pages = {557},
Volume = {198},
DOI = {10.1017/s002211208900025x}
}
@Article{shch04fli,
Title = {Analyzing intramolecular dynamics by fast {Lyapunov} indicators},
Author = {E. Shchekinova and C. Chandre and Y. Lan and T. Uzer},
Journal = {J. Chem. Phys.},
Year = {2004},
Pages = {3471},
Volume = {121},
DOI = {10.1063/1.1756875}
}
@Article{sheng02,
Title = {Stochastic heating and acceleration of electrons in colliding laser fields in plasma},
Author = {Sheng, Z.-M. and Mima, K. and Sentoku, Y. and Jovanovi\'c, M. S. and Taguchi, T. and Zhang, J. and Meyer-ter-Vehn, J.},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Pages = {055004},
Volume = {88},
Abstract = {We propose a mechanism that leads to efficient acceleration of electrons
in plasma by two counterpropagating laser pulses. It is triggered
by stochastic motion of electrons when the laser fields exceed some
threshold amplitudes, as found in single-electron dynamics. It is
further confirmed in particle-in-cell simulations. In vacuum or tenuous
plasma, electron acceleration in the case with two colliding laser
pulses can be much more efficient than with one laser pulse only.
In plasma at moderate densities, such as a few percent of the critical
density, the amplitude of the Raman-backscattered wave is high enough
to serve as the second counterpropagating pulse to trigger the electron
stochastic motion. As a result, even with one intense laser pulse
only, electrons can be heated up to a temperature much higher than
the corresponding laser ponderomotive potential.},
DOI = {10.1103/PhysRevLett.88.055004}
}
@Article{ShenKad82,
Title = {Critical behavior of a {KAM} surface: I. {Empirical} results},
Author = {S. J. Shenker and L. P. Kadanoff},
Journal = {J. Stat. Phys.},
Year = {1982},
Pages = {631--656},
Volume = {27},
DOI = {10.1007/bf01013439}
}
@Article{Shepherd88,
Title = {Nonlinear saturation of baroclinic instability. {Part I: The} two-layer model},
Author = {Shepherd, T. G.},
Journal = {J. Atmos. Sci.},
Year = {1988},
Pages = {2014--2025},
Volume = {45},
DOI = {10.1175/1520-0469(1988)045<2014:NSOBIP>2.0.CO;2}
}
@Article{Sherman60,
Title = {Combinatorial aspects of the {Ising} model for ferromagnetism. {I. A} conjecture of {Feynman} on paths and graphs},
Author = {Sherman, S.},
Journal = {J. Math. Phys.},
Year = {1960},
Pages = {202--217},
Volume = {1},
DOI = {10.1063/1.1703653}
}
@Article{Shimada79,
Title = {Gibbsian distribution on the {Lorenz} attractor},
Author = {Shimada, I.},
Journal = {Progr. Nonlinear Differential Equations Appl.. Theor. Phys.},
Year = {1979},
Pages = {61--69},
Volume = {62},
DOI = {10.1143/PTP.62.61}
}
@Article{ShiNag79,
Title = {A numerical approach to ergodic problem of dissipative dynamical systems},
Author = {Shimada, I. and Nagashima, T.},
Journal = {Progr. Nonlinear Differential Equations Appl.. Theor. Phys.},
Year = {1979},
Pages = {1605--1616},
Volume = {61},
DOI = {10.1143/ptp.61.1605}
}
@Article{Shkad77,
author = {V. Y. Shkadov},
title = {Solitary waves in a layer of viscous liquid},
journal = {Fluid Dynam.},
year = {1977},
volume = {12},
pages = {52--55},
doi = {10.1007/BF01074624},
}
@Article{SPScgl92,
Title = {Spatiotemporal chaos in the one-dimensional complex {Ginzburg-Landau} equation},
Author = {B. I. Shraiman and A. Pumir and van Saarloos, W. and Hohenberg, P. C. and H. Chat\'{e} and M. Holen},
Journal = {Physica D},
Year = {1992},
Pages = {241--248},
Volume = {57},
DOI = {10.1016/0167-2789(92)90001-4}
}
@Article{shroff1099,
author = {G. M. Shroff and H. B. Keller},
title = {Stabilization of unstable procedures: the recursive projection method},
journal = {SIAM J. Numer. Anal.},
year = {1993},
volume = {30},
pages = {1099--1120},
doi = {10.1137/0730057},
}
@Book{lyschm,
Title = {{Lyapunov-Schmidt} Methods in Nonlinear Analysis and Applications},
Author = {N. Sidorov and B. Loginov and A. Sinitsyn and M. Falaleev},
Publisher = {Kluwer},
Year = {2002},
Address = {Dordrecht}
}
@Article{Sieber2002,
Title = {Numerical bifurcation analysis for multisection semiconductor lasers},
Author = {J. Sieber},
Journal = {SIAM J. Appl. Math.},
Year = {2002},
Pages = {248--270},
Volume = {1},
DOI = {10.1137/s1111111102401746}
}
@Article{SieRic01,
Title = {Correlations between periodic orbits and their rôle in spectral statistics},
Author = {M. Sieber and K. Richter},
Journal = {Phys. Scr.},
Year = {2001},
Pages = {128},
Volume = {2001},
DOI = {10.1238/Physica.Topical.090a00128}
}
@Article{siegel42,
Title = {Iteration of analytic functions},
Author = {C. L. Siegel},
Journal = {Ann. Math.},
Year = {1942},
Pages = {607--612},
Volume = {43},
DOI = {10.2307/1968952}
}
@InProceedings{carsim,
Title = {On the analytical and numerical approximation of invariant manifolds},
Author = {Sim{\'o}, C.},
Booktitle = {Les M\'{e}thodes Modernes de la M\'{e}canique C\'{e}leste (Goutelas '89)},
Year = {1989},
Address = {Gif-sur-Yvette, France},
Editor = {D. Benest and C. Froeschl\'{e}},
Pages = {285--329},
Publisher = {Editions Frontieres}
}
@Phdthesis{SiminosThesis,
Title = {Recurrent Spatio-temporal Structures in Presence of Continuous Symmetries},
Author = {Siminos, E.},
School = {School of Physics, Georgia Inst. of Technology},
Year = {2009},
Address = {Atlanta},
URL = {http://ChaosBook.org/projects/theses.html}
}
@Misc{siminos2014c,
author = {Siminos, E.},
title = {Signatures of relativistic chaos in optical lattices, work in progress},
year = {2014},
}
@Article{siminos11,
Title = {Stability of nonlinear {Vlasov-Poisson} equilibria through spectral deformation and {Fourier-{Hermit}e} expansion},
Author = {Siminos, Evangelos and B\'enisti, Didier and Gremillet, Laurent},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {056402},
Volume = {83},
Abstract = {We study the stability of spatially periodic, nonlinear Vlasov-Poisson
equilibria as an eigenproblem in a Fourier-Hermite basis (in the
space and velocity variables, respectively) of finite dimension,
N. When the advection term in the Vlasov equation is dominant, the
convergence with N of the eigenvalues is rather slow, limiting the
applicability of the method. We use the method of spectral deformation
introduced by Crawford and Hislop Ann. Phys. ({NY)} 189 265 (1989)
to selectively damp the continuum of neutral modes associated with
the advection term, thus accelerating convergence. We validate and
benchmark the performance of our method by reproducing the kinetic
dispersion relation results for linear (spatially homogeneous) equilibria.
Finally, we study the stability of a periodic Bernstein-Greene-Kruskal
mode with multiple phase-space vortices, compare our results with
numerical simulations of the Vlasov-Poisson system, and show that
the initial unstable equilibrium may evolve to different asymptotic
states depending on the way it was perturbed.},
DOI = {10.1103/PhysRevE.83.056402}
}
@Unpublished{SCD09b,
Title = {Symmetry reduction: {Geometry} of a {Kuramoto-Sivashinsky} attractor revealed},
Author = {Siminos, E. and Budanur, N. B. and Cvitanovi{\'c}, P. and Davidchack, R. L.},
Note = {In preparation},
Year = {2015}
}
@Article{SiCvi10,
Title = {Continuous symmetry reduction and return maps for high-dimensional flows},
Author = {Siminos, E. and Cvitanovi{\'c}, P.},
Journal = {Physica D},
Year = {2011},
Pages = {187--198},
Volume = {240},
DOI = {10.1016/j.physd.2010.07.010}
}
@Misc{siminos2014p,
author = {Siminos, E. and Grech, M. and Skupin, S.},
title = {Onset of self-induced transparency in the hole boring regime in relativistic laser-plasma interaction, in preparation},
year = {2014},
}
@Article{siminos2012,
Title = {Effect of electron heating on self-induced transparency in relativistic-intensity laser-plasma interactions},
Author = {Siminos, E. and Grech, M. and Skupin, S. and Schlegel, T. and Tikhonchuk, V. T.},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {056404},
Volume = {86},
Abstract = {The effective increase of the critical density associated with the
interaction of relativistically intense laser pulses with overcritical
plasmas, known as self-induced transparency, is revisited for the
case of circular polarization. A comparison of particle-in-cell simulations
to the predictions of a relativistic cold-fluid model for the transparency
threshold demonstrates that kinetic effects, such as electron heating,
can lead to a substantial increase of the effective critical density
compared to cold-fluid theory. These results are interpreted by a
study of separatrices in the single-electron phase space corresponding
to dynamics in the stationary fields predicted by the cold-fluid
model. It is shown that perturbations due to electron heating exceeding
a certain finite threshold can force electrons to escape into the
vacuum, leading to laser pulse propagation. The modification of the
transparency threshold is linked to the temporal pulse profile, through
its effect on electron heating.},
DOI = {10.1103/PhysRevE.86.056404}
}
@Article{siminos2014,
Title = {Modeling relativistic soliton interactions in overdense plasmas: {A} perturbed nonlinear {Schr{\"o}dinger} equation framework},
Author = {E. Siminos and G. S{\'a}nchez-Arriaga and V. Saxena and I. Kourakis},
Journal = {Phys. Rev. E},
Year = {2014},
Pages = {063104},
Volume = {90},
Abstract = {We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude.},
DOI = {10.1103/PhysRevE.90.063104},
Shorttitle = {Modeling relativistic soliton interactions in overdense plasmas}
}
@Misc{siminos2014s,
author = {Siminos, E. and S\'anchez-Arriaga, G. and Saxena, V. and Kourakis, I.},
title = {Describing relativistic soliton interactions through envelope equations, in preparation},
year = {2014},
}
@Phdthesis{Simonis2006,
author = {Simonisk, J. P.},
title = {{Inexact {Newton} Methods Applied to Under-Determined Systems}},
school = {Polytechnic Inst.},
year = {2006},
address = {Worcester, MA},
url = {https://web.wpi.edu/Pubs/ETD/Available/etd-050406-103442/unrestricted/simonis.pdf},
}
@Article{Sinai59,
Title = {On the concept of entropy of a dynamical system},
Author = {Sinai, Ya. G.},
Journal = {Dokl. Akad. Nauk. SSSR},
Year = {1959},
Pages = {768--771},
Volume = {124}
}
@Article{Sinai70,
Title = {Dynamical systems with elastic reflections},
Author = {Sinai, Ya. G.},
Journal = {Russ. Math. Surv.},
Year = {1970},
Pages = {137--189},
Volume = {25},
DOI = {10.1070/RM1970v025n02ABEH003794}
}
@Article{sinai,
Title = {Gibbs measures in ergodic theory},
Author = {Ya. G. Sinai},
Journal = {Russian Math. Surveys},
Year = {1972},
Pages = {21},
Volume = {27},
DOI = {10.1070/RM1972v027n04ABEH001383}
}
@Book{sinai76,
Title = {{Introduction to Ergodic Theory}},
Author = {Ya. G. Sinai},
Publisher = {Princeton Univ. Press},
Year = {1976},
Address = {Princeton},
ISBN = {9780691081823}
}
@Article{Sinai90,
Title = {Some mathematical problems in the theory of quantum chaos},
Author = {Ya. G. Sinai},
Journal = {Physica A},
Year = {1990},
Pages = {197--204},
Volume = {163},
DOI = {10.1016/0378-4371(90)90329-Q}
}
@Article{Sinai04,
Title = {What is ...a billiard},
Author = {Sinai, Ya. G.},
Journal = {Notices Amer. Math. Soc.},
Year = {2004},
Pages = {412--413},
Volume = {51},
URL = {http://www.ams.org/notices/200404/what-is.pdf}
}
@Article{Singer78,
Title = {Some Remarks on the {Gribov} Ambiguity},
Author = {Singer, I. M.},
Journal = {Commun. Math. Phys.},
Year = {1978},
Pages = {7--12},
Volume = {60},
DOI = {10.1007/BF01609471}
}
@Article{SiRo87,
Title = {Coherent structures and chaos: {A} model problem},
Author = {L. Sirovich and J. D. Rodriguez},
Journal = {Phys. Lett. A},
Year = {1987},
Pages = {211--214},
Volume = {120},
DOI = {10.1016/0375-9601(87)90209-x},
URL = {http://dx.doi.org/10.1016/0375-9601(87)90209-x}
}
@Article{Sirovich94,
author = {L. Sirovich and X. Zhou},
title = {Reply to ``{Observations} regarding '{Coherenc}e and chaos in a model of turbulent boundary layer' by {X}. {Z}hou and {L}. {S}irovich''},
journal = {Phys. Fluids},
year = {1994},
volume = {6},
pages = {1579--1582},
}
@Article{siv,
Title = {Nonlinear analysis of hydrodynamical instability in laminar flames - {I}. {D}erivation of basic equations},
Author = {G. I. Sivashinsky},
Journal = {Acta Astronaut.},
Year = {1977},
Pages = {1177--1206},
Volume = {4},
DOI = {10.1016/0094-5765(77)90096-0}
}
@Article{sivmich80,
author = {G. I. Sivashinsky and D. M. Michelson},
title = {On irregular wavy flow of a liquid down a vertical plane},
journal = {Progr. Theor. Phys.},
year = {1980},
pages = {2112--2114},
doi = {10.1143/PTP.63.2112},
}
@Article{Skarka06,
Title = {Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic {Ginzburg-Landau} equations},
Author = {Skarka, V. and Aleksi{\'c} N. B.},
Journal = {Phys. Rev. Lett.},
Year = {2006},
Pages = {013903},
Volume = {96},
DOI = {10.1103/PhysRevLett.96.013903}
}
@Proceedings{SDS11,
title = {{Chaos Theory: Modeling, Simulation and Applications}},
year = {2011},
editor = {Skiadas, C.H. and Dimotikalis, I. and Skiadas, C.},
publisher = {World Scientific},
isbn = {9789814460477},
}
@Article{Skokos02,
Title = {Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits},
Author = {Skokos, C.},
Journal = {J. Phys. A},
Year = {2001},
Pages = {10029},
Volume = {34},
DOI = {10.1088/0305-4470/34/47/309}
}
@Incollection{Skokos08,
author = {Skokos, C.},
title = {The {Lyapunov} characteristic exponents and their computation},
booktitle = {Dynamics of Small Solar System Bodies and Exoplanets},
publisher = {Springer},
year = {2010},
editor = {Souchay, J. J. and Dvorak, R.},
volume = {790},
series = {Lect. Notes Phys.},
pages = {63--135},
address = {New York},
doi = {10.1007/978-3-642-04458-8_2},
}
@Article{SYE05,
Title = {{Edge of Chaos} in a parallel shear flow},
Author = {J. D. Skufca and J. A. Yorke and B. Eckhardt},
Journal = {Phys. Rev. Lett.},
Year = {2006},
Pages = {174101},
Volume = {96},
DOI = {10.1103/PhysRevLett.96.174101}
}
@Article{SlBaJu13,
Title = {On the relation between {Lyapunov} exponents and exponential decay of correlations},
Author = {J. Slipantschuk and O. F. Bandtlow and W. Just},
Journal = {J. Phys. A},
Year = {2013},
Pages = {075101},
Volume = {46},
Abstract = {Chaotic dynamics with sensitive dependence on initial conditions may
result in exponential decay of correlation functions. We show that
for one-dimensional interval maps the corresponding quantities, that
is, Lyapunov exponents and exponential decay rates, are related.
More specifically, for piecewise linear expanding Markov maps observed
via piecewise analytic functions, we show that the decay rate is
bounded above by twice the Lyapunov exponent, that is, we establish
lower bounds for the subleading eigenvalue of the corresponding Perron-Frobenius
operator. In addition, we comment on similar relations for general
piecewise smooth expanding maps.},
DOI = {10.1088/1751-8113/46/7/075101}
}
@Article{smale_61,
Title = {Generalized {Poincar\'e}'s conjecture in dimensions greater than four},
Author = {S. Smale},
Journal = {Ann. Math.},
Year = {1961},
Pages = {199},
Volume = {74},
DOI = {10.2307/1970239}
}
@Article{smale,
Title = {Differentiable dynamical systems},
Author = {S. Smale},
Journal = {Bull. Amer. Math. Soc.},
Year = {1967},
Pages = {747--817},
Volume = {73},
DOI = {10.1090/S0002-9904-1967-11798-1}
}
@Article{Smale70I,
Title = {Topology and mechanics, {I}.},
Author = {S. Smale},
Journal = {Inv. Math.},
Year = {1970},
Pages = {305--331},
Volume = {10},
DOI = {10.1007/BF01418778}
}
@Article{Smale70II,
Title = {Topology and mechanics, {II}.},
Author = {S. Smale},
Journal = {Inv. Math.},
Year = {1970},
Pages = {45--64},
Volume = {11},
DOI = {10.1007/BF01389805}
}
@Book{Smale80,
Title = {The Mathematics of Time},
Author = {S. Smale},
Publisher = {Springer},
Year = {1980},
Address = {New York},
ISBN = {9781461381013},
Annote = {Subtitle: Essays on Dynamical Systems, Economic Processes and related topics}
}
@Book{Smale00,
Title = {The collected papers of {Stephen Smale}},
Author = {S. Smale and F. Cucker and R. Wong},
Publisher = {World Scientific},
Year = {2000},
Address = {Singapore}
}
@Phdthesis{SmithThesis12,
Title = {Point Vortices: Finding Periodic Orbits and their Topological Classification},
Author = {Smith, S. A.},
School = {Mathematics Dept., Tufts University},
Year = {2012},
Address = {Medford, Mass},
URL = {http://gradworks.umi.com/3541851.pdf}
}
@Article{SmiBog11,
Title = {Robust numerical method for integration of point-vortex trajectories in two dimensions},
Author = {Smith, S. A. and Boghosian, B. M.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {056702},
Volume = {83},
DOI = {10.1103/PhysRevE.83.056702},
Issue = {5}
}
@Article{SmMoehHo05,
Title = {Heteroclinic cycles and periodic orbits for the {O(2)}-equivariant 0:1:2~{m}ode interaction},
Author = {T. R. Smith and J. Moehlis and P. Holmes},
Journal = {Physica D},
Year = {2005},
Pages = {347--376},
Volume = {211},
DOI = {10.1016/j.physd.2005.09.002}
}
@Article{So91,
Title = {Inertial manifold for a reaction diffusion equation model of competition in a chemostat},
Author = {J. W.-H. So},
Journal = {J. Austral. Math. Soc. Ser. B},
Year = {1991},
Pages = {9},
Volume = {33},
DOI = {10.1017/s0334270000008584}
}
@Article{solLagr03,
Title = {Lagrangian chaos and multiphase processes in vortex flows},
Author = {T. H. Solomon and B. R. Wallace and . S. Miller and C. J. L. Spohn},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2003},
Pages = {239--252},
Volume = {8},
DOI = {10.1016/S1007-5704(03)00047-9}
}
@Article{solomon1994chaotic,
Title = {Chaotic advection in a two-dimensional flow: {L{\'e}vy} flights and anomalous diffusion},
Author = {Solomon, T. H. and Weeks, E. R. and Swinney, H. L.},
Journal = {Physica D},
Year = {1994},
Pages = {70--84},
Volume = {76},
DOI = {10.1016/0167-2789(94)90251-8}
}
@Article{Sorensen1992,
Title = {{Implicit application of polynomial filters in a k-step Arnoldi method}},
Author = {Sorensen, D.C.},
Journal = {SIAM J. Matrix Anal. Appl.},
Year = {1992},
Pages = {357--385},
Volume = {13},
DOI = {10.1137/0613025}
}
@Article{SoAk05b,
Title = {Exploding soliton and front solutions of the complex cubic--quintic {Ginzburg--Landau} equation},
Author = {Soto-Crespo, J. M. and Akhmediev, N.},
Journal = {Math. Comput. Simulat.},
Year = {2005},
Pages = {526--536},
Volume = {69},
DOI = {10.1016/j.matcom.2005.03.006}
}
@Article{SoAk05,
Title = {Soliton as strange attractor: nonlinear synchronization and chaos},
Author = {Soto-Crespo, J. M and Akhmediev, N.},
Journal = {Phys. Rev. Lett.},
Year = {2005},
Pages = {024101},
Volume = {95},
DOI = {10.1103/PhysRevLett.95.024101}
}
@Article{SoAkAn00,
Title = {Pulsating, creeping, and erupting solitons in dissipative systems},
Author = {Soto-Crespo, J. M. and Akhmediev, N. and Ankiewicz, A.},
Journal = {Phys. Rev. Lett.},
Year = {2000},
Pages = {2937--2940},
Volume = {85},
DOI = {10.1103/PhysRevLett.85.2937}
}
@Article{SoAkCh01,
Title = {Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems},
Author = {J. M. Soto-Crespo and N. Akhmediev and K. S. Chiang},
Journal = {Phys. Lett. A},
Year = {2001},
Pages = {115--123},
Volume = {291},
DOI = {10.1016/S0375-9601(01)00634-X}
}
@Article{SoAkDeMe08,
Title = {Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons},
Author = {J. M. Soto-Crespo and N. Akhmediev and N. Devine and C. Mej\'{i}a-Cort\'{e}s},
Journal = {Opt. Express},
Year = {2008},
Pages = {15388--15401},
Volume = {16},
DOI = {10.1364/OE.16.015388}
}
@Article{SoAkAf96,
Title = {Stability of the pulselike solutions of the quintic complex {Ginzburg--Landau} equation},
Author = {Soto-Crespo, J. M. and Akhmediev, N. N. and Afanasjev, V. V.},
Journal = {J. Opt. Soc. Am. B},
Year = {1996},
Pages = {1439--1449},
DOI = {10.1364/JOSAB.13.001439}
}
@Article{SoAkAfWa97,
Title = {Pulse solutions of the cubic-quintic complex {Ginzburg-Landau} equation in the case of normal dispersion},
Author = {Soto-Crespo, J. M. and Akhmediev, N. N. and Afanasjev, V. V. and Wabnitz, S.},
Journal = {Phys. Rev. E},
Year = {1997},
Pages = {4783},
Volume = {55},
DOI = {10.1103/PhysRevE.55.4783}
}
@Book{Sou70,
Title = {Structure des syst\`emes dynamiques},
Author = {J.-M. Souriau},
Publisher = {Dunod},
Year = {1970},
Address = {Paris}
}
@Book{Sou97,
Title = {Structure of Dynamical Systems},
Author = {J.-M. Souriau},
Publisher = {Birkh\"auser},
Year = {1997},
Address = {Boston}
}
@Article{Spalart91,
Title = {Spectral methods for the {Navier-Stokes} equations with one infinite and two periodic directions},
Author = {P. R. Spalart and R. D. Moser and M. M. Rogers},
Journal = {J. Comput. Phys.},
Year = {1990},
Pages = {297--324},
Volume = {96},
DOI = {10.1016/0021-9991(91)90238-g}
}
@Article{spald91,
Title = {Kolmogorov's two-equation model of turbulence},
Author = {D. B. Spalding},
Journal = {Proc. R. Soc. Lond. A},
Year = {1991},
Pages = {211--216},
Volume = {434},
DOI = {10.1098/rspa.1991.0089}
}
@Book{sparrow,
title = {The {Lorenz} Equations: {Bifurcations}, Chaos and Strange Attractors},
publisher = {Springer},
year = {1982},
author = {C. Sparrow},
address = {New York},
doi = {10.1007/978-1-4612-5767-7},
}
@Article{EAS87,
Title = {Chaos: a mixed metaphor for turbulence},
Author = {E. A. Spiegel},
Journal = {Proc. Roy. Soc.},
Year = {1987},
Pages = {87},
Volume = {A413},
Booktitle = {Dynamical Chaos},
DOI = {10.1515/9781400860197.87},
Publisher = {Walter de Gruyter {GmbH}}
}
@Article{StaSte11,
Title = {Asymptotic estimates and stability analysis of {Kuramoto-Sivashinsky} type models},
Author = {M. Stanislavova and A. Stefanov},
Journal = {J. Evol. Eqs.},
Year = {2011},
Pages = {605--635},
Volume = {11},
DOI = {10.1007/s00028-011-0103-5}
}
@Article{StaNich12,
Title = {A suspension of the {H\'enon} map by periodic orbits},
Author = {J. Starrett and C. Nicholas},
Journal = {Chaos Solit. Fract.},
Year = {2012},
Pages = {1486--1493},
Volume = {45},
Abstract = {We create polynomial differential equations for a suspension of the
{H\'enon} map embedded in R 3 . By globalizing the local tangent
vectors to suspended periodic orbits of the {H\'enon} map, we are
able to find approximate autonomous differential equations for that
geometric suspension. Using as few as two suspended periodic orbits,
we can generate a robust three dimensional attractor whose Poincar\'e
map has very nearly the dynamics of the original {H\'enon} map on
the attractor.},
DOI = {10.1016/j.chaos.2012.07.013}
}
@Article{StMaKh08,
Title = {Nonlinear dynamics of hydrostatic internal gravity waves},
Author = {S. N. Stechmann and A. J. Majda and B. Khouider},
Journal = {Theor. Comput. Fluid Dyn.},
Year = {2008},
Pages = {407--432},
Volume = {22},
DOI = {10.1007/s00162-008-0080-7}
}
@Book{stein2012transport,
Title = {Transport and Diffusion Across Cell Membranes},
Author = {Stein, W.},
Publisher = {Elsevier},
Year = {2012},
Address = {New York}
}
@Article{sten94sol,
author = {L. Stenflo and O. M. Gradov},
title = {Solitary surface-wave deformation of a plasma boundary},
journal = {Phys. Plasmas},
year = {1994},
volume = {1},
pages = {2804--2805},
doi = {10.1063/1.870516},
}
@Article{sten98osc,
author = {L. Stenflo and M. Y. Yu},
title = {Plasma oscillons in spherically bounded magnetized plasmas},
journal = {Phys. Plasmas},
year = {1998},
volume = {5},
pages = {3122--3125},
doi = {10.1063/1.873038},
}
@Article{NLSstn03,
author = {L. Stenflo and M. Y. Yu},
title = {Oscillons at a plasma surface},
journal = {Phys. Plasmas},
year = {2003},
volume = {10},
pages = {912--913},
doi = {10.1063/1.1555625},
abstract = {Under the external driving force, an oscillon solutions is found.},
}
@Book{SKMacHH09,
Title = {{Exact Solutions of {Einstein's} Field Equations}},
Author = {Stephani, H and Kramer, D. and MacCallum, M. and Hoenselaers, C. and Herlt, E.},
Publisher = {Cambridge Univ. Press},
Year = {2003},
Address = {Cambridge},
DOI = {10.1017/cbo9780511535185}
}
@Article{StMeiss98,
author = {D. Sterling and J. D. Meiss},
title = {Computing periodic orbits using the anti-integrable limit},
journal = {Phys. Lett. A},
year = {1998},
volume = {241},
pages = {46--52},
doi = {10.1016/s0375-9601(98)00094-2},
}
@Article{HamSteDuMei99,
Title = {Homoclinic bifurcations for the {H\'enon} map},
Author = {D. G. Sterling and H. R. Dullin and J. D. Meiss},
Journal = {Physica D},
Year = {1999},
Pages = {153--184},
Volume = {134},
DOI = {10.1016/S0167-2789(99)00125-6}
}
@Article{sternb57,
Title = {Local contractions and a theorem of {Poincar\'e}},
Author = {S. Sternberg},
Journal = {Amer. J. Math.},
Year = {1957},
Pages = {809--824},
Volume = {79},
DOI = {10.2307/2372437}
}
@Article{sternb58,
Title = {On the structure of local homeomorphisms of {Euclidean} n-space, {II}},
Author = {S. Sternberg},
Journal = {Amer. J. Math.},
Year = {1958},
Pages = {623--631},
Volume = {80},
DOI = {10.2307/2372774}
}
@Article{sternb59,
Title = {The structure of local homeomorphisms},
Author = {S. Sternberg},
Journal = {Amer. J. Math.},
Year = {1959},
Pages = {578},
Volume = {81},
DOI = {10.2307/2372915}
}
@Article{Stewart77,
Title = {Perturbation bounds for the {QR} factorization of a matrix},
Author = {G. W. Stewart},
Journal = {SIAM J. Numer. Anal.},
Year = {1977},
Pages = {509--518},
Volume = {14},
DOI = {10.1137/0714030}
}
@Article{Stewart02,
Title = {A {Krylov--Schur} algorithm for large eigenproblems},
Author = {G. W. Stewart},
Journal = {SIAM J. Matrix Anal. Appl.},
Year = {2002},
Pages = {601--614},
Volume = {23},
DOI = {10.1137/S0895479800371529}
}
@Article{Stewart02add,
Title = {Addendum to ``{A Krylov--Schur} algorithm for large eigenproblems"},
Author = {G. W. Stewart},
Journal = {SIAM J. Matrix Anal. Appl.},
Year = {2002},
Pages = {599--601},
Volume = {24},
DOI = {10.1137/S0895479802403150}
}
@Book{bl,
Title = {Introduction to Numerical Analysis},
Author = {J. Stoer and R. Bulirsch},
Publisher = {Springer},
Year = {1983},
Address = {New York}
}
@Book{StGo09,
Title = {Mathematics for Physics: A Guided Tour for Graduate Students},
Author = {Stone, M. and Goldbart, P.},
Publisher = {Cambridge Univ. Press},
Year = {2009},
Address = {Cambridge}
}
@Article{SWG02,
Title = {Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows},
Author = {P. A. Stone and F. Waleffe and M. D. Graham},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Pages = {20831},
Volume = {89},
DOI = {10.1103/physrevlett.89.208301}
}
@Article{HSGsize98,
Title = {Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable media},
Author = {M. C. Strain and H. S. Greenside},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {2306--2309},
Volume = {80},
DOI = {10.1103/physrevlett.80.2306}
}
@Article{Strang1968,
Title = {On the construction and comparison of difference schemes},
Author = {Strang, G.},
Journal = {SIAM J. Numer. Anal.},
Year = {1968},
Pages = {506--517},
Volume = {5},
DOI = {10.1137/0705041}
}
@Article{StrWan02,
Title = {Instability of traveling waves of the {Kuramoto-Sivashinsky} equation},
Author = {Strauss, W. and Wang, G.},
Journal = {Chin. Ann. Math.},
Year = {2002},
Pages = {267--276},
Volume = {23},
DOI = {10.1142/S0252959902000250}
}
@Mastersthesis{Strepparava95,
Author = {R. Strepparava},
School = {Universit{\'a} degli Studi di Milano},
Year = {1995},
Note = {Laurea thesis}
}
@InProceedings{DDS90,
Title = {Automated pattern eduction from turbulent flow diagnostics},
Author = {D. D. Stretch},
Booktitle = {Annual Research Briefs},
Year = {1990},
Pages = {145--157},
Publisher = {Center for Turbulence Research, Stanford University}
}
@Book{strogb,
title = {{Nonlinear Dynamics and Chaos}},
publisher = {Westview Press},
year = {2014},
author = {S. H. Strogatz},
address = {Boulder, CO},
isbn = {9780813349107},
}
@Article{Strut68a,
Title = {Shell effects in nuclear masses and deformation energies},
Author = {Strutinsky, V. M.},
Journal = {Nucl. Phys. A},
Year = {1967},
Pages = {420--442},
Volume = {95},
DOI = {10.1016/0375-9474(67)90510-6}
}
@Article{Strut68b,
Title = {``Shells'' in deformed nuclei},
Author = {Strutinsky, V. M.},
Journal = {Nucl. Phys. A},
Year = {1968},
Pages = {1--33},
Volume = {122},
DOI = {10.1016/0375-9474(68)90699-4}
}
@Article{StrMag76,
Title = {Quasiclassical theory of nuclear shell structure},
Author = {Strutinsky, V. M. and Magner, A. G.},
Journal = {Sov. J. Particles Nucl.},
Year = {1976},
Pages = {138--163},
Volume = {7}
}
@Book{StOtWt06,
title = {{The Mathematical Foundations of Mixing}},
publisher = {Cambridge Univ. Press},
year = {2006},
author = {Sturman, R. and Ottino, J. M. and Wiggins, S.},
isbn = {9781139459204},
}
@Article{StuWhi89,
Title = {Gr\"obner bases and invariant theory},
Author = {B. Sturmfels and N. White},
Journal = {Adv. Math.},
Year = {1989},
Pages = {245--259},
Volume = {76},
DOI = {10.1016/0001-8708(89)90053-4}
}
@Article{SunKanZha11,
Title = {A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics},
Author = {Sun, L.-S. and Kang, X.-Y. and Zhang, Q. and Lin, L.-X.},
Journal = {Chin. Phys. B},
Year = {2011},
Pages = {120507},
Volume = {20},
DOI = {10.1088/1674-1056/20/12/120507}
}
@Article{suri16,
author = {B. Suri and J. Tithof and R. O. Grigoriev and M. F. Schatz},
title = {Forecasting fluid flows using the geometry of turbulence},
journal = {Phys. Rev. Lett.},
year = {2017},
volume = {118},
doi = {10.1103/physrevlett.118.114501},
}
@Article{pimstag,
author = {D. Sweet and H. E. Nusse. and J. A. Yorke},
title = {{Stagger-and-Step} method: {Detecting} and computing chaotic saddles in higher dimensions},
journal = {Phys. Rev. Lett.},
year = {2001},
volume = {86},
pages = {2261--2264},
doi = {10.1103/physrevlett.86.2261},
}
@Article{SwiWie84,
Title = {Suppression of period doubling in symmetric systems},
Author = {Swift, J. W. and Wiesenfeld, K.},
Journal = {Phys. Rev. Lett.},
Year = {1984},
Pages = {705--708},
Volume = {52},
DOI = {10.1103/PhysRevLett.52.705}
}
@Article{SwiHoh77,
title = {Hydrodynamic fluctuations at the convective instability},
author = {Swift, J. and Hohenberg, P. C.},
journal = {Phys. Rev. A},
year = {1977},
pages = {319--328},
volume = {15},
doi = {10.1103/PhysRevA.15.319}
}
@Book{rtb,
Title = {Theory of orbits},
Author = {V. Szebehely},
Publisher = {Academic},
Year = {1967},
Address = {New York}
}
@Article{szendro-2007,
Title = {Spatiotemporal structure of {Lyapunov} vectors in chaotic coupled-map lattices},
Author = {Szendro, I. G. and Paz{\'o}, D. and Rodr{\'i}guez, M. A. and L{\'o}pez, J. M.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {025202},
Volume = {76},
Abstract = {useful list of references on Lyapunov vectors},
DOI = {10.1103/PhysRevE.76.025202}
}
@Article{Tel2000,
Title = {Chaotic advection, diffusion, and reactions in open flows},
Author = {T. {T\'el} and G. K\'{a}rolyi and {\'{A}}. P\'{e}ntek and I. Scheuring and Z. Toroczkai and C. Grebogi and J. Kadtke},
Journal = {Chaos},
Year = {2000},
Pages = {89},
Volume = {10},
DOI = {10.1063/1.166478}
}
@Book{Tabor89,
Title = {{Chaos and Integrability in Nonlinear Dynamics: An Introduction}},
Author = {M. Tabor},
Publisher = {Wiley},
Year = {1989},
Address = {New York}
}
@Article{tajima02,
Title = {Microextensive chaos of a spatially extended system},
Author = {S. Tajima and H. S. Greenside},
Journal = {Phys. Rev. E},
Year = {2002},
Pages = {017205},
Volume = {66},
DOI = {10.1103/physreve.66.017205}
}
@Article{toricgl,
Title = {Invariant 2-tori in the time-dependent {Ginzburg-Landau} equation},
Author = {P. Tak\'{a}\v{c}},
Journal = {Nonlinearity},
Year = {1992},
Pages = {289--321},
Volume = {5},
DOI = {10.1088/0951-7715/5/2/002}
}
@Article{takac98,
Title = {Bifurcations to invariant 2-tori for the complex {Ginzburg-Landau} equation},
Author = {P. Tak\'{a}\v{c}},
Journal = {Appl. Math. Comput.},
Year = {1998},
Pages = {241--257},
Volume = {89},
DOI = {10.1016/S0096-3003(97)81661-X}
}
@Article{TakJun00,
Title = {A nonstiff {Euler} discretization of the complex {Ginzburg--Landau} equation in one space dimension},
Author = {P. Tak\'{a}\v{c} and A. J{\"u}ngel},
Journal = {SIAM J. Numer. Anal.},
Year = {2000},
Pages = {292--328},
Volume = {38},
DOI = {10.1137/S0036142998332852}
}
@Incollection{Takens81,
author = {Takens, F.},
title = {Detecting strange attractors in turbulence},
booktitle = {{Dynamical Systems and Turbulence}},
publisher = {Springer},
year = {1981},
editor = {Rand, D. A. and Young, L.-S.},
isbn = {978-3-540-11171-9},
pages = {366--381},
address = {New York},
}
@Misc{TaCh11,
Title = {Can the inertial manifold be captured by unstable periodic orbits?},
Author = {Takeuchi, K. A. and Chat\'{e}, H.},
Year = {2011}
}
@Article{TaCh12,
author = {Takeuchi, K. A. and Chat\'e, H.},
title = {Collective {Lyapunov} modes},
journal = {J. Phys. A},
year = {2013},
volume = {46},
pages = {254007},
doi = {10.1088/1751-8113/46/25/254007},
}
@Article{TaGiCh09,
Title = {{Lyapunov} analysis captures the collective dynamics of large chaotic systems},
Author = {Takeuchi, K. A. and Ginelli, F. and Chat\'{e}, H.},
Journal = {Phys. Rev. Lett.},
Year = {2009},
Pages = {154103},
Volume = {103},
DOI = {10.1103/physrevlett.103.154103}
}
@Article{TaGiCh11,
author = {Takeuchi, K. A. and Yang, H. L. and Ginelli, F. and Radons, G. and Chat\'{e}, H.},
title = {Hyperbolic decoupling of tangent space and effective dimension of dissipative systems},
journal = {Phys. Rev. E},
year = {2011},
volume = {84},
pages = {046214},
doi = {10.1103/PhysRevE.84.046214},
}
@Article{TaSa07,
Title = {Role of unstable periodic orbits in phase transitions of coupled map lattices},
Author = {Takeuchi, K. and Sano, M.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {036201},
Volume = {75},
DOI = {10.1103/PhysRevE.75.036201}
}
@Article{Takh93,
author = {Takhtajan, L.},
title = {On foundation of the generalized {Nambu} mechanics},
journal = {Commun. Math. Phys.},
year = {1994},
volume = {160},
pages = {295--316},
doi = {10.1007/BF02103278},
}
@Article{Talamini06,
Title = {P-matrices in orbit spaces and invariant theory},
Author = {V. Talamini},
Journal = {J. Phys.: Conference Series},
Year = {2006},
Pages = {30},
Volume = {30},
DOI = {10.1088/1742-6596/30/1/005}
}
@Article{Talamini10,
Title = {Flat bases of invariant polynomials and {P-matrices} of {E7} and {E8}},
Author = {Talamini, V.},
Journal = {J. Math. Phys.},
Year = {2010},
Pages = {023520},
Volume = {51},
DOI = {10.1063/1.3272569}
}
@Article{Talamini11,
Title = {Invariant theory to study symmetry breakings in the adjoint representation of {E8}},
Author = {Talamini, V.},
Journal = {J. Phys.: Conference Series},
Year = {2011},
Pages = {012057},
Volume = {284},
DOI = {10.1088/1742-6596/284/1/012057}
}
@Article{Taleei14,
Title = {Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear {Schr\"odinger} equations},
Author = {A. Taleei and M. Dehghan},
Journal = {Comput. Phys. Commun.},
Year = {2014},
Pages = {1515--1528},
Volume = {185},
DOI = {10.1016/j.cpc.2014.01.013}
}
@Article{TaWi92,
Title = {Quantization of chaotic systems},
Author = {G. Tanner and D. Wintgen},
Journal = {Chaos},
Year = {1992},
Pages = {53},
Volume = {2},
DOI = {10.1063/1.165897}
}
@Misc{MTao16,
Title = {Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions},
Author = {M. Tao},
Year = {2016},
URL = {https://arxiv.org/abs/1609.03922}
}
@Article{TarPer09,
Title = {An {Ihara} formula for partially directed graphs},
Author = {A. Tarfulea and R. Perlis},
Journal = {Linear Algebra Appl.},
Year = {2009},
Pages = {73--85},
Volume = {431},
DOI = {10.1016/j.laa.2009.02.006}
}
@Article{TeiLoe12,
Title = {Bass' identity and a coin arrangements lemma},
Author = {Teimoori Faal, H. and M. Loebl},
Journal = {Eur. J. Combinatorics },
Year = {2012},
Pages = {736--742},
Volume = {33},
DOI = {10.1016/j.ejc.2011.09.028}
}
@Article{temam90,
author = {T{\'e}mam, R.},
title = {Inertial manifolds},
journal = {Math. Intelligencer},
year = {1990},
volume = {12},
pages = {68--74},
doi = {10.1007/BF03024036},
}
@Article{temam91edd,
author = {R. T{\'e}mam},
title = {Approximation of attractors, large eddy simulations and multiscale methods},
journal = {Proc. R. Soc. Lond. A},
year = {1991},
volume = {434},
pages = {23--39},
doi = {10.1098/rspa.1991.0078},
}
@Book{infdymnon,
title = {{Infinite-Dimensional Dynamical Systems in Mechanics and Physics}},
publisher = {Springer},
year = {2013},
author = {T{\'e}mam, R.},
isbn = {9781461206453},
address = {New York},
edition = {2},
doi = {10.1007/978-1-4612-0645-3},
}
@Book{spfunc1,
Title = {Special Functions: an Introduction to the classical Functions of Mathematical Physics},
Author = {N. M. Temme},
Publisher = {Wiley},
Year = {1996},
Address = {New York}
}
@Article{TeHaHe10,
Title = {Spatial optimal growth in three-dimensional boundary layers},
Author = {Tempelmann, D. and Hanifi, A. and Henningson, D. S.},
Journal = {J. Fluid Mech.},
Year = {2010},
Pages = {5--37},
Volume = {646},
DOI = {10.1017/S0022112009993260}
}
@Article{tenenbaum2000,
Title = {A global geometric framework for nonlinear dimensionality reduction},
Author = {Tenenbaum, J. B. and Silva, V. de and Langford, J. C.},
Journal = {Science},
Year = {2000},
Pages = {2319--2323},
Volume = {290},
DOI = {10.1126/science.290.5500.2319}
}
@Book{Terras10,
Title = {Zeta Functions of Graphs: A Stroll through the Garden},
Author = {Terras, A.},
Publisher = {Cambridge Univ. Press},
Year = {2010},
ISBN = {9780521113670}
}
@Article{teubner09,
Title = {High-order harmonics from laser-irradiated plasma surfaces},
Author = {Teubner, U. and Gibbon, P.},
Journal = {Rev. Mod. Phys.},
Year = {2009},
Pages = {445--479},
Volume = {81},
DOI = {10.1103/RevModPhys.81.445}
}
@Phdthesis{Thum05,
Title = {Numerical Analysis of the Method of Freezing Traveling Waves},
Author = {V. Th\"ummler},
School = {Bielefeld Univ.},
Year = {2005}
}
@Article{ThiBoo99,
author = {Thiffeault, {J.-L.} and Boozer, A. H.},
title = {Geometrical constraints on finite-time {Lyapunov} exponents in two and three dimensions},
journal = {Chaos},
year = {2001},
volume = {11},
number = {1},
pages = {16},
doi = {10.1063/1.1342079},
}
@Article{Thiffeault2001,
author = {Thiffeault, J.-L.},
title = {Derivatives and constraints in chaotic flows: asymptotic behaviour and a numerical method},
journal = {Physica D},
year = {2002},
volume = {172},
pages = {139--161},
doi = {10.1016/s0167-2789(02)00588-2},
}
@Article{Thiffeault11,
author = {Thiffeault, J.-L.},
title = {Using multiscale norms to quantify mixing and transport},
journal = {Nonlinearity},
year = {2012},
volume = {25},
pages = {1--44},
doi = {10.1088/0951-7715/25/2/R1},
}
@Book{ns,
Title = {Numerical Partial Differential Equations},
Author = {J. W. Thomas},
Publisher = {Springer},
Year = {1995},
Address = {New York}
}
@Book{Tinkham,
Title = {Group Theory and Quantum Mechanics},
Author = {Tinkham, M.},
Publisher = {Dover},
Year = {2003},
Address = {New York}
}
@Article{Todd05,
Title = {Cats, maps and nanoflows: some recent developments in nonequilibrium nanofluidics},
Author = {B. D. Todd},
Journal = {Molec. Simul.},
Year = {2005},
Pages = {411--428},
Volume = {31},
DOI = {10.1080/08927020412331332730}
}
@Article{TofMar90,
Title = {Invertible cellular automata: {A} review},
Author = {T. Toffoli and N. H. Margolus},
Journal = {Physica D},
Year = {1990},
Pages = {229--253},
Volume = {45},
DOI = {10.1016/0167-2789(90)90185-R}
}
@Article{TI03,
Title = {A periodic-like solution in channel flow},
Author = {Toh, S. and Itano, T.},
Journal = {J. Fluid Mech.},
Year = {2003},
Pages = {67-76},
Volume = {481},
DOI = {10.1017/s0022112003003768}
}
@Article{tompaid96,
Title = {Numerical study of invariant sets of a quasiperiodic perturbation of a symplectic map},
Author = {S. Tompaidis},
Journal = {Experimental Math.},
Year = {1996},
Pages = {211--230},
Volume = {5},
DOI = {10.1080/10586458.1996.10504589}
}
@Article{ToKa78,
author = {J. Topper and T. Kawahara},
title = {Approximate equation for long nonlinear waves on a viscous fluid},
journal = {J. Phys. Soc. Japan},
year = {1978},
volume = {44},
pages = {663--666},
doi = {10.1143/JPSJ.44.663},
}
@Article{torc96,
Title = {Order parameter for the transition from phase to amplitude turbulence},
Author = {A. Torcini},
Journal = {Phys. Rev. Lett.},
Year = {1996},
Pages = {1047--1050},
Volume = {77},
DOI = {10.1103/physrevlett.77.1047}
}
@Article{TFGphase97,
Title = {Studies of phase turbulence in the one-dimensional complex {Ginzburg-Landau} equation},
Author = {A. Torcini and H. Frauenkron and P. Grassberger},
Journal = {Phys. Rev. E},
Year = {1997},
Pages = {5073},
Volume = {55},
DOI = {10.1103/PhysRevE.55.5073}
}
@Article{ToDe94,
author = {Toronov, V. Y. and Derbov, V. L.},
title = {Geometric phases in lasers and liquid flows},
journal = {Phys. Rev. E},
year = {1994},
volume = {49},
pages = {1392--1399},
doi = {10.1103/physreva.49.1392},
}
@Article{ToDe94a,
author = {Toronov, V. Y. and Derbov, V. L.},
title = {Geometric-phase effects in laser dynamics},
journal = {Phys. Rev. A},
year = {1994},
volume = {50},
pages = {878--881},
doi = {10.1103/physreva.50.878},
}
@Article{ToDe97a,
author = {Toronov, V. Y. and Derbov, V. L.},
title = {Boundedness of attractors in the complex {Lorenz} model},
journal = {Phys. Rev. E},
year = {1997},
volume = {55},
pages = {3689--3692},
doi = {10.1103/physreve.55.3689},
}
@Article{ToDe97,
author = {Toronov, V. Y. and Derbov, V. L.},
title = {Geometric phases in a ring laser},
journal = {Quantum Electronics},
year = {1997},
volume = {27},
pages = {644--648},
doi = {10.1070/qe1997v027n07abeh001007},
}
@Article{ToDe98,
author = {Toronov, V. Y. and Derbov, V. L.},
title = {Topological properties of laser phase},
journal = {J. Optical Soc. of America B},
year = {1998},
volume = {15},
pages = {1282},
doi = {10.1364/josab.15.001282},
}
@Article{TSYTES15,
Title = {Phase-lag synchronization in networks of coupled chemical oscillators},
Author = {Totz, J. F. and Snari, R. and Yengi, D. and Tinsley, M. R. and Engel, H. and Showalter, K.},
Journal = {Phys. Rev. E},
Year = {2015},
Pages = {022819},
Volume = {92},
DOI = {10.1103/PhysRevE.92.022819}
}
@Book{Townsend76,
Title = {The Structure of Turbulent Shear Flows, 2\textsuperscript{nd} Edn.},
Author = {A. A. Townsend},
Publisher = {Cambridge U. Press},
Year = {1976},
Address = {Cambridge}
}
@Misc{TrThNi14,
author = {{Tranchida}, J. and {Thibaudeau}, P. and {Nicolis}, S.},
title = {Knotted strange attractors and matrix {Lorenz} systems},
year = {2014},
url = {http://arXiv.org/abs/1404.7774},
}
@Article{TreWei14,
Title = {The exponentially convergent trapezoidal rule},
Author = {Trefethen, L. and Weideman, J.},
Journal = {SIAM Rev.},
Year = {2014},
Pages = {385--458},
Volume = {56},
DOI = {10.1137/130932132}
}
@Book{trefethenSpectral,
Title = {{Spectral Methods in MATLAB}},
Author = {L. N. Trefethen},
Publisher = {SIAM},
Year = {2000},
Address = {Philadelphia},
DOI = {10.1137/1.9780898719598}
}
@Book{Trefethen97,
title = {{Numerical Linear Algebra}},
publisher = {SIAM},
year = {1997},
author = {L. N. Trefethen and D. Bau},
address = {Philadelphia},
isbn = {978-0898713619},
}
@Article{TTRD93,
Title = {Hydrodynamic stability without eigenvalues},
Author = {L. N. Trefethen and A. E. Trefethen and S. C. Reddy and T. A. Driscoll},
Journal = {Science},
Year = {1993},
Pages = {578--584},
Volume = {261},
DOI = {10.1126/science.261.5121.578}
}
@Article{TrIsTa09,
Title = {Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension},
Author = {A. Trevisan and M. D'Isidoro and O. Talagrand},
Journal = {Quart. J. Roy. Meteorol. Soc.},
Year = {2010},
Addendum = {\arXiv{0902.2714}},
Number = {647},
Pages = {487--496},
Volume = {136},
DOI = {10.1002/qj.571}
}
@Article{TrePan98,
Title = {Periodic orbits, {Lyapunov} vectors, and singular vectors in the {Lorenz} system},
Author = {Trevisan, A. and Pancotti, F.},
Journal = {J. Atmos. Sci.},
Year = {1998},
Pages = {390},
Volume = {55},
DOI = {10.1175/1520-0469(1998)055%3C0390:POLVAS%3E2.0.CO;2}
}
@Article{kstroy89,
Title = {The existence of steady solutions of the {Kuramoto-Sivashinsky} equation},
Author = {W. C. Troy},
Journal = {J. Diff. Eqn.},
Year = {1989},
Pages = {269--313},
Volume = {82},
DOI = {10.1016/0022-0396(89)90134-4}
}
@Book{Truesdell91,
Title = {A First Course in Rational Continuum Mechanics: {General} concepts},
Author = {Truesdell, C.},
Publisher = {Academic},
Year = {1991},
Address = {New York},
Volume = {1}
}
@Article{GL-Tsa03,
Title = {Strange attractors are classified by bounding tori},
Author = {T. Tsankov and R. Gilmore},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Pages = {134104},
Volume = {91},
DOI = {10.1103/PhysRevLett.91.134104}
}
@Article{GoJoOt15,
author = {M. Goldman and M. Josien and F. Otto},
title = {New bounds for the inhomogenous {Burgers} and the {Kuramoto-Sivashinsky} equations},
journal = {Commun. Partial Diff. Eqs.},
year = {2015},
volume = {40},
pages = {2237--2265},
doi = {10.1080/03605302.2015.1076003},
}
@Article{Tsoy2005,
Title = {Bifurcations from stationary to pulsating solitons in the cubic-quintic complex {Ginzburg-Landau} equation},
Author = {Tsoy, E. N. and Akhmediev, N.},
Journal = {Phys. Lett. A},
Year = {2005},
Pages = {417--422},
Volume = {343},
DOI = {10.1016/j.physleta.2005.05.102}
}
@Article{Tsoy06,
Title = {Dynamical models for dissipative localized waves of the complex {Ginzburg-Landau} equation},
Author = {Tsoy, E. N. and Ankiewicz, A. and Akhmediev, N.},
Journal = {Phys. Rev. E},
Year = {2006},
Pages = {036621},
Volume = {73},
DOI = {10.1103/PhysRevE.73.036621}
}
@Article{tucker1-2,
Title = {The {Lorenz} attractor exists},
Author = {W. Tucker},
Journal = {C. R. Acad. Sci. Paris S\'er. I},
Year = {1999},
Pages = {1197--1202},
Volume = {328},
DOI = {10.1016/s0764-4442(99)80439-x}
}
@Article{tuckerman89,
Title = {Divergence-free velocity fields in nonperiodic geometries},
Author = {L.S. Tuckerman},
Journal = {J. Comput. Phys.},
Year = {1989},
Note = {see also \weblink{www.pmmh.espci.fr/~laurette/highlights/polar/polar.html}},
Pages = {403--441},
Volume = {80},
DOI = {10.1016/0021-9991(89)90108-3}
}
@Article{TuckBar03,
author = {L. S. Tuckerman and D. Barkley},
title = {Symmetry breaking and turbulence in perturbed plane {Couette} flow},
journal = {Theor. Comp. Fluid Dyn.},
year = {2002},
volume = {16},
pages = {91--97},
doi = {10.1007/s00162-002-0064-y},
}
@Book{Tung85,
Title = {Group Theory in Physics},
Author = {Tung, W.-K.},
Publisher = {World Scientific},
Year = {1985},
Address = {Singapore},
ISBN = {978-9971-966-57-7}
}
@Book{Vallis06,
Title = {Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation},
Author = {G. K. Vallis},
Publisher = {Cambridge Univ. Press},
Year = {2006},
Address = {Cambridge}
}
@Article{VanHove54,
Title = {Correlations in space and time and {Born} approximation scattering in systems of interacting particles},
Author = {Van Hove, L.},
Journal = {Phys. Rev.},
Year = {1954},
Pages = {249--262},
Volume = {95},
DOI = {10.1103/PhysRev.95.249}
}
@Article{Vance92,
Title = {Unstable periodic-orbits and transport-properties of nonequilibrium steady-states},
Author = {W. N. Vance},
Journal = {Phys. Rev. Lett.},
Year = {1992},
Pages = {1356--1359},
Volume = {69},
DOI = {10.1103/PhysRevLett.69.1356}
}
@Phdthesis{vanderbauwhede_lokale_1980,
Title = {Lokale Bifurcatietheorie en Symmetrie},
Author = {Vanderbauwhede, A.},
School = {Rijksuniv. Gent, Fac. van de Wetenschappen},
Year = {1980}
}
@Book{vanderbauwhede_local_1982,
Title = {Local Bifurcation and Symmetry},
Author = {Vanderbauwhede, A.},
Publisher = {Pitman},
Year = {1982},
Address = {Boston}
}
@InProceedings{Vanderbauwhede1989,
author = {A. Vanderbauwhede},
title = {Centre manifolds, normal forms and elementary bifurcations},
booktitle = {{Dynamics Reported}},
year = {1989},
editor = {Kirchgraber, U. and Walther, H.-O.},
volume = {2},
pages = {89--169},
address = {New York},
publisher = {Springer},
doi = {10.1007/978-3-322-96657-5_4},
}
@Book{vanderbauwhede_heteroclinic_1992,
Title = {Heteroclinic Cycles and Periodic Orbits in Reversible Systems},
Author = {Vanderbauwhede, A.},
Publisher = {Pitman},
Year = {1992},
Address = {Boston},
Pages = {250}
}
@Article{vanderbauwhede_topics_1994,
Title = {Topics in Bifurcation Theory and Applications {(Gerard Iooss and Moritz Adelmeyer)}},
Author = {Vanderbauwhede, A.},
Journal = {SIAM Rev.},
Year = {1994},
Pages = {323},
Volume = {36},
DOI = {10.1137/1036090}
}
@Incollection{vanderbauwhede_normal_1995,
author = {Vanderbauwhede, A.},
title = {Normal forms and versal unfoldings of symplectic linear mappings},
booktitle = {{Dynamical Systems and Applications}},
publisher = {World Scientific},
year = {1995},
editor = {Agarwal, R. P.},
isbn = {978-981-02-2383-0},
pages = {685--700},
doi = {10.1142/9789812796417_0045},
}
@TechReport{vanderbauwhede_short_1997,
author = {Vanderbauwhede, A.},
title = {A short tutorial on {Hamiltonian} systems and their reduction near a periodic orbit},
institution = {U. Gent},
year = {1997},
pages = {1-23},
url = {http://cage.ugent.be/~avdb/articles/TutorialHamSys.pdf},
}
@Incollection{vanderbauwhede_example_2000,
author = {Vanderbauwhede, A.},
title = {An example of symmetry reduction in {Hamiltonian} systems},
booktitle = {Equadiff 99},
publisher = {World Scientific},
year = {2000},
pages = {210--212},
doi = {10.1142/9789812792617_0043},
}
@InProceedings{diepenbeek_continuation_????,
Title = {Continuation and bifurcation of periodic orbits in symmetric {Hamiltonian} systems},
Author = {Vanderbauwhede, A.},
Booktitle = {Equadiff 2003},
Year = {2003},
Address = {Hasselt, Belgium},
Editor = {L. U. C. Diepenbeek and F. Dumortier and H. Broer and J. P. Gossez and J. Mawhin and Vanderbauwhede, A. and S. V. Lunel},
Publisher = {LUC Diepenbeek},
URL = {http://at.yorku.ca/c/a/l/o/73.htm}
}
@Misc{Vanderb,
author = {Vanderbauwhede, A.},
title = {On the continuation of relative periodic orbits in reversible systems},
url = {http://cage.ugent.be/~avdb/english/publications.htm},
}
@Article{VaZw12,
author = {Vandersickel, N. and Zwanziger, D.},
title = {The {Gribov} problem and {QCD} dynamics},
journal = {Phys. Rep.},
year = {2012},
volume = {520},
pages = {175--251},
doi = {10.1016/j.physrep.2012.07.003},
}
@Article{vp98,
Title = {Gradient-based approach to solve optimal periodic output feedback control problems},
Author = {A. Varga and S. Pieters},
Journal = {Automatica},
Year = {1998},
Pages = {477--481},
Volume = {34},
DOI = {10.1016/s0005-1098(97)00214-8}
}
@Article{Vdov65,
Title = {A calculation of the partition function for a plane dipole lattice},
Author = {Vdovichenko, N. V.},
Journal = {Sov. Phys. JETP},
Year = {1965},
Pages = {477--479},
Volume = {20},
URL = {http://www.jetp.ac.ru/cgi-bin/dn/e_020_02_0477.pdf}
}
@Article{VaKa11,
Title = {Homoclinic tangle on the edge of shear turbulence},
Author = {L. van Veen and G. Kawahara},
Journal = {Phys. Rev. Lett.},
Year = {2011},
Pages = {114501},
Volume = {107},
DOI = {10.1103/PhysRevLett.107.114501}
}
@Article{VaKaAt11,
Title = {On matrix-free computation of {2D} unstable manifolds},
Author = {L. van Veen and G. Kawahara and M. Atsushi},
Journal = {SIAM J. Sci. Comput.},
Year = {2011},
Pages = {25--44},
Volume = {33},
DOI = {10.1137/100789804}
}
@Article{VKK05,
Title = {Periodic motion representing isotropic turbulence},
Author = {L. van Veen and S. Kida and G. Kawahara},
Journal = {Fluid Dynamics Research},
Year = {2006},
Pages = {19--46},
Volume = {38},
DOI = {10.1016/j.fluiddyn.2005.09.001}
}
@Article{Vergini00,
Title = {Semiclassical theory of short periodic orbits in quantum chaos},
Author = {E. G. Vergini},
Journal = {J. Phys. A},
Year = {2000},
Pages = {4709},
Volume = {33},
DOI = {10.1088/0305-4470/33/25/311}
}
@Article{Vergini12,
Title = {Semiclassical approach to long time propagation in quantum chaos: predicting scars},
Author = {Vergini, E. G.},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Pages = {264101},
Volume = {108},
DOI = {10.1103/PhysRevLett.108.264101}
}
@Article{Vergini13,
Title = {Semiclassical propagation up to the {Heisenberg} time},
Author = {Vergini, E. G.},
Journal = {Europhys. Lett.},
Year = {2013},
Pages = {20003},
Volume = {103},
DOI = {10.1209/0295-5075/103/20003}
}
@Article{VeCa00,
Title = {Semiclassical quantization with short periodic orbits},
Author = {Vergini, E. G. and Carlo, G. G.},
Journal = {J. Phys. A},
Year = {2000},
Pages = {4717},
Volume = {33},
DOI = {10.1088/0305-4470/33/25/312}
}
@Article{VeCa01,
Title = {Semiclassical construction of resonances with hyperbolic structure: the scar function},
Author = {Vergini, E. G. and Carlo, G. G.},
Journal = {J. Phys. A},
Year = {2001},
Pages = {4525},
Volume = {34},
DOI = {10.1088/0305-4470/34/21/308}
}
@Article{VSRBB10,
Title = {Diagonal matrix elements in a scar function basis set},
Author = {E. G. Vergini and E. L. Sibert III and F. Revuelta and R. M. Benito and F. Borondo},
Journal = {Europhys. Lett.},
Year = {2010},
Pages = {40013},
Volume = {89},
DOI = {10.1209/0295-5075/89/40013}
}
@Article{Vierkandt1892,
Title = {\"Uber gleitende und rollende bewegung},
Author = {Vierkandt, A.},
Journal = {Monatshefte f\"ur Math. und Phys.},
Year = {1892},
Pages = {31--54},
Volume = {III}
}
@Article{vincenti12,
Title = {Attosecond lighthouses: {How} to use spatiotemporally coupled light fields to generate isolated attosecond pulses},
Author = {Vincenti, H. and Qu\'er\'e, F.},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Pages = {113904},
Volume = {108},
DOI = {10.1103/PhysRevLett.108.113904}
}
@Article{DV00,
author = {Viswanath, D.},
title = {Random {Fibonacci} sequences and the number 1.13198824...},
journal = {Math. Comput.},
year = {2000},
volume = {69},
pages = {1131--1155},
doi = {10.1090/S0025-5718-99-01145-X},
}
@Article{DV01,
author = {D. Viswanath},
title = {Global errors of numerical {ODE} solvers and {Lyapunov}'s theory of stability},
journal = {IMA J. Numer. Anal.},
year = {2001},
volume = {21},
pages = {387--406},
doi = {10.1093/imanum/21.1.387},
}
@Article{DV02,
Title = {The {Lindstedt-Poincar{\'e}} technique as an algorithm for finding periodic orbits},
Author = {D. Viswanath},
Journal = {SIAM Rev.},
Year = {2002},
Pages = {478--496},
Volume = {43},
DOI = {10.1137/S0036144500375292}
}
@Article{DV03,
Title = {Symbolic dynamics and periodic orbits of the {Lorenz} attractor},
Author = {D. Viswanath},
Journal = {Nonlinearity},
Year = {2003},
Pages = {1035--1056},
Volume = {16},
DOI = {10.1088/0951-7715/16/3/314}
}
@Article{DV04,
Title = {The fractal property of the {Lorenz} attractor},
Author = {D. Viswanath},
Journal = {Physica D},
Year = {2004},
Pages = {115--128},
Volume = {190},
DOI = {10.1016/j.physd.2003.10.006}
}
@Article{Visw07b,
author = {D. Viswanath},
title = {Recurrent motions within plane {Couette} turbulence},
journal = {J. Fluid Mech.},
year = {2007},
volume = {580},
pages = {339--358},
doi = {10.1017/S0022112007005459},
}
@Article{Visw08,
author = {D. Viswanath},
title = {The critical layer in pipe flow at high {Reynolds} number},
journal = {Philos. Trans. Royal Soc. A},
year = {2009},
volume = {367},
pages = {561--576},
doi = {10.1098/rsta.2008.0225},
}
@InCollection{Visw07a,
author = {D. Viswanath},
title = {The dynamics of transition to turbulence in plane {Couette} flow},
booktitle = {Mathematics and Computation, a Contemporary View},
publisher = {Springer},
year = {2008},
pages = {109--127},
address = {New York},
doi = {10.1007/978-3-540-68850-1_6},
}
@Article{DVLindstedt,
author = {D. Viswanath},
title = {An extension of the {Lindstedt-Poincar\'e} algorithm for computing periodic orbits},
journal = {{SIAM} Review},
year = {2001},
volume = {43},
pages = {478--495},
doi = {10.1137/s0036144500375292},
}
@Article{ViSa09,
author = {Viswanath, D. and \c{S}ahuto\u{g}lu, S.},
title = {Complex singularities and the {Lorenz} attractor},
journal = {SIAM Rev.},
year = {2010},
volume = {52},
pages = {294--314},
doi = {10.1137/090753474},
}
@Article{VC08,
author = {Viswanath, D. and Cvitanovi{\'c}, P.},
title = {Stable manifolds and the transition to turbulence in pipe flow},
journal = {J. Fluid Mech.},
year = {2009},
volume = {627},
pages = {215--233},
doi = {10.1017/S0022112009006041},
}
@Article{VlToDe98a,
author = {Vladimirov, A. G. and Toronov, V. Y. and Derbov, V. L.},
title = {Properties of the phase space and bifurcations in the complex {Lorenz} model},
journal = {Tech. Phys.},
year = {1998},
volume = {43},
pages = {877--884},
doi = {10.1134/1.1259094},
}
@Article{VlToDe98,
author = {Vladimirov, A. G. and Toronov, V. Y. and Derbov, V. L.},
title = {The complex {Lorenz} model: {Geometric} structure, homoclinic bifurcation and one-dimensional map},
journal = {Int. J. Bifur. Chaos},
year = {1998},
volume = {8},
pages = {723--729},
doi = {10.1142/s0218127498000516},
}
@Article{yu93bd,
author = {S. V. Vladimirov and M. Y. Yu},
title = {Boundary effects on the nonlinear interactions of surface waves},
journal = {Phys. Fluids B},
year = {1993},
volume = {5},
pages = {2888},
doi = {10.1063/1.860676},
}
@Article{yu94sur,
author = {S. V. Vladimirov and M. Y. Yu},
title = {Nonlinear interaction of surface plasmons in electron slabs},
journal = {Phys. Lett. A},
year = {1994},
volume = {184},
pages = {459--463},
doi = {10.1016/0375-9601(94)90524-X},
}
@Article{Volevich91,
Title = {Kinetics of coupled map lattices},
Author = {V. L. Volevich},
Journal = {Nonlinearity},
Year = {1991},
Pages = {37--48},
Volume = {4},
DOI = {10.1088/0951-7715/4/1/004}
}
@Article{voth02,
author = {G. A. Voth and G. Haller and J. P. Gollub},
title = {Experimental measurements of streching fields in fluid mixing},
journal = {Phys. Rev. Lett.},
year = {2002},
volume = {88},
pages = {254501},
doi = {10.1103/physrevlett.88.254501},
}
@Article{Vrah95,
Title = {An efficient method for locating and computing periodic orbits of nonlinear mappings},
Author = {Vrahatis, M.},
Journal = {J. Comput. Phys.},
Year = {1995},
Pages = {105--119},
Volume = {119},
DOI = {10.1006/jcph.1995.1119}
}
@Incollection{WaKo12,
Author = {G. M. Wadsworth and D. T. Kovari},
Booktitle = {{ChaosBook.org/projects}},
Publisher = {Georgia Inst. of Technology},
Year = {2012},
Chapter = {Optimal resolution of state space in chaotic hyperbolic 2-dimensional maps},
URL = {http://ChaosBook.org/projects/index.shtml#Kovari}
}
@InProceedings{W90b,
Title = {On the origin of the streak spacing in turbulent shear flow},
Author = {F. Waleffe},
Booktitle = {Annual Research Briefs},
Year = {1990},
Pages = {159--168},
Publisher = {Center for Turbulence Research, Stanford University}
}
@Unpublished{Waleffe90,
Title = {Proposal for a self-sustaining process in shear flows},
Author = {F. Waleffe},
Note = {Center for Turbulence Research, Stanford University/NASA Ames},
Year = {1990},
URL = {http://www.math.wisc.edu/~waleffe/ECS/sspctr90.pdf}
}
@Article{W95a,
Title = {Hydrodynamic stability and turbulence: {Beyond} transients to a self-sustaining process},
Author = {F. Waleffe},
Journal = {Stud. Appl. Math.},
Year = {1995},
Pages = {319--343},
Volume = {95}
}
@Article{W95b,
Title = {Transition in shear flows: {Nonlinear} normality versus non-normal linearity},
Author = {F. Waleffe},
Journal = {Phys. Fluids},
Year = {1995},
Pages = {3060--3066},
Volume = {7}
}
@Article{Waleffe97,
author = {F. Waleffe},
title = {On a {Self-Sustaining Process} in shear flows},
journal = {Phys. Fluids},
year = {1997},
volume = {9},
pages = {883--900},
doi = {10.1063/1.869185},
}
@Article{W98,
Title = {Three-dimensional coherent states in plane shear flows},
Author = {F. Waleffe},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {4140--4148},
Volume = {81}
}
@Article{W01,
author = {F. Waleffe},
title = {Exact coherent structures in channel flow},
journal = {J. Fluid Mech.},
year = {2001},
volume = {435},
pages = {93--102},
doi = {10.1017/s0022112001004189},
}
@InProceedings{W02,
Title = {Exact coherent structures and their instabilities: Toward a dynamical-system theory of shear turbulence},
Author = {F. Waleffe},
Booktitle = {Proceedings of the International Symposium on ``Dynamics and Statistics of Coherent Structures in Turbulence: Roles of Elementary Vortices''},
Year = {2002},
Editor = {S. Kida},
Pages = {115--128},
Publisher = {National Center of Sciences, Tokyo, Japan}
}
@Article{W03,
Title = {Homotopy of exact coherent structures in plane shear flows},
Author = {F. Waleffe},
Journal = {Phys. Fluids},
Year = {2003},
Pages = {1517--1543},
Volume = {15}
}
@Incollection{WalPant97,
Title = {How streamwise rolls and streaks self-sustain in a shear flow},
Author = {F. Waleffe and J. Kim},
Booktitle = {Self-Sustaining Mechanisms of Wall Bounded Turbulence},
Publisher = {Computational Mechanics Publications},
Year = {1997},
Address = {Southampton},
Editor = {R. L. Panton},
Pages = {385--422},
URL = {http://www.math.wisc.edu/~waleffe/ECS/WK97.pdf}
}
@InProceedings{WKH93,
author = {F. Waleffe and J. Kim and J. Hamilton},
title = {On the origin of streaks in turbulent shear flows},
booktitle = {{Turbulent Shear Flows 8: selected papers from the Eighth International Symposium on Turbulent Shear Flows, Munich, Germany, Sept. 9-11, 1991}},
year = {1993},
editor = {F. Durst and R. Friedrich and B. E. Launder and F. W. Schmidt and U. Schumann and J. H. Whitelaw},
pages = {37--49},
address = {New York},
publisher = {Springer},
doi = {10.1007/978-3-642-77674-8_4},
}
@InProceedings{WW05,
Title = {Transition threshold and the {Self-Sustaining Process}},
Author = {F. Waleffe and J. Wang},
Booktitle = {Non-uniqueness of Solutions to the Navier-Stokes Equations and their Connection with Laminar-Turbulent Transition},
Year = {2005},
Address = {Dordrecht},
Editor = {T. Mullin and R. R. Kerswell},
Pages = {85--106},
Publisher = {Kluwer}
}
@Book{Walt82,
Title = {{An Introduction to Ergodic Theory}},
Author = {P. Walters},
Publisher = {Springer},
Year = {1981},
Address = {New York},
ISBN = {9780387951522}
}
@Article{Wan11,
Title = {An adaptive high-order minimum action method},
Author = {X. Wan},
Journal = {J. Comput. Phys.},
Year = {2011},
Pages = { - },
DOI = {10.1016/j.jcp.2011.08.006}
}
@Article{WanZhoE10,
author = {Wan, X. and Zhou, X. and E, W.},
title = {Study of the noise-induced transition and the exploration of the phase space for the {Kuramoto-Sivashinsky} equation using the minimum action method},
journal = {Nonlinearity},
year = {2010},
volume = {23},
pages = {475--493},
doi = {10.1088/0951-7715/23/3/002},
}
@Misc{FYWang09,
Title = {Pioneer women in chaos theory},
Author = {Wang, F. Y.},
Year = {2009},
URL = {http://arXiv.org/abs/0903.2671}
}
@Article{WaLiLi11,
author = {Wang, P. F. and Li, J. P. and Li, Q.},
title = {Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of {Lorenz} equations},
journal = {Numerical Algorithms},
year = {2011},
volume = {59},
pages = {147--159},
doi = {10.1007/s11075-011-9481-6},
}
@Article{Wang10,
Title = {An efficient {Chebyshev--Tau} spectral method for {Ginzburg--Landau--Schr\"odinger} equations},
Author = {Wang, H.},
Journal = {Comput. Phys. Commum.},
Year = {2010},
Pages = {325--340},
Volume = {181},
DOI = {10.1016/j.cpc.2009.10.007}
}
@Article{Wang13,
author = {Wang, Q.},
title = {Forward and adjoint sensitivity computation of chaotic dynamical systems},
journal = {J. Comput. Phys.},
year = {2013},
volume = {235},
pages = {1--13},
doi = {10.1016/j.jcp.2012.09.007},
}
@Article{Wang2013,
Title = {{An efficient split-step compact finite difference method for cubic--quintic complex Ginzburg--Landau equations}},
Author = {Wang, S. and Zhang, L.},
Journal = {Comput. Phys. Commun.},
Year = {2013},
Pages = {1511--1521},
Volume = {184},
DOI = {10.1016/j.cpc.2013.01.019}
}
@Article{Ward94,
Title = {Automorphisms of {$Z^d$}-subshifts of finite type},
Author = {Ward, T.},
Journal = {Indag. Math.},
Year = {1994},
Pages = {495--504},
Volume = {5},
DOI = {10.1016/0019-3577(94)90020-5}
}
@Article{Ward93,
Title = {An algebraic obstruction to isomorphism of {Markov} shifts with group alphabets},
Author = {Ward, T. B.},
Journal = {Bull. London Math. Soc.},
Year = {1993},
Pages = {240--246},
Volume = {25},
DOI = {10.1112/blms/25.3.240}
}
@Article{Wat2005,
Title = {Product eigenvalue problems},
Author = {Watkins, D. S.},
Journal = {SIAM Rev.},
Year = {2005},
Pages = {3--40},
Volume = {47},
DOI = {10.1137/S0036144504443110}
}
@Book{Wat07,
Title = {The Matrix Eigenvalue Problem: {GR} and {Krylov} Subspace Methods},
Author = {Watkins, D. S.},
Publisher = {SIAM},
Year = {2007},
Address = {Philadelphia},
DOI = {10.1137/1.9780898717808},
ISBN = {978-0-89871-641-2}
}
@Book{Wat10,
Title = {Fundamentals of Matrix Computations},
Author = {Watkins, D. S.},
Publisher = {Wiley},
Year = {2010},
Address = {New York},
ISBN = {978-0-470-52833-4}
}
@Article{DSWatkins,
Title = {Francis's algorithm},
Author = {Watkins, D. S.},
Journal = {Amer. Math. Monthly},
Year = {2011},
Pages = {387--403},
Volume = {118},
DOI = {10.4169/amer.math.monthly.118.05.387}
}
@Misc{WeBoHaZa13,
author = {Wedin, H. and Bottaro, A. and Hanifi, A. and Zampogna, G.},
title = {Three-dimensional nonlinear states in the {Blasius} boundary layer},
year = {2013},
url = {http://www.aimeta.dicam.unibo.it/sites/www.aimeta.dicam.unibo.it/files/static/www.aimetatorino2013.it/cdrom/cdrom_pdf_fullpaper/000550004201.pdf},
}
@Article{WK04,
Title = {Exact coherent structures in pipe flow},
Author = {H. Wedin and R. R. Kerswell},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {333--371},
Volume = {508},
DOI = {10.1017/S0022112004009346}
}
@Article{WeiMaWu02,
author = {K. Weibert and J. Main and G. Wunner},
title = {Periodic orbit quantization of the closed three-disk billiard as an example of a chaotic system with strong pruning},
journal = {Nonlin. Phenom. Complex Sys.},
year = {2002},
volume = {5},
pages = {393--406},
url = {http://www.j-npcs.org/abstracts/vol2002/v5no4/v5no4p393.html},
}
@Article{WeHa89,
Title = {Chaotic behavior and subcritical formation of flow patterns of baroclinic waves for finite dissipation},
Author = {Weimer, W. and Haken, H.},
Journal = {J. Atmos. Sci.},
Year = {1989},
Pages = {1207--1218},
Volume = {46},
DOI = {10.1175/1520-0469(1989)046<1207:CBASFO>2.0.CO;2}
}
@Article{Weinstein85,
author = {Weinstein, A.},
title = {Periodic nonlinear waves on a half-line},
journal = {Commun. Math. Phys.},
year = {1985},
volume = {99},
pages = {385--388},
url = {http://projecteuclid.org/euclid.cmp/1103942768},
}
@Article{weiss83,
author = {J. Weiss},
title = {The {P}ainlev\'{e} for partial differential equations {II}: {B\"{a}}cklund transformation, {Lax} pairs, and the {Schwarzian} derivative},
journal = {J. Math. Phys.},
year = {1983},
volume = {24},
pages = {1405--1413},
doi = {10.1063/1.525875},
}
@Article{weiss86,
author = {J. Weiss},
title = {{B\"{a}}cklund transformation and the {P}ainlev\'{e} property},
journal = {J. Math. Phys.},
year = {1986},
volume = {27},
pages = {1293--1305},
doi = {10.1063/1.527134},
}
@Article{weiss82,
Title = {The {P}ainlev\'{e} property for partial differential equations},
Author = {J. Weiss and M. Tabor and G. Carnevale},
Journal = {J. Math. Phys.},
Year = {1983},
Pages = {522},
Volume = {24},
DOI = {10.1063/1.525721}
}
@Misc{WolframArnCatMap,
Title = {{Arnold's Cat Map}},
Author = {Weisstein, E. W.},
Note = {{MathWorld--A Wolfram Web Resource}},
URL = {http://mathworld.wolfram.com/ArnoldsCatMap.html}
}
@Article{WeBa88,
Title = {Wavenumber selection for single-wave steady states in a nonlinear baroclinic system},
Author = {Weng, {H-Y.} and Barcilon, A.},
Journal = {J. Atmos. Sci.},
Year = {1988},
Pages = {1039--1051},
Volume = {45},
DOI = {10.1175/1520-0469(1988)045<1039:WSFSWS>2.0.CO;2}
}
@Book{Werner09,
Title = {Percolation et mod{\`e}le d'{Ising}},
Author = {Werner, W.},
Publisher = {Soci{\'e}t{\'e} math{\'e}matique de France},
Year = {2009},
ISBN = {978-2-85629-276-1}
}
@Book{Weyl31,
Title = {The Theory of Groups and Quantum Mechanics},
Author = {Weyl, H.},
Publisher = {Dover},
Year = {1931},
Address = {New York},
ISBN = {9780486602691}
}
@Book{Weyl39,
title = {{The Classical Groups: Their Invariants and Representations}},
publisher = {Princeton Univ. Press},
year = {1939},
author = {Weyl, H.},
address = {Princeton NJ},
isbn = {9780691057569},
doi = {10.1515/9781400883905},
}
@Article{Whalen2015,
Title = {Exponential time-differencing with embedded {Runge-Kutta} adaptive step control},
Author = {Whalen, P. and Brio, M. and Moloney, J. V.},
Journal = {J. Comput. Phys.},
Year = {2015},
Pages = {579--601},
Volume = {280},
DOI = {10.1016/j.jcp.2014.09.038}
}
@Article{wheeler12,
Title = {Attosecond lighthouses from plasma mirrors},
Author = {Wheeler, J. A. and Borot, A. and Monchoc\'e, S. and Vincenti, H. and Ricci, A. and Malvache, A. and Lopez-Martens, R. and Qu\'er\'e, F.},
Journal = {Nature Photon},
Year = {2012},
Pages = {829--833},
Volume = {6},
DOI = {10.1038/nphoton.2012.284}
}
@Article{Wieczorek2005,
author = {S. Wieczorek and B. Krauskopf and T. B. Simpson and D. Lenstra},
title = {The dynamical complexity of optically injected semiconductor lasers},
journal = {Phys. Rep.},
year = {2005},
volume = {416},
pages = {1--128},
doi = {10.1016/j.physrep.2005.06.003},
}
@Book{wiggb,
title = {{Global Bifurcations and Chaos}},
publisher = {Springer},
year = {1988},
author = {S. Wiggins},
address = {New York},
doi = {10.1007/978-1-4612-1042-9},
}
@Book{Wiggins90,
title = {{Introduction to Applied Dynamical Systems and Chaos}},
publisher = {Springer},
year = {1990},
author = {S. Wiggins},
address = {New York},
doi = {10.1007/b97481},
}
@Book{Wigner59,
Title = {{Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra}},
Author = {Wigner, E. P.},
Publisher = {Academic},
Year = {1959},
Address = {New York},
ISBN = {9781483275765}
}
@Article{Wigner60,
Title = {The unreasonable effectiveness of mathematics in the natural sciences},
Author = {Wigner, E. P.},
Journal = {Commun. Pure Appl. Math.},
Year = {1960},
Pages = {534--549},
Volume = {13},
Booktitle = {Philosophical Reflections and Syntheses},
DOI = {10.1007/978-3-642-78374-6_41}
}
@Misc{wikiHamMat,
author = {Wikipedia},
title = {Hamiltonian matrix},
year = {2016},
url = {http://en.wikipedia.org/wiki/Hamiltonian\_matrix},
}
@Article{Wilczak03,
Title = {Chaos in the {Kuramoto-Sivashinsky} equations -- a computer-assisted proof},
Author = {D. Wilczak},
Journal = {J. Diff. Eqn.},
Year = {2003},
Pages = {433--459},
Volume = {194},
DOI = {10.1016/S0022-0396(03)00104-9}
}
@Article{WilZgl09,
Title = {Computer assisted proof of the existence of homoclinic tangency for the {H\'enon} map and for the forced damped pendulum},
Author = {D. Wilczak and P. Zgliczy\'nski},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2009},
Pages = {1632--1663},
Volume = {8},
DOI = {10.1137/090759975}
}
@Incollection{Wilczak09,
author = {R. Wilczak},
title = {Reducing the state-space of the complex {Lorenz} flow},
booktitle = {{ChaosBook.org/projects}},
publisher = {U. of Chicago},
year = {2009},
note = {{NSF REU} summer project},
url = {http://ChaosBook.org/projects/index.shtml#Wilczak},
}
@Article{Williams79,
Title = {The structure of {Lorenz} attractors},
Author = {Williams, R. F.},
Journal = {Publ. Math. IHES},
Year = {1979},
Pages = {73--99},
Volume = {50},
DOI = {10.1007/BF02684770}
}
@Techreport{openpipeflow,
Title = {{Openpipeflow}: {Pipe} flow code for incompressible flow},
Author = {Willis, A. P.},
Institution = {U. Sheffield},
Year = {2014},
Note = {{\tt {Openpipeflow.org}}},
Publisher = {A. P. Willis},
URL = {http://Openpipeflow.org}
}
@Misc{WiAvCv12,
Title = {Symmetries of turbulent flows: {How} to slice them},
Author = {Willis, A. P. and Avila, M. and Cvitanovi{\'c}, P.},
Year = {2012}
}
@Article{ACHKW11,
Title = {Revealing the state space of turbulent pipe flow by symmetry reduction},
Author = {Willis, A. P. and Cvitanovi{\'c}, P. and Avila, M.},
Journal = {J. Fluid Mech.},
Year = {2013},
Pages = {514--540},
Volume = {721},
DOI = {10.1017/jfm.2013.75}
}
@Misc{WFSBC15,
author = {Budanur, N. B. and Short, K. Y. and Farazmand, M. and Willis, A. P. and Cvitanovi{\'c}, P.},
title = {Relative periodic orbits form the backbone of turbulent pipe flow},
year = {2017},
note = {J. Fluid. Mech., to appear},
url = {https://arxiv.org/abs/1705.03720},
}
@Article{WK09,
author = {Willis, A. P. and Kerswell, R. R.},
title = {Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarisation and localised edge states},
journal = {J. Fluid Mec.},
year = {2009},
volume = {619},
pages = {213--233},
doi = {10.1017/s0022112008004618},
}
@Article{WiShCv15,
Title = {Symmetry reduction in high dimensions, illustrated in a turbulent pipe},
Author = {Willis, A. P. and Short, K. Y. and Cvitanovi{\'c}, P.},
Journal = {Phys. Rev. E},
Year = {2016},
Pages = {022204},
Volume = {93},
DOI = {10.1103/PhysRevE.93.022204}
}
@Article{Winfree73,
author = {A. T. Winfree},
title = {Scroll-shaped waves of chemical activity in 3 dimensions},
journal = {Science},
year = {1973},
volume = {181},
pages = {937--939},
doi = {10.1126/science.181.4103.937},
}
@Book{Winfree1980,
Title = {The Geometry of Biological Time},
Author = {A. T. Winfree},
Publisher = {Springer},
Year = {1980},
Address = {New York}
}
@Article{Winfree91,
author = {A. T. Winfree},
title = {Varieties of spiral wave behavior: {An} experimentalist's approach to the theory of excitable media},
journal = {Chaos},
year = {1991},
volume = {1},
pages = {303--334},
doi = {10.1063/1.165844},
}
@Article{WRT92,
Title = {The semiclassical helium atom},
Author = {Wintgen, D. and Richter, K. and Tanner, G.},
Journal = {Chaos},
Year = {1992},
Pages = {19--33},
Volume = {2},
DOI = {10.1063/1.165920}
}
@Article{WHKW07,
Title = {Generalized {Potts-models} and their relevance for gauge theories},
Author = {Wipf, A. and Heinzl, T. and Kaestner, T. and Wozar, C.},
Journal = {SIGMA},
Year = {2007},
Pages = {6--14},
Volume = {3},
DOI = {10.3842/SIGMA.2007.006}
}
@Article{Wirzba99,
Title = {Quantum mechanics and semiclassics of hyperbolic n-disk scattering systems},
Author = {A. Wirzba},
Journal = {Phys. Rep.},
Year = {1999},
Pages = {1--116},
Volume = {309},
DOI = {10.1016/S0370-1573(98)00036-2}
}
@Incollection{CBook:appendSymm,
Title = {Appendix: {Discrete} symmetries of dynamics},
Author = {A. Wirzba and P. Cvitanovi{\'c}},
Booktitle = {{Chaos: Classical and Quantum}},
Publisher = {Niels Bohr Inst.},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/paper.shtml#appendSymm}
}
@Article{WiVeBeBo04,
author = {D. A. Wisniacki and E. Vergini and R. M. Benito and F. Borondo},
title = {Classical invariants and the quantization of chaotic systems},
journal = {Phys. Rev. E},
year = {2004},
volume = {70},
pages = {035202},
doi = {10.1103/physreve.70.035202},
}
@Article{Witte02,
Title = {Dissipativity, analyticity and viscous shocks in the (de)stabilized {Kuramoto-Sivashinsky} equation},
Author = {R. W. Wittenberg},
Journal = {Phys. Lett. A},
Year = {2002},
Pages = {407--416},
Volume = {300},
DOI = {10.1016/S0375-9601(02)00861-7}
}
@Article{witt99hol,
Title = {Scale and space localization in the {Kuramoto-Sivashinsky} equation},
Author = {R. W. Wittenberg and P. Holmes},
Journal = {Chaos},
Year = {1999},
Pages = {452},
Volume = {9},
DOI = {10.1063/1.166419}
}
@Article{Wold1987,
Title = {Principal component analysis},
Author = {Wold, S. and Esbensen, K. and Geladi, P.},
Journal = {Chemometr. Intell. Lab.},
Year = {1987},
Note = {Proceedings of the Multivariate Statistical Workshop for Geologists and Geochemists},
Pages = {37--52},
Volume = {2},
DOI = {10.1016/0169-7439(87)80084-9}
}
@Article{WolfSwift85,
Title = {Determining {Lyapunov} exponents from a time series},
Author = {Wolf, A. and Swift, J. B. and Swinney, H. L. and Vastano, J. A.},
Journal = {Physica D},
Year = {1985},
Pages = {285--317},
Volume = {16},
DOI = {10.1016/0167-2789(85)90011-9}
}
@Article{samelson06,
Title = {Normal-mode analysis of a baroclinic wave-mean oscillation},
Author = {Wolfe, C. L. and Samelson, R. M.},
Journal = {J. Atmos. Sci.},
Year = {2006},
Pages = {2795--2812},
Volume = {63},
DOI = {10.1175/jas3788.1}
}
@Article{WoSa07,
Title = {An efficient method for recovering {Lyapunov} vectors from singular vectors},
Author = {Wolfe, C. L. and Samelson, R. M.},
Journal = {Tellus A},
Year = {2007},
Pages = {355--366},
Volume = {59},
DOI = {10.1111/j.1600-0870.2007.00234.x}
}
@Article{samelson08,
Title = {Singular vectors and time-dependent normal modes of a baroclinic wave-mean oscillation},
Author = {Wolfe, C. L. and Samelson, R. M.},
Journal = {J. Atmos. Sci.},
Year = {2008},
Pages = {875--894},
Volume = {65},
DOI = {10.1175/2007jas2364.1}
}
@Book{cellwolf,
Title = {Cellular Automata and Complexity},
Author = {S. Wolfram},
Publisher = {Wesley},
Year = {1994},
Address = {Redwood City}
}
@Article{WKWTP06,
Title = {Phase structure of {$\mathbb{Z}(3)$-Polyakov}-loop models},
Author = {Wozar, C. and Kaestner, T. and Wipf, A. and Heinzl, T. and Pozsgay, B.},
Journal = {Phys. Rev. D},
Year = {2006},
Pages = {114501},
Volume = {74},
DOI = {10.1103/PhysRevD.74.114501}
}
@Article{Wright04,
Title = {Local spline approximation of discontinuous functions and location of discontinuities, given low-order {Fourier} coefficient information},
Author = {Wright, R. K.},
Journal = {J. Comput. Appl. Math.},
Year = {2004},
Pages = {783--795},
Volume = {164-165},
DOI = {10.1016/S0377-0427(03)00647-2}
}
@Article{wc2ph10,
Title = {Two-parameter homotopy method for nonlinear equations},
Author = {Wu, Y. and Chueng, K. F.},
Journal = {Numerical Algorithms},
Year = {2010},
Pages = {555--572},
Volume = {53},
DOI = {10.1007/s11075-009-9319-7}
}
@Article{Wulff00,
author = {C. Wulff},
title = {Transitions from relative equilibria to relative periodic orbits},
journal = {Doc. Math.},
year = {2000},
volume = {5},
pages = {227--274},
url = {http://emis.ams.org/journals/DMJDMV/vol-05/09.pdf},
}
@Article{Wulff02,
Title = {Spiral waves and {Euclidean} symmetries},
Author = {Wulff, C.},
Journal = {Z. Phys. Chem.},
Year = {2002},
Pages = {535},
Volume = {216},
DOI = {10.1524/zpch.2002.216.4.535}
}
@Article{Wulff03,
Title = {Persistence of {Hamiltonian} relative periodic orbits},
Author = {C. Wulff},
Journal = {J. Geom. Phys.},
Year = {2003},
Pages = {309--338},
Volume = {48},
DOI = {10.1016/S0393-0440(03)00046-9}
}
@Techreport{Wulff94,
Title = {Numerical continuation of periodic orbits with symmetry},
Author = {C. Wulff and A. Hohmann and P. Deuflhard},
Institution = {Konrad-Zuse-Zentrum Berlin},
Year = {1994},
Number = {SC 94-12},
URL = {http://personal.maths.surrey.ac.uk/st/C.Wulff/preprints/Wulff_Hoh_Deuf_94-12.ps.gz}
}
@Article{Wulff01,
Title = {Bifurcation from relative periodic solutions},
Author = {Wulff, C. and Lamb, J. S. W. and Melbourne, I.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {2001},
Pages = {605--635},
Volume = {21},
DOI = {10.1017/s0143385701001298}
}
@Article{WuSche06,
Title = {Numerical continuation of symmetric periodic orbits},
Author = {Wulff, C. and Schebesch, A.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2006},
Pages = {435--475},
Volume = {5},
DOI = {10.1137/050637170}
}
@Article{Wylie07,
Title = {Linked by loops: {Network} structure and switch integration in complex dynamical systems},
Author = {D. C. Wylie},
Journal = {Physica A},
Year = {2009},
Pages = {1946--1958},
Volume = {388},
DOI = {10.1016/j.physa.2009.01.018}
}
@Article{Xia92,
Title = {Existence of invariant tori in volume-preserving diffeomorphisms},
Author = {Xia, Z.},
Journal = {Ergod. Theor. Dynam. Syst.},
Year = {1992},
Pages = {621--31},
Volume = {12},
DOI = {10.1017/S0143385700006969}
}
@Article{XuMiLi16,
author = {Xu, J. and Miao, Y. and Liu, J.},
title = {Strong averaging principle for two-time-scale non-autonomous stochastic {FitzHugh-Nagumo} system with jumps},
journal = {J. Math. Phys.},
year = {2016},
volume = {57},
pages = {092704},
doi = {10.1063/1.4963173},
}
@Article{YamSai97,
Title = {Chaotic properties of a fully developed model turbulence},
Author = {M. Yamada and Y. Saiki},
Journal = {Nonlin. Proc. Geophys.},
Year = {2007},
Pages = {631--640},
Volume = {14},
DOI = {10.5194/npg-14-631-2007}
}
@Article{YaRa06,
Title = {Universal features of hydrodynamic {Lyapunov} modes in extended systems with continuous symmetries},
Author = {Yang, {H.-l.} and Radons, G.},
Journal = {Phys. Rev. Lett.},
Year = {2006},
Pages = {074101},
Volume = {96},
DOI = {10.1103/PhysRevLett.96.074101}
}
@Article{YaRaKa12,
Title = {Covariant {Lyapunov} vectors from reconstructed dynamics: {The} geometry behind true and spurious {Lyapunov} exponents},
Author = {Yang, {H.-l.} and G. Radons and H. Kantz},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Pages = {244101},
Volume = {109},
DOI = {10.1103/physrevlett.109.244101}
}
@Article{Yang52,
Title = {The spontaneous magnetization of a two-dimensional {Ising} model},
Author = {Yang, C. N.},
Journal = {Phys. Rev.},
Year = {1952},
Pages = {808--816},
Volume = {85},
DOI = {10.1103/PhysRev.85.808}
}
@Article{YaRa11,
Title = {Geometry of inertial manifold probed via {Lyapunov} projection method},
Author = {Yang, H. L. and Radons, G.},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Pages = {154101},
Volume = {108},
DOI = {10.1103/PhysRevLett.108.154101}
}
@Article{YaTaGiChRa08,
author = {Yang, H. L. and Takeuchi, K. A. and Ginelli, F. and Chat\'{e}, H. and Radons, G.},
title = {Hyperbolicity and the effective dimension of spatially extended dissipative systems},
journal = {Phys. Rev. Lett.},
year = {2009},
volume = {102},
pages = {074102},
doi = {10.1103/PhysRevLett.102.074102},
}
@Article{Yang.Radons-PRL2008,
Title = {When can one observe good hydrodynamic {Lyapunov} modes?},
Author = {Yang, H.-l. and Radons, G.},
Journal = {Phys. Rev. Lett.},
Year = {2008},
Pages = {024101},
Volume = {100},
DOI = {10.1103/PhysRevLett.100.024101}
}
@Article{YaRa10,
author = {Yang, H.-l. and Radons, G.},
title = {Comparison between covariant and orthogonal {Lyapunov} vectors},
journal = {Phys. Rev. E},
year = {2010},
volume = {82},
pages = {046204},
doi = {10.1103/PhysRevE.82.046204},
}
@Article{YaWoHu09,
Title = {Kinematics of the swimming of {Spiroplasma}},
Author = {Yang, J. and Wolgemuth, C. W. and Huber, G.},
Journal = {Phys. Rev. Lett.},
Year = {2009},
Pages = {218102},
Volume = {102},
DOI = {10.1103/physrevlett.102.218102}
}
@Article{optp2,
Title = {Optimal periodic orbits of continuous time chaotic systems},
Author = {T.-H. Yang and B. R. Hunt and E. Ott},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {1950},
Volume = {62},
DOI = {10.1103/physreve.62.1950}
}
@Article{Otto09,
author = {F. Otto},
title = {Optimal bounds on the {Kuramoto–Sivashinsky} equation},
journal = {J. Funct. Anal.},
year = {2009},
volume = {257},
pages = {2188--2245},
doi = {10.1016/j.jfa.2009.01.034},
}
@Article{ksyang97,
Title = {On travelling-wave solutions of the {Kuramoto-Sivashinsky} equation},
Author = {T.-S. Yang},
Journal = {Physica D},
Year = {1997},
Pages = {25--42},
Volume = {110},
DOI = {10.1016/S0167-2789(97)00121-8}
}
@Article{YeuPop06,
author = {Yeung, P. K. and Pope, S. B.},
title = {Lagrangian statistics from direct numerical simulations of isotropic turbulence},
journal = {J. Fluid Mech.},
year = {1989},
volume = {207},
pages = {531},
doi = {10.1017/s0022112089002697},
}
@Article{Yi1993a,
Title = {Stability of integral manifold and orbital attraction of quasi-periodic motion},
Author = {Y. Yi},
Journal = {J. Diff. Eqn.},
Year = {1993},
Pages = {278--322},
Volume = {103},
DOI = {10.1006/jdeq.1993.1051}
}
@Article{Yildiz11,
Title = {Monotonicity of the {Lozi} family and the zero entropy locus},
Author = {Yildiz, I. B.},
Journal = {Nonlinearity},
Year = {2011},
Pages = {1613},
Volume = {24},
DOI = {10.1088/0951-7715/24/5/012}
}
@Article{YoNo93,
Title = {Finite-time {Lyapunov} stability analysis and its application to atmospheric predictability},
Author = {Yoden, S. and Nomura, M.},
Journal = {J. Atmos. Sci.},
Year = {1993},
Pages = {1531--1543},
Volume = {50},
DOI = {10.1175/1520-0469(1993)050<1531:ftlsaa>2.0.co;2}
}
@Book{Yode88,
title = {{Unrolling Time: {Christiaan Huygens} and the Mathematization of Nature}},
publisher = {Cambridge Univ. Press},
year = {1988},
author = {J. G. Yoder},
address = {Cambridge},
isbn = {9780521524810},
}
@Article{YokSak13,
Title = {A projection method for nonlinear eigenvalue problems using contour integrals},
Author = {S. Yokota and T. Sakurai},
Journal = {JSIAM Lett.},
Year = {2013},
Pages = {41--44},
Volume = {5},
DOI = {10.14495/jsiaml.5.41}
}
@Article{Yoshida90,
Title = {Construction of higher order symplectic integrators},
Author = {H. Yoshida},
Journal = {Phys. Lett. A},
Year = {1990},
Pages = {262--268},
Volume = {150},
DOI = {10.1016/0375-9601(90)90092-3}
}
@Article{Young02,
Title = {What are {SRB} measures, and which dynamical systems have them?},
Author = {Young, L.-S.},
Journal = {J. Stat. Phys.},
Year = {2002},
Pages = {733--754},
Volume = {108},
DOI = {10.1023/A:1019762724717}
}
@Article{Young13,
Title = {Mathematical theory of {Lyapunov} exponents},
Author = {L.-S. Young},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254001},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254001}
}
@Article{Young87,
Title = {Selective decay of enstrophy and the excitation of barotropic waves in a channel},
Author = {Young, W. R.},
Journal = {J. Atmos. Sci.},
Year = {1987},
Pages = {2804--2812},
Volume = {44},
DOI = {10.1175/1520-0469(1987)044<2804:SDOEAT>2.0.CO;2}
}
@Article{yuan00id,
author = {G.-C. Yuan and J. A. Yorke and T. L. Carroll and E. Ott and L. M. Pecora},
title = {Testing whether two chaotic one dimensional processes are dynamically identical},
journal = {Phys. Rev. Lett.},
year = {2000},
volume = {85},
pages = {4265--4268},
doi = {10.1103/physrevlett.85.4265},
}
@Article{kruskal65,
Title = {Interaction of solitons in a collisionless plasma and the recurrence of initial states},
Author = {N. J. Zabusky and M. D. Kruskal},
Journal = {Phys. Rev. Lett.},
Year = {1965},
Pages = {240--243},
Volume = {15},
DOI = {10.1103/physrevlett.15.240}
}
@Article{Zagarola98,
Title = {Mean flow scaling of turbulent pipe flow},
Author = {M. V. Zagarola and A. J. Smits},
Journal = {J. Fluid Mech.},
Year = {1998},
Pages = {33--79},
Volume = {373},
DOI = {10.1017/s0022112098002419}
}
@Article{ZaZha70,
author = {Zaikin, A. N. and Zhabotinsky, A. M.},
title = {Concentration wave propagation in 2-dimensional liquid-phase self-oscillating system},
journal = {Nature},
year = {1970},
volume = {225},
pages = {535--537},
doi = {10.1038/225535b0},
}
@Article{ZakGol10,
author = {Zaks, M. A. and Goldobin, D. S.},
title = {Comment on ``{Time-averaged} properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems''},
journal = {Phys. Rev. E},
year = {2010},
volume = {81},
pages = {018201},
doi = {10.1103/PhysRevE.81.018201},
}
@Article{ZamEck15,
Title = {Crisis bifurcations in plane {Poiseuille} flow},
Author = {Zammert, S. and Eckhardt, B.},
Journal = {Phys. Rev. E},
Year = {2015},
Pages = {041003},
Volume = {91},
DOI = {10.1103/PhysRevE.91.041003}
}
@Article{Zang91,
Title = {On the rotation and skew-symmetric forms for incompressible flow simulations},
Author = {T. A. Zang},
Journal = {Appl. Numer. Math.},
Year = {1991},
Pages = {27--40},
Volume = {7},
DOI = {10.1016/0168-9274(91)90102-6}
}
@Phdthesis{Zarrin06,
Title = {{CUPOLETS}: {Chaotic} unstable periodic orbits theory and applications},
Author = {Zarringhalam, K.},
School = {Univ. New Hampshire},
Year = {2007}
}
@Article{ZarSho08,
Title = {Generating an adaptive multiresolution image analysis with compact cupolets},
Author = {Zarringhalam, K. and Short, K. M.},
Journal = {Nonlin. Dyn.},
Year = {2008},
Pages = {51--70},
Volume = {52},
DOI = {10.1007/s11071-007-9257-7}
}
@Book{Zee10,
Title = {{Quantum Field Theory in a Nutshell}},
Author = {Zee, A.},
Publisher = {Princeton Univ. Press},
Year = {2010},
Address = {Princeton NJ},
Edition = {2},
ISBN = {9781400835324}
}
@Article{ZeMa85,
author = {{Zeghlache}, H. and {Mandel}, P.},
title = {Influence of detuning on the properties of laser equations},
journal = {J. Optical Soc. of America B},
year = {1985},
volume = {2},
pages = {18},
doi = {10.1364/josab.2.000018},
}
@Article{Zelik14,
Title = {Inertial manifolds and finite-dimensional reduction for dissipative {PDEs}},
Author = {Zelik, S.},
Journal = {Proc. Roy. Soc. Edinburgh Sect. A},
Year = {2014},
Pages = {1245--1327},
Volume = {144},
DOI = {10.1017/S0308210513000073}
}
@Article{ZePiEy93,
Title = {Chaos theory and its applications to the atmosphere},
Author = {Zeng, X. and Pielke, R. A. and Eykholt, R.},
Journal = {Bull. Amer. Meteor. Soc.},
Year = {1993},
Pages = {631--644},
Volume = {74},
DOI = {10.1175/1520-0477(1993)074<0631:CTAIAT>2.0.CO;2}
}
@Article{ZgRi01,
author = {P. Zgliczynski and K. Mischaikow},
title = {Rigorous numerics for partial differential equations: the {Kuramoto-Sivashinsky} equation},
journal = {Foundations of Comp. Math.},
year = {2001},
volume = {1},
pages = {255--288},
doi = {10.1007/s002080010010},
}
@Article{ZhaLan13,
Title = {Computation of growth rates of random sequences with multi-step memory},
Author = {Zhang, C. and Lan, Y.},
Journal = {J. Stat. Phys.},
Year = {2013},
Pages = {722--743},
Volume = {150},
DOI = {10.1007/s10955-013-0712-1}
}
@Article{HKZhang11,
Title = {Current in periodic {Lorentz} gases with twists},
Author = {Zhang, H.-K.},
Journal = {Commun. Math. Phys.},
Year = {2011},
Pages = {747--776},
Volume = {306},
DOI = {10.1007/s00220-011-1262-5}
}
@Unpublished{ZhCvGo15,
Title = {Diffuse globally, compute locally: a cyclist tale},
Author = {Zhang, T. and Cvitanovi\'c, P. and Goldman, D. I.},
Note = {In preparation},
Year = {2015}
}
@Article{Xu10,
Title = {Hyperbolic invariant sets of the real generalized {H\'enon} maps},
Author = {Zhang, Xu},
Journal = {Chaos Solit. Fract.},
Year = {2010},
Pages = {31--41},
Volume = {43},
DOI = {10.1016/j.chaos.2010.07.003}
}
@Article{ZhangMar97,
Title = {Convergence and {Gibbs}' phenomena in cubic spline interpolation of discontinuous functions},
Author = {Zhang, Z. and Martin, C.},
Journal = {J. Comput. Appl. Math.},
Year = {1997},
Pages = {359--371},
Volume = {87},
DOI = {10.1016/S0377-0427(97)00199-4}
}
@Article{ZhLuRo01,
Title = {A numerical and analytical study of {F}loquet multipliers of periodic solutions near a homoclinic orbit},
Author = {Z. Zheng and K. Lust and D. Roose},
Journal = {Nonlinear Anal.},
Year = {2001},
Pages = {3369--3378},
Volume = {47},
DOI = {10.1016/s0362-546x(01)00452-7}
}
@Article{ZGBG94,
Title = {Spatiotemporally periodic patterns in symmetrically coupled map lattices},
Author = {Zhilin, Q. and Gangal, A. and Benkun, M. and Gang, T.},
Journal = {Phys. Rev. E},
Year = {1994},
Pages = {163--170},
Volume = {50},
DOI = {10.1103/PhysRevE.50.163}
}
@Article{ZhoRenE08,
Title = {Adaptive minimum action method for the study of rare events},
Author = {Zhou, X. and Ren, W. and E, W.},
Journal = {J. Chem. Phys.},
Year = {2008},
Pages = {104111},
Volume = {128},
DOI = {10.1063/1.2830717}
}
@Article{Zhou92,
Title = {Coherence and chaos in a model of turbulent boundary layer},
Author = {X. Zhou and L. Sirovich},
Journal = {Phys. Fluids A},
Year = {1992},
Pages = {2855},
Volume = {4},
DOI = {10.1063/1.858340}
}
@PhdThesis{zimmermann-global,
author = {Zimmermann, M. G.},
title = {{Global Bifurcations and Chaotic Dynamics in Physical Applications}},
school = {Upsala Univ.},
year = {1997},
isbn = {9155439721},
url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.46.4304&rep=rep1&type=pdf},
}
@Book{Zinn-Justin89,
Title = {Quantum Field Theory and Critical Phenomena},
Author = {J. Zinn-Justin},
Publisher = {Oxford University Press},
Year = {1989},
Address = {Oxford}
}
@Article{Z-JG08,
author = {Zinn-Justin, J. and Guida, R.},
title = {Gauge invariance},
journal = {Scholarpedia},
year = {2008},
volume = {3},
pages = {8287},
doi = {10.4249/scholarpedia.8287},
}
@Article{Zoldi98,
author = {S. M. Zoldi},
title = {Unstable periodic orbits analysis of histograms of chaotic time series},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {81},
pages = {3375--3378},
doi = {10.1103/physrevlett.81.3375},
}
@Misc{Zoldi99,
Title = {Escape time weighting of unstable stationary solutions of spatiotemporal chaos},
Author = {S. M. Zoldi},
Year = {1999},
URL = {http://arXiv.org/abs/chao-dyn/9903020}
}
@Article{ZG96,
author = {S. M. Zoldi and H. S. Greenside},
title = {Spatially localized unstable periodic orbits of a high-dimensional chaotic system},
journal = {Phys. Rev. E},
year = {1998},
volume = {57},
pages = {R2511--R2514},
doi = {10.1103/physreve.57.r2511},
}
@Article{Zwanz89,
Title = {Local and renormalizable action from the {Gribov} horizon},
Author = {D. Zwanziger},
Journal = {Nucl. Phys. B},
Year = {1989},
Pages = {513--544},
Volume = {323},
DOI = {10.1016/0550-3213(89)90122-3}
}
@Article{Zwanz92,
Title = {Critical limit of lattice gauge theory},
Author = {D. Zwanziger},
Journal = {Nucl. Phys. B},
Year = {1992},
Pages = {525--590},
Volume = {378},
DOI = {10.1016/0550-3213(92)90608-E}
}
@Article{Zwanz93,
Title = {Renormalizability of the critical limit of lattice gauge theory by {BRS} invariance},
Author = {D. Zwanziger},
Journal = {Nucl. Phys. B},
Year = {1993},
Pages = {477--513},
Volume = {399},
DOI = {10.1016/0550-3213(93)90506-K}
}
@Book{Holden86,
Title = {Chaos},
Editor = {Holden, A.V.},
Publisher = {Princeton University Press},
Year = {1986},
Address = {Princeton NJ},
DOI = {10.1515/9781400858156},
ISBN = {9781400858156}
}
@Misc{CNS,
Note = {Center for Nonlinear Science,\weblink{www.cns.gatech.edu}}
}
@Article{PolVyt16,
author = {M. Pollicott and P. Vytnova},
title = {Linear response and periodic points},
journal = {Nonlinearity},
year = {2016},
volume = {29},
pages = {3047--3066},
doi = {10.1088/0951-7715/29/10/3047},
}
@Misc{CviSon98,
author = {P. Cvitanovi{\'c}},
title = {Periodic orbit formulation of linear response (working notes for {N. S{\o}ndergaard})},
year = {1998},
note = {ChaosBook.org/~predrag/papers/unfinished.html},
url = {http://ChaosBook.org/~predrag/papers/unfinished.html},
}
@Article{ArPaPuVi09,
author = {Araujo, V. and Pacifico, M. and Pujals, E. and Viana, M.},
title = {Singular-hyperbolic attractors are chaotic},
journal = {Trans. Amer. Math. Soc.},
year = {2008},
volume = {361},
pages = {2431--2485},
doi = {10.1090/s0002-9947-08-04595-9},
}
@Article{Lucarini15,
author = {Lucarini, V.},
title = {Response operators for {Markov} processes in a finite state space: radius of convergence and link to the response theory for {Axiom A} systems},
journal = {Journal of Statistical Physics},
year = {2015},
volume = {162},
pages = {312--333},
doi = {10.1007/s10955-015-1409-4},
}
@Article{FR06,
author = {F. Faure and N. Roy},
title = {{Ruelle--Pollicott} resonances for real analytic hyperbolic maps},
journal = {Nonlinearity},
year = {2006},
volume = {19},
pages = {123--1252},
doi = {10.1088/0951-7715/19/6/002},
}
@Article{BaMaSa13,
author = {V. Baladi and S. Marmi and D. Sauzin},
title = {Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps},
journal = {Ergod. Theor. Dynam. Syst.},
year = {2013},
volume = {34},
pages = {777--800},
doi = {10.1017/etds.2012.161},
}
@Article{BoCaVa16,
author = {T. Bomfim and A. Castro and P. Varandas},
title = {Differentiability of thermodynamical quantities in non-uniformly expanding dynamics},
journal = {Adv. Math.},
year = {2016},
volume = {292},
pages = {478--528},
doi = {10.1016/j.aim.2016.01.017},
}
@Article{ConDol16,
author = {F.Contreras and D. Dolgopyat},
title = {Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps},
journal = {Nonlinearity},
year = {2016},
volume = {29},
pages = {2775--2797},
doi = {10.1088/0951-7715/29/9/2775},
}
@Phdthesis{Contreras14,
author = {Contreras-Barraza, F. E.},
title = {Regularity of measures for piecewise expanding unimodal maps},
school = {U. Maryland},
year = {2014},
url = {http://gradworks.umi.com/36/82/3682511.html},
}
@Article{LiXie16,
author = {D. Li and J. Xie},
title = {Symbolic dynamics of {Belykh}-type maps},
journal = {Appl. Math. Mech.},
year = {2016},
volume = {37},
pages = {671--682},
doi = {10.1007/s10483-016-2080-9},
}
@Article{Tel83,
author = {T. T{\'{e}}l},
title = {Fractal dimension of the strange attractor in a piecewise linear two-dimensional map},
journal = {Phys. Lett. A},
year = {1983},
volume = {97},
pages = {219--223},
doi = {10.1016/0375-9601(83)90751-x},
}
@Article{CviKin72,
author = {Kinoshita, T. and Cvitanovi{\'c}, P.},
title = {Sixth-order radiative corrections to the electron magnetic moment},
journal = {Phys. Rev. Lett.},
year = {1972},
volume = {29},
pages = {1534--1537},
doi = {10.1103/PhysRevLett.29.1534},
}
@Article{Knauf87,
author = {Knauf, A.},
title = {Ergodic and topological properties of {Coulombic} periodic potentials},
journal = {Commun. Math. Phys.},
year = {1987},
volume = {110},
pages = {89--112},
doi = {10.1007/bf01209018},
}
@Article{FeKaSh82,
author = {M. J. Feigenbaum and L. P. Kadanoff and S. J. Shenker},
title = {Quasiperiodicity in dissipative systems: {A} renormalization group analysis},
journal = {Physica D},
year = {1982},
volume = {5},
pages = {370--386},
doi = {10.1016/0167-2789(82)90030-6},
}
@Article{WGBGQ13,
author = {Q. Wang and S. A. Gomez and P. J. Blonigan and A. L. Gregory and E. Y. Qian},
title = {Towards scalable parallel-in-time turbulent flow simulations},
journal = {Phys. Fluids},
year = {2013},
volume = {25},
pages = {110818},
doi = {10.1063/1.4819390},
}
@Inproceedings{BloWan15,
author = {P. J. Blonigan and Q. Wang},
title = {Multiple shooting shadowing for sensitivity analysis of chaotic systems and turbulent fluid flowsflows},
booktitle = {{53rd {AIAA} Aerospace Sciences Meeting}},
year = {2015},
publisher = {AIAA},
doi = {10.2514/6.2015-1534},
}
@InProceedings{BloWan16,
author = {Blonigan, P.J. and Wang, Q. and Nielsen, E.J. and Diskin, B.},
title = {Least squares shadowing sensitivity analysis of chaotic flow around a two-dimensional airfoil},
booktitle = {{54th AIAA Aerospace Sciences Meeting}},
year = {2016},
doi = {10.2514/6.2016-0296},
isbn = {978-162410393-3},
}
@Article{FaIo01,
author = {B. F. Farrell and P. J. Ioannou},
title = {Accurate low-dimensional approximation of the linear dynamics of fluid flow},
journal = {J. Atmos. Sci.},
year = {2001},
volume = {58},
pages = {2771},
doi = {10.1175/1520-0469(2001)058¡2771:ALDAOT¿2.0.CO;2},
}
@Incollection{FaIo06,
author = {B. F. Farrell and P. J. Ioannou},
title = {Approximating optimal state estimation},
booktitle = {Predictability of Weather and Climate},
publisher = {Cambridge Univ. Press},
year = {2006},
editor = {Palmer, T. and Hagedorn, R.},
pages = {181--216},
address = {Cambridge},
doi = {10.1017/cbo9780511617652.009},
}
@Misc{FaIo14,
author = {B. F. Farrell and P. J. Ioannou},
title = {{Statistical State Dynamics}: a new perspective on turbulence in shear flow},
year = {2014},
note = {\arXiv{1412.8290}},
}
@Article{IoFa69II,
author = {B. F. Farrell and P. J. Ioannou},
title = {Generalized stability theory. {Part II: Nonautonomous} operators},
journal = {J. Atmos. Sci.},
year = {1996},
volume = {53},
pages = {2041--2053},
doi = {10.1175/1520-0469(1996)053<2041:gstpin>2.0.co;2},
}
@Article{IoFa69,
author = {P. J. Ioannou and B. F. Farrell},
title = {Generalized stability theory. {Part I: Autonomous} operators},
journal = {J. Atmos. Sci.},
year = {1996},
volume = {53},
pages = {2025--2040},
doi = {10.1175/1520-0469(1996)053<2025:gstpia>2.0.co;2},
}
@Article{Thomas2014,
author = {Thomas, V.L. and Lieu, B.K. and Jovanovi\'c, M.R. and Farrell, B.F. and Ioannou, P.J. and Gayme, D.F.},
title = {Self-sustaining turbulence in a restricted nonlinear model of plane {Couette} flow},
journal = {Phys. Fluids},
year = {2014},
volume = {26},
doi = {10.1063/1.4898159},
}
@Article{DonAdi14,
author = {D. A. Donzis and K. Aditya},
title = {Asynchronous finite-difference schemes for partial differential equations},
journal = {J. Comput. Phys.},
year = {2014},
volume = {274},
pages = {370--392},
doi = {10.1016/j.jcp.2014.06.017},
}
@Book{John78,
title = {{Partial Differential Equations}},
publisher = {Springer},
year = {1978},
author = {F. John},
address = {New York},
doi = {10.1007/978-1-4684-0059-5},
}
@Article{ClMoSh01,
author = {B. Clair and S. Mokhtari-Sharghi},
title = {Zeta functions of discrete groupsacting on trees},
journal = {J. Algebra},
year = {2001},
volume = {237},
pages = {591--620},
doi = {10.1006/jabr.2000.8600},
}
@Article{ClMoSh02,
author = {B. Clair and S. Mokhtari-Sharghi},
title = {Convergence of zeta functions of graphs},
journal = {Proc. Amer. Math. Soc.},
year = {2002},
volume = {130},
pages = {1881--1887},
doi = {10.1090/s0002-9939-02-06532-2},
}
@Inproceedings{Pollicott01,
author = {Pollicott, M.},
title = {Dynamical zeta functions},
booktitle = {{Smooth Ergodic Theory and Its Applications}},
year = {2001},
editor = {A. Katok and de la Llave, R. and Y. Pesin and H. Weiss},
volume = {69},
pages = {409--428},
address = {Providence RI},
publisher = {Amer. Math. Soc.},
doi = {10.1090/pspum/069},
url = {https://homepages.warwick.ac.uk/~masdbl/grenoble-16july.pdf},
}
@Book{PikPol16,
title = {{Lyapunov Exponents: A Tool to Explore Complex Dynamics}},
publisher = {Cambridge Univ. Press},
year = {2016},
author = {Pikovsky, A. and Politi, A.},
isbn = {9781316467701},
address = {Cambridge},
doi = {10.1017/cbo9781139343473},
}
@Book{Vargas14,
title = {{Differential Geometry For Physicists And Mathematicians: Moving Frames And Differential Forms: From Euclid Past Riemann}},
publisher = {World Scientific},
year = {2013},
author = {Vargas, J. G.},
isbn = {9789814566391},
doi = {10.1142/8888},
}
@Misc{Devaney95,
author = {R. L. Devaney},
title = {{Chaos in the Classroom}},
howpublished = {Boston Univ.},
year = {1995},
url = {http://math.bu.edu/DYSYS/chaos-game/chaos-game.html},
}
@Article{Lyapunov1892en,
author = {A. M. Lyapunov},
title = {The general problem of the stability of motion},
journal = {Int. J. Control},
year = {1992},
volume = {55},
pages = {531--534},
doi = {10.1080/00207179208934253},
}
@Misc{BaGuGr16,
author = {Barnett, J. and Gurevich, D. R. and Grigoriev, R. O.},
title = {Streamwise localization of traveling wave solutions in channel flow},
year = {2016},
url = {https://arxiv.org/abs/1609.06608},
}
@Article{PaSaLSQR,
author = {Paige, C. C. and Saunders, M. A.},
title = {{LSQR: An} algorithm for sparse linear equations and sparse least squares},
journal = {ACM Trans. Math. Softw.},
year = {1982},
volume = {8},
pages = {43--71},
doi = {10.1145/355984.355989},
}
@Article{WGTR13,
author = {D. Waltner and S. Gnutzmann and G. Tanner and K. Richter},
title = {Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs},
journal = {Phys. Rev. E},
year = {2013},
volume = {87},
pages = {052919},
doi = {10.1103/physreve.87.052919},
}
@Article{BanLinLin07,
author = {Ban, J.-C. and Lin, S.-S. and Lin, Y.-H.},
title = {Patterns generation and spatial entropy in two-dimensional lattice models},
journal = {Asian J. Math.},
year = {2007},
volume = {11},
pages = {497--534},
doi = {10.4310/ajm.2007.v11.n3.a7},
}
@Article{DBHL82,
author = {D'Humieres, D. and Beasley, M. R. and Huberman, B. A. and Libchaber, A.},
title = {Chaotic states and routes to chaos in the forced pendulum},
journal = {Phys. Rev. A},
year = {1982},
volume = {26},
pages = {3483--3496},
doi = {10.1103/PhysRevA.26.3483},
}
@Book{Hamermesh62,
title = {{Group Theory and Its Application to Physical Problems}},
publisher = {Dover},
year = {1962},
author = {Hamermesh, M.},
address = {New York},
}
@Book{Gas97,
title = {{Chaos, Scattering and Statistical Mechanics}},
publisher = {Cambridge Univ. Press},
year = {1997},
author = {P. Gaspard},
address = {Cambridge},
isbn = {9780521018258},
}
@InCollection{CBook:appendHist,
author = {R. Mainieri and P. Cvitanovi{\'c}},
title = {Appendix: {A} brief history of chaos},
booktitle = {{Chaos: Classical and Quantum}},
publisher = {Niels Bohr Inst.},
year = {2016},
address = {Copenhagen},
url = {http://ChaosBook.org/paper.shtml#appendHist},
}
@PhdThesis{McLellan12,
author = {McLellan, K. A.},
title = {{Periodic Coefficients and Random Fibonacci Sequences}},
school = {Dalhousie Univ.},
year = {2012},
address = {Halifax, Nova Scotia},
url = {http://hdl.handle.net/10222/15381},
}
@Article{Riley12,
author = {P. Riley},
title = {On the probability of occurrence of extreme space weather events},
journal = {Space Weather},
year = {2012},
volume = {10},
pages = {S02012},
doi = {10.1029/2011sw000734},
}
@Article{RAEWH10,
author = {P. Ren and T. Aleksi{\'{c}} and D. Emms and R. C. Wilson and E. R. Hancock},
title = {Quantum walks, {Ihara} zeta functions and cospectrality in regular graphs},
journal = {Quantum Inf. Process.},
year = {2010},
volume = {10},
pages = {405--417},
doi = {10.1007/s11128-010-0205-y},
}
@Article{HKSS14,
author = {Y. Higuchi and N. Konno and I. Sato and E. Segawa},
title = {A remark on zeta functions of finite graphs via quantum walks},
journal = {Pacific J. Math. Industry},
year = {2014},
volume = {6},
pages = {1--8},
doi = {10.1186/s40736-014-0009-6},
publisher = {Springer Nature},
}
@Article{SetSto13,
author = {A. Setyadi and C. K. Storm},
title = {Enumeration of graphs with the same {Ihara} zeta function},
journal = {Linear Algebra Appl.},
year = {2013},
volume = {438},
pages = {564--572},
doi = {10.1016/j.laa.2012.07.018},
}
@Article{GuIsLa09,
author = {Guido, D. and Isola, T. and Lapidus, M. L.},
title = {A trace on fractal graphs and the {Ihara} zeta function},
journal = {Transactions of the American Mathematical Society},
year = {2009},
volume = {361},
pages = {3041--3041},
doi = {10.1090/s0002-9947-08-04702-8},
}
@Article{GuIsLa08a,
author = {Guido, D. and Isola, T. and Lapidus, M. L.},
title = {Ihara's zeta function for periodic graphs and its approximation in the amenable case},
journal = {J. Funct. Analysis},
year = {2008},
volume = {255},
pages = {1339--1361},
doi = {10.1016/j.jfa.2008.07.011},
}
@Misc{GuBuCv17,
author = {M.Gudorf and N. B. Budanur and P. Cvitanovi{\'c}},
title = {Is space time? {A} spatio-temporal theory of transitional turbulence},
year = {2017},
note = {In preparationi},
}
@Misc{ShWi16,
author = {Short, K. Y. and Willis, A. P.},
title = {Bifurcation structure of relative periodic orbits in pipe flow},
year = {2017},
note = {In preparation.},
}
@Article{KK04jfnk,
author = {D.A. Knoll and D.E. Keyes},
title = {Jacobian-free {Newton-Krylov methods}: a survey of approaches and applications},
journal = {J. Comput. Phys.},
year = {2004},
volume = {193},
pages = {357--397},
doi = {10.1016/j.jcp.2003.08.010},
}
@Article{BroSa90,
author = {P. N. Brown and Y. Saad},
title = {Hybrid {Krylov} methods for nonlinear systems of equations},
journal = {SIAM J. Sci. Statist. Comput.},
year = {1990},
volume = {11},
pages = {450--481},
doi = {10.1137/0911026},
}
@Article{ChaJac84,
author = {T. F. Chan and K. R. Jackson},
title = {Nonlinearly preconditioned {Krylov} subspace methods for discrete {Newton} algorithms},
journal = {SIAM J. Sci. Statist. Comput.},
year = {1984},
volume = {5},
pages = {533--542},
doi = {10.1137/0905039},
}
@Incollection{seg05,
author = {Sleijpen, G. L. G. and van den Eshof, J. and van Gijzen, M. B.},
title = {Restarted GMRES with Inexact Matrix--Vector Products},
booktitle = {{Lecture Notes in Computer Science}},
publisher = {Springer},
year = {2005},
editor = {Li, Z. and Vulkov, L. and Wa{\'{s}}niewski, J.},
pages = {494--502},
address = {Berlin},
doi = {10.1007/978-3-540-31852-1_60},
}
@Article{EshSle04,
author = {J. van den Eshof and G. L. G. Sleijpen},
title = {Inexact {Krylov} subspace methods for linear systems},
journal = {SIAM J. Matrix Anal. Appl.},
year = {2004},
volume = {26},
pages = {125--153},
doi = {10.1137/S0895479802403459},
}
@Article{BoFra05,
author = {A. Bouras and V. Frayss{\'e}},
title = {Inexact matrix-vector products in {Krylov} methods for solving linear systems: {A} relaxation strategy},
journal = {SIAM J. Matrix Anal. Appl.},
year = {2005},
volume = {26},
pages = {660--678},
doi = {10.1137/S0895479801384743},
}
@Article{LiuQia11,
author = {Q. Liu and D. Qian},
title = {Modulated amplitude waves with nonzero phases in {Bose-Einstein} condensates},
journal = {J. Math. Phys.},
year = {2011},
volume = {52},
pages = {082702},
doi = {10.1063/1.3623415},
publisher = {{AIP} Publishing},
}
@Misc{MojBal17,
author = {R. Mojgani and M. Balajewicz},
title = {Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows},
year = {2015},
url = {https://arxiv.org/abs/1701.04343},
}
@Misc{GoPaDu16,
author = {A. Gouasmi and E. Parish and K. Duraisamy},
title = {Characterizing memory effects in coarse-grained nonlinear systems using the {Mori-Zwanzig} formalism},
year = {2016},
url = {https://arxiv.org/abs/1611.06277},
}
@Article{SzMoRu13,
author = {B. Szczesny and M. Mobilia and A. M. Rucklidge},
title = {When does cyclic dominance lead to stable spiral waves?},
journal = {Europhysics Letters},
year = {2013},
volume = {102},
pages = {28012},
doi = {10.1209/0295-5075/102/28012},
}
@Article{ConMus93,
author = {R. Conte and M. Musette},
title = {Linearity inside nonlinearity: exact solutions to the complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {1993},
volume = {69},
pages = {1--17},
doi = {10.1016/0167-2789(93)90177-3},
}
@Book{RKbook07,
title = {Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics},
publisher = {World Scientific},
year = {2007},
author = {R. Klages},
isbn = {978-981-256-507-5},
address = {Singapore},
doi = {10.1142/9789812771513},
}
@Article{Moores93,
author = {J. D. Moores},
title = {On the {Ginzburg-Landau} laser mode-locking model with fifth-order saturable absorber term},
journal = {Opt. Commun.},
year = {1993},
volume = {96},
pages = {65--70},
doi = {10.1016/0030-4018(93)90524-9},
}
@Book{Taflove1995,
title = {{Computational Electrodynamics: The Finite-difference Time-domain Method}},
publisher = {Artech House},
year = {2005},
author = {Taflove, A. and Hagness, S. C.},
isbn = {9781580538329},
}
@Article{SoGrGrAk04,
author = {Soto-Crespo, J. M. and M. Grapinet and P. Grelu and Akhmediev, N.},
title = {Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser},
journal = {Phys. Rev. E},
year = {2004},
volume = {70},
pages = {066612},
doi = {10.1103/physreve.70.066612},
}
@Article{RuRuBrEr15,
author = {A. F. J. Runge and N. G. R. Broderick and M. Erkintalo},
title = {Observation of soliton explosions in a passively mode-locked fiber laser},
journal = {Optica},
year = {2015},
volume = {2},
pages = {36--39},
doi = {10.1364/optica.2.000036},
}
@Article{Deissler89,
author = {R. J. Deissler},
title = {External noise and the origin and dynamics of structure in convectively unstable systems},
journal = {J. Stat. Phys.},
year = {1989},
volume = {54},
pages = {1459--1488},
doi = {10.1007/bf01044729},
}
@Article{Deissler87,
author = {R. J. Deissler},
title = {Turbulent bursts, spots and slugs in a generalized {Ginzburg-Landau} equation},
journal = {Phys. Lett. A},
year = {1987},
volume = {120},
pages = {334--340},
doi = {10.1016/0375-9601(87)90726-2},
}
@Article{Marcotte2015,
author = {Marcotte, C. D. and Grigoriev, R. O.},
title = {Unstable spiral waves and local {Euclid}ean symmetry in a model of cardiac tissue},
journal = {Chaos},
year = {2015},
volume = {25},
pages = {063116},
doi = {10.1063/1.4922596},
}
@Article{Karma:1991un,
author = {A. Karma},
title = {Universal limit of spiral wave propagation in excitable media},
journal = {Phys. Rev. Lett.},
year = {1991},
volume = {66},
pages = {2274--2277},
doi = {10.1103/physrevlett.66.2274},
}
@Article{BSMLAH15,
author = {Barkley, D. and Song, B. and Mukund, V. and Lemoult, G. and Avila, M. and Hof, B.},
title = {The rise of fully turbulent flow},
journal = {Nature},
year = {2015},
volume = {526},
pages = {550--553},
doi = {10.1038/nature15701},
}
@Article{LlChWi05,
author = {D. J. B. Lloyd and A. R. Champneys and R. E. Wilson},
title = {Robust heteroclinic cycles in the one-dimensional complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {2005},
volume = {204},
pages = {240--268},
doi = {10.1016/j.physd.2005.04.019},
}
@Article{NewWhi69,
author = {A. C. Newell and J. A. Whitehead},
title = {Finite bandwidth, finite amplitude convection},
journal = {J. Fluid Mech.},
year = {1969},
volume = {38},
pages = {279--403},
doi = {10.1017/s0022112069000176},
}
@Phdthesis{DingThesis,
author = {Ding, X.},
title = {{Geometry of Inertial Manifolds in Nonlinear Dissipative Dynamical Systems}},
school = {School of Physics, Georgia Inst. of Technology},
year = {2017},
address = {Atlanta},
url = {http://ChaosBook.org/projects/theses.html},
}
@Phdthesis{LoeweThesis,
author = {Loewe, B.},
title = {{Bridges Between Quantum and Classical Mechanics: Directed Polymers, Flocking and Transitionless Quantum Driving}},
school = {School of Physics, Georgia Inst. of Technology},
year = {2017},
address = {Atlanta},
url = {http://hdl.handle.net/1853/54445},
}
@Misc{LoHiGo17,
author = {B. Loewe and R. Hipolito and P. M. Goldbart},
title = {A semi-classical approach to transitionless quantum driving},
note = {In preparation},
}
@Article{Berry09,
author = {M. V. Berry Berry},
title = {Transitionless quantum driving},
journal = {J. Phys. A},
year = {2009},
volume = {42},
pages = {365303},
doi = {10.1088/1751-8113/42/36/365303},
}
@Article{Saad93,
author = {Y. Saad},
title = {A flexible inner-outer preconditioned {GMRES} algorithm},
journal = {SIAM J. Sci. Comput.},
year = {1993},
volume = {14},
pages = {461--469},
doi = {10.1137/0914028},
}
@Article{MoReHa14,
author = {K. Morikun and L. Reichel and K. Hayami},
title = {{FGMRES} for linear discrete ill-posed problems},
journal = {Appl. Numer. Math.},
year = {2014},
volume = {75},
pages = {175--187},
doi = {10.1016/j.apnum.2013.08.004},
}
@Article{EldSim12,
author = {L. Elden and V. Simoncini},
title = {Solving ill-posed linear systems with {GMRES }and a singular preconditioner},
journal = {SIAM J. Matrix. Anal. Appl.},
year = {2012},
volume = {33},
pages = {1369--1394},
doi = {10.1137/110832793},
}
@Article{LotYe05,
author = {L. Reichel and Q. Ye},
title = {Breakdown-free {GMRES} for singular systems},
journal = {SIAM J. Matrix. Anal. Appl.},
year = {2005},
volume = {26},
pages = {1001-1021},
doi = {10.1137/110832793},
}
@Article{GrGrReSz16,
author = {C. Greif and T. Rees and D. Szyld},
title = {{GMRES} with multiple preconditioners},
journal = {SeMA Journal},
year = {2016},
pages = {1--19},
doi = {10.1007/s40324-016-0088-7},
}
@Article{Gijzen95,
author = {M.B. van Gijzen},
title = {A polynomial preconditioner for the {GMRES} algorithm},
journal = {J. Comput. Appl. Math.},
year = {1995},
volume = {59},
pages = {91--107},
doi = {10.1016/0377-0427(94)00015-S},
}
@Article{ReSaWo10,
author = {D. Reynolds and R. Samtaney and C. Woodward},
title = {Operator-based preconditioning of stiff hyperbolic systems},
journal = {SIAM J. Sci. Comput.},
year = {2010},
volume = {32},
pages = {150--170},
doi = {10.1137/080713331},
}
@Misc{Tourigny17,
author = {Tourigny, D. S.},
title = {Networks of planar {Hamiltonian} systems},
year = {2017},
url = {https://arXiv.org/abs/1701.03149},
}
@Article{Heiss99,
author = {W. D. Heiss},
title = {Phases of wave functions and level repulsion},
journal = {Eur. Phys. J. D},
year = {1999},
volume = {7},
pages = {1--4},
doi = {10.1007/s100530050339},
}
@Article{Heiss12,
author = {W. D. Heiss},
title = {The physics of exceptional points},
journal = {J. Phys. A},
year = {2012},
volume = {45},
pages = {444016},
doi = {10.1088/1751-8113/45/44/444016},
}
@Article{Heiss04,
author = {W. D. Heiss},
title = {Exceptional points of non-{Hermitian} operators},
journal = {J. Phys. A},
year = {2004},
volume = {37},
pages = {2455},
doi = {10.1088/0305-4470/37/6/034},
}
@Book{Kato80,
title = {{Perturbation Theory for Linear Operators}},
publisher = {Springer},
year = {1980},
author = {Kato, T.},
isbn = {9783662126783},
address = {Berlin},
doi = {10.1007/978-3-662-12678-3},
}
@Book{Moiseyev11,
title = {{Non-Hermitian Quantum Mechanics}},
publisher = {Cambridge Univ. Press},
year = {2011},
author = {Moiseyev, N.},
isbn = {9781139496995},
address = {Cambridge},
doi = {10.1017/cbo9780511976186},
}
@Misc{LiMaWu17,
author = {Liebermann, N. and Main, J. and Wunner, G.},
title = {Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization},
year = {2017},
url = {https://arxiv.org/abs/1705.00197},
}
@Article{FBCL10,
author = {L. Fazendeiro and B.M. Boghosian and P.V. Coveney and J. L{\"a}tt},
title = {Unstable periodic orbits in weak turbulence},
journal = {J. Comput. Sci.},
year = {2010},
volume = {1},
pages = {13--23},
doi = {10.1016/j.jocs.2010.03.004},
}
@Article{FiBoKo05,
author = {Finn, L. I. and Boghosian, B. M. and Kottke, C. N.},
title = {Vortex core identification in viscous hydrodynamics},
journal = {Philos. Trans. Royal Soc. A},
year = {2005},
volume = {363},
pages = {1937--1948},
doi = {10.1098/rsta.2005.1620},
}
@Misc{BKKR17,
author = {Balanov, Z. and {Kravetc}, P. and {Krawcewicz}, W. and {Rachinskii}, D.},
title = {Hopf bifurcation of relative periodic solutions: {Case} study of a ring of passively mode-locked lasers},
year = {2017},
url = {http://arXiv.org/abs/1703.09154},
}
@Article{SoGrAkDe07,
author = {J. M. Soto-Crespo and Ph. Grelu and N. Akhmediev and N. Devine},
title = {Soliton complexes in dissipative systems: {Vibrating}, shaking, and mixed soliton pairs},
journal = {Phys. Rev. E},
year = {2007},
volume = {75},
pages = {016613},
doi = {10.1103/physreve.75.016613},
}
@TechReport{Meza95,
author = {J.C. Meza},
title = {A modification to the {GMRES} method for ill-conditioned linear systems},
institution = {Sandia National Laboratories},
year = {1995},
url = {http://crd-legacy.lbl.gov/~meza/papers/gmsvd.pdf},
}
@Article{BroWal97,
author = {P. N. Brown and H. F. Walker},
title = {{GMRES} on (nearly) singular systems},
journal = {SIAM J. Matrix. Anal. Appl.},
year = {1997},
volume = {18},
pages = {37--51},
doi = {10.1137/S0895479894262339},
}
@Article{MiAK03,
author = {R. C. Mittal and A. H. Al-Kurdi},
title = {An efficient method for constructing an {ILU} preconditioner for solving large sparse nonsymmetric linear systems by the {GMRES} method},
journal = {Comput. Math. Appl.},
year = {2003},
volume = {45},
pages = {1757--1772},
doi = {10.1016/S0898-1221(03)00154-8},
}
@Article{Chu09,
author = {K. T. Chu},
title = {A direct matrix method for computing analytical {Jacobians} of discretized nonlinear integro-differential equations},
journal = {J. Comput. Phys.},
year = {2009},
volume = {228},
pages = {5526--5538},
doi = {10.1016/j.jcp.2009.04.031},
}
@Article{XuPaul16,
author = {Xu, M. and Paul, M. R.},
title = {Covariant {Lyapunov} vectors of chaotic {Rayleigh-B{\'e}nard} convection},
journal = {Phys. Rev. E},
year = {2016},
volume = {93},
pages = {062208},
doi = {10.1103/PhysRevE.93.062208},
}
@Article{W97,
author = {F. Waleffe},
title = {On a {Self-Sustaining Process} in shear flows},
journal = {Phys. Fluids},
year = {1997},
volume = {9},
pages = {883--900},
doi = {10.1063/1.869185},
}
@Article{YaRa09,
author = {Yang, {H.-l.} and Radons, G.},
title = {{Lyapunov} modes in extended systems},
journal = {Philos. Trans. Royal Soc. A},
year = {2009},
volume = {367},
pages = {3197--3212},
doi = {10.1098/rsta.2009.0067},
}
@Article{Drmac00,
author = {Z. Drma{\v{c}}},
title = {On principal angles between subspaces of {Euclidean} space},
journal = {SIAM J. Matrix Anal. Appl.},
year = {2000},
volume = {22},
pages = {173--194},
doi = {10.1137/S0895479897320824},
}
@Article{CarDes16,
author = {Cartes, C. and Descalzi, O.},
title = {Periodic exploding dissipative solitons},
journal = {Phys. Rev. A},
year = {2016},
volume = {93},
pages = {031801},
doi = {10.1103/PhysRevA.93.031801},
}
@Article{SALMM10,
author = {Skarka, V. and Aleksi{\'c}, N. B. and Leblond, H. and Malomed, B. A. and Mihalache, D.},
title = {Varieties of stable vortical solitons in {Ginzburg-Landau} media with radially inhomogeneous Losses},
journal = {Phys. Rev. Lett.},
year = {2010},
volume = {105},
pages = {213901},
doi = {10.1103/PhysRevLett.105.213901},
}
@Article{DCCB11,
author = {Descalzi, O. and Cartes, C. and Cisternas, J. and Brand, H. R.},
title = {Exploding dissipative solitons: {The} analog of the {Ruelle-Takens} route for spatially localized solutions},
journal = {Phys. Rev. E},
year = {2011},
volume = {83},
pages = {056214},
doi = {10.1103/PhysRevE.83.056214},
}
@Book{HCFLM16,
title = {{The Parameterization Method for Invariant Manifolds}},
publisher = {Springer},
year = {2016},
author = {Haro, {\'A}. and Canadell, M. and Luque, A. and Mondelo, J. M. and Figueras, J.-L.},
address = {New York},
isbn = {9783319296609},
doi = {10.1007/978-3-319-29662-3},
}
@Article{JuRi90,
author = {C. Jung and P. Richter},
title = {Classical chaotic scattering-periodic orbits, symmetries, multifractal invariant sets},
journal = {J. Phys. A},
year = {1990},
volume = {23},
pages = {2847},
doi = {10.1088/0305-4470/23/13/023},
}
@Article{JuScho87,
author = {C. Jung and H. J. Scholz},
title = {Cantor set structures in the singularities of classical potential scattering},
journal = {J. Phys. A},
year = {1987},
volume = {20},
pages = {3607},
doi = {10.1088/0305-4470/20/12/015},
}
@Article{KrZaEc14,
author = {T. Kreilos and S. Zammert and B. Eckhardt},
title = {Comoving frames and symmetry-related motions in parallel shear flows},
journal = {J. Fluid Mech.},
year = {2014},
volume = {751},
pages = {685--697},
doi = {10.1017/jfm.2014.305},
}
@Article{ShFrMa08,
author = {A. S. Shiriaev and L. B. Freidovich and I. R. Manchester},
title = {Can we make a robot ballerina perform a pirouette? {Orbital} stabilization of periodic motions of underactuated mechanical systems},
journal = {Ann. Rev. Control},
year = {2008},
volume = {32},
pages = {200--211},
doi = {10.1016/j.arcontrol.2008.07.001},
}
@Misc{Lasagna17a,
author = {D. Lasagna},
title = {Sensitivity analysis of systems using unstable periodic orbits},
year = {2017},
url = {https://arxiv.org/abs/1708.04121},
}
@Misc{Lasagna17,
author = {D. Lasagna},
title = {Sensitivity analysis of turbulence using unstable periodic orbits: a demonstration on the {Kuramoto-Sivashinsky} equation},
year = {2017},
note = {{10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA}},
url = {https://eprints.soton.ac.uk/408114/1/Sensitivity_analysis_of_turbulence_using_unstable_periodic_orbits.pdf},
}
@Article{Elouafi14,
author = {M. Elouafi},
title = {On a relationship between {Chebyshev} polynomials and {Toeplitz} determinants},
journal = {Appl. Math. Comput.},
year = {2014},
volume = {229},
pages = {27-- 33},
doi = {10.1016/j.amc.2013.12.029},
}
@Article{Gover94,
author = {M. J. C. Gover},
title = {The eigenproblem of a tridiagonal 2-{Toeplitz} matrix},
journal = {Linear Algebra Appl.},
year = {1994},
volume = {197},
pages = {63--78},
doi = {10.1016/0024-3795(94)90481-2},
}
@Misc{AGBWG17,
author = {Akila, M. and Gutkin, B. and {Braun}, P. and Waltner, D. and Guhr, T.},
title = {Semiclassical prediction of large spectral fluctuations in interacting kicked spin chains},
year = {2017},
url = {https://arxiv.org/abs/1709.03601},
}
@Article{JimMan09,
author = {Jim{\'e}nez Madrid, J. A. and Mancho, A. M.},
title = {Distinguished trajectories in time dependent vector fields},
journal = {Chaos},
year = {2009},
volume = {19},
pages = {013111},
doi = {10.1063/1.3056050},
}
@Article{JuMWuHe17,
author = {Junginger, A. and Main, J. and Wunner, G. and Hernandez, R.},
title = {Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points},
journal = {Phys. Rev. A},
year = {2017},
volume = {95},
pages = {032130},
doi = {10.1103/PhysRevA.95.032130},
}
@Article{MaHoLaLi15,
author = {Ma, H. and Ho, D. W. C. and Lai, Y.-C. and Lin, W.},
title = {Detection meeting control: {Unstable} steady states in high-dimensional nonlinear dynamical systems},
journal = {Phys. Rev. E},
year = {2015},
volume = {92},
pages = {042902},
doi = {10.1103/PhysRevE.92.042902},
}
@Article{InTaYa15,
author = {Inubushi, M. and Takehiro, S.-i. and Yamada, M.},
title = {Regeneration cycle and the covariant {Lyapunov} vectors in a minimal wall turbulence},
journal = {Phys. Rev. E},
year = {2015},
volume = {92},
pages = {023022},
doi = {10.1103/PhysRevE.92.023022},
}
@Article{BeiGal16,
author = {Beims, M. W. and Gallas, J. A. C.},
title = {Alignment of {Lyapunov} vectors: {A} quantitative criterion to predict catastrophes?},
journal = {Sci. Reps.},
year = {2016},
volume = {6},
pages = {37102},
url = {10.1038/srep37102},
}
@Manual{Mathematica,
title = {Mathematica 11},
author = {{Wolfram Research, Inc.}},
date = {2017},
url = {https://www.wolfram.com/mathematica/},
}
@Article{HuCon96,
author = {G. Y. Hu and R. F. {O'Connell}},
title = {Analytical inversion of symmetric tridiagonal matrices},
journal = {J. Phys. A},
year = {1996},
volume = {29},
pages = {1511},
doi = {10.1088/0305-4470/29/7/020},
}
@Article{Dorr70,
author = {F. W. Dorr},
title = {The direct solution of the discrete {Poisson} equation on a rectangle},
journal = {SIAM Rev.},
year = {1970},
volume = {12},
pages = {248--263},
doi = {10.1137/1012045},
}
@Article{HuCon94,
author = {Hu, G. Y. and {O'Connell}, R. F.},
title = {Exact solution for the charge soliton in a one-dimensional array of small tunnel junctions},
journal = {Phys. Rev. B},
year = {1994},
volume = {49},
pages = {16773--16776},
doi = {10.1103/PhysRevB.49.16773},
}
@Article{HuCon95,
author = {Hu, G. Y. and O'Connell, R. F.},
title = {Exact solution of the electrostatic problem for a single electron multijunction trap},
journal = {Phys. Rev. Lett.},
year = {1995},
volume = {74},
pages = {1839--1842},
doi = {10.1103/PhysRevLett.74.1839},
}
@Article{NoPaRe13,
author = {Noschese, S. and Pasquini, L. and Reichel, L.},
title = {Tridiagonal {Toeplitz matrices}: properties and novel applications},
journal = {Numer. Linear Algebra Appl.},
year = {2013},
volume = {20},
pages = {302--326},
doi = {10.1002/nla.1811},
}
@Article{Yueh06,
author = {Yueh, W.-C.},
title = {Explicit inverses of several tridiagonal matrices},
journal = {Appl. Math. E-Notes},
year = {2006},
volume = {6},
pages = {74--83},
url = {http://www.emis.ams.org/journals/AMEN/2006/2006.htm},
}
@Article{HuRyCo98,
author = {Hu, G. Y. and Ryu, J. Y. and O'Connell, R. F.},
title = {Analytical solution of the generalized discrete {Poisson} equation},
journal = {J. Phys. A},
year = {1998},
volume = {31},
pages = {9279},
doi = {10.1088/0305-4470/31/46/017},
}
@Article{PapTho13,
author = {Papathanasiou, G. and Thorn, C. B.},
title = {Worldsheet propagator on the lightcone worldsheet lattice},
journal = {Phys. Rev. D},
year = {2013},
volume = {87},
pages = {066005},
doi = {10.1103/PhysRevD.87.066005},
}
@Article{GilTho77,
author = {Giles, R. and Thorn, C. B.},
title = {Lattice approach to string theory},
journal = {Phys. Rev. D},
year = {1977},
volume = {16},
pages = {366--386},
doi = {10.1103/PhysRevD.16.366},
}
@Article{ChuYau00,
author = {F. Chung and S.-T. Yau},
title = {Discrete {Green's} functions},
journal = {J. Combin. Theory A},
year = {2000},
volume = {91},
pages = {19--214},
doi = {10.1006/jcta.2000.3094},
}
@Article{YamAbd97,
author = {H. A. Yamani and M. S. Abdelmonem},
title = {The analytic inversion of any finite symmetric tridiagonal matrix},
journal = {J. Phys. A},
year = {1997},
volume = {30},
pages = {2889},
doi = {10.1088/0305-4470/30/8/029},
}
@Article{Streater79,
author = {Streater, R. F.},
title = {A bound for the difference {Laplacian}},
journal = {Bull. London Math. Soc.},
year = {1979},
volume = {11},
pages = {354--357},
doi = {10.1112/blms/11.3.354},
}
@Article{Simons97,
author = {S. Simons},
title = {Analytical inversion of a particular type of banded matrix},
journal = {J. Phys. A},
year = {1997},
volume = {30},
pages = {755},
doi = {10.1088/0305-4470/30/2/034},
}
@Book{Smith85,
title = {{Numerical Solution of Partial Differential Equations: Finite Difference Methods}},
publisher = {Clarendon Press},
year = {1985},
author = {Smith, G. D.},
isbn = {9780198596509},
address = {Oxford UK},
}
@Article{KatIna71,
author = {S. Katsura and S. Inawashiro},
title = {Lattice {Green's} functions for the rectangular and the square lattices at arbitrary points},
journal = {J. Math. Phys.},
year = {1971},
volume = {12},
pages = {1622--1630},
doi = {10.1063/1.1665785},
}
@Article{KMIHA71,
author = {S. Katsura and T. Morita and S. Inawashiro and T. Horiguchi and Y. Abe},
title = {Lattice {Green's} function. {Introduction}},
journal = {J. Math. Phys.},
year = {1971},
volume = {12},
pages = {892--895},
doi = {10.1063/1.1665662},
}
@Article{KaInAb71,
author = {S. Katsura and S. Inawashiro and Y. Abe},
title = {Lattice {Green's} function for the simple cubic lattice in terms of a {Mellin‐Barnes} type integral},
journal = {J. Math. Phys.},
year = {1971},
volume = {12},
pages = {895-899},
doi = {10.1063/1.1665663},
}
@Article{Cserti00,
author = {J. Cserti},
title = {Application of the lattice {Green’s} function for calculating the resistance of an infinite network of resistors},
journal = {Amer. J. Physics},
year = {2000},
volume = {68},
pages = {896--906},
doi = {10.1119/1.1285881},
}
@Article{BhaOst10,
author = {H. S. Bhat and B. Osting},
title = {Diffraction on the two-dimensional square lattice},
journal = {SIAM J. Appl. Math.},
year = {2010},
volume = {70},
pages = {1389--1406},
doi = {10.1137/080735345},
}
@Book{Economou79,
title = {{Green’s Functions in Quantum Physics}},
publisher = {Springer},
year = {1979},
author = {Economou, E. N.},
isbn = {9783662119006},
address = {Berlin},
doi = {10.1007/978-3-662-11900-6},
}
@Article{Morita71,
author = {T. Morita},
title = {Useful procedure for computing the lattice {Green's} function - square, tetragonal, and bcc lattices},
journal = {J. Math. Phys.},
year = {1971},
volume = {12},
pages = {1744--1747},
doi = {10.1063/1.1665800},
}
@Article{Horiguchi71,
author = {T. Horiguchi},
title = {Lattice {Green’s} function for the simple cubic lattice},
journal = {J. Phys. Soc. Jpn.},
year = {1971},
volume = {30},
pages = {1261--1272},
doi = {10.1143/JPSJ.30.1261},
}
@Article{Asad07,
author = {Asad, J. H.},
title = {DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION},
journal = {Mod. Phys. Lett. B},
year = {2007},
volume = {21},
pages = {139--154},
doi = {10.1142/S021798490701244X},
}
@Article{HorMor75,
author = {T. Horiguchi and T. Morita},
title = {Note on the lattice {Green’s} function for the simple cubic lattice},
journal = {J. Phys. C},
year = {1975},
volume = {8},
pages = {L232},
doi = {10.1088/0022-3719/8/11/002},
}
@Book{Gunzburger02,
title = {{Perspectives in Flow Control and Optimization}},
publisher = {SIAM},
year = {2002},
author = {Gunzburger, M.},
doi = {10.1137/1.9780898718720},
}
@Article{Dow03,
author = {M. Dow},
title = {Explicit inverses of {Toeplitz} and associated matrices},
journal = {ANZIAM J.},
year = {2003},
volume = {44},
pages = {E185--E215},
doi = {10.21914/anziamj.v44i0.493},
}
@Article{MorHor71,
author = {T. Morita and T. Horiguchi},
title = {Calculation of the lattice {Green's} function for the bcc, fcc, and rectangular lattices},
journal = {J. Math. Phys.},
year = {1971},
volume = {12},
pages = {986-992},
doi = {10.1063/1.1665693},
}
@Article{BHJ12,
author = {R. Band and J. M. Harrison and C. H. Joyner},
title = {Finite pseudo orbit expansions for spectral quantities of quantum graphs},
journal = {J. Phys. A},
year = {2012},
volume = {45},
pages = {325204},
doi = {10.1088/1751-8113/45/32/325204},
}
@Article{ZaPeWi16,
author = {M. Zahr and P.-O. Persson and J. Wilkening},
title = {A fully discrete adjoint method for optimization of flow problems on deforming domains with time-periodicity constraints},
journal = {J. Comp. Fluid.},
year = {2016},
doi = {10.1016/j.compfluid.2016.05.021},
}
@Article{SlBaJu16,
author = {Slipantschuk, J. and {Bandtlow}, O. F. and {Just}, W.},
title = {Complete spectral data for analytic {Anosov} maps of the torus},
journal = {Nonlinearity},
year = {2017},
volume = {30},
pages = {2667},
doi = {10.1088/1361-6544/aa700f},
}
@Article{Kirchgassner82,
author = {K. Kirchg{\"a}ssner},
title = {Wave-solutions of reversible systems and applications},
journal = {J. Diff. Equ.},
year = {1982},
volume = {45},
pages = {113--127},
doi = {10.1016/0022-0396(82)90058-4},
}
@Article{SanSch01,
author = {B. Sandstede and A. Scheel},
title = {On the structure of spectra of modulated travelling waves},
journal = {Math. Nachr.},
year = {2001},
volume = {232},
pages = {39--93},
doi = {10.1002/1522-2616(200112)232:1},
}
@Article{ValSar99,
author = {R. O. Vallejos and M. Saraceno},
title = {The construction of a quantum {Markov} partition},
journal = {J. Phys. A},
year = {1999},
volume = {32},
pages = {7273},
doi = {10.1088/0305-4470/32/42/304},
abstract = {We present a method for constructing a quantum Markov partition. Its elements are obtained by quantizing the characteristic function of the classical rectangles. The result is a set of quantum operators which behave asymptotically as projectors over the classical rectangles apart from edge and corner effects. We investigate their spectral properties and different methods of construction. The quantum partition is shown to induce a symbolic decomposition of the quantum evolution operator. In particular, an exact expression for the traces of the propagator is obtained having the same structure as the Gutzwiller periodic orbit sum.},
}
@Article{KirchSch78,
author = {K. Kirchg{\"a}ssner and J. Scheurle},
title = {On the bounded solutions of a semilinear elliptic equation in a strip},
journal = {J. Diff. Equ.},
year = {1978},
volume = {32},
pages = {119--148},
doi = {10.1016/0022-0396(79)90055-X},
}
@Article{Vaienti92,
author = {Vaienti, S.},
title = {Ergodic properties of the discontinuous sawtooth map},
journal = {J. Stat. Phys.},
year = {1992},
volume = {67},
pages = {251--269},
doi = {10.1007/BF01049033},
}
@Article{Sinai68,
author = {Sinai, Ya. G.},
title = {Construction of {Markov} partitions},
journal = {Funct. Anal. Appl.},
year = {1968},
volume = {2},
pages = {245--253},
doi = {10.1007/BF01076126},
}
@Misc{WilZgl17,
author = {Wilczak, D. and Zgliczynski, P.},
title = {Symbolic dynamics for {Kuramoto-Sivashinsky PDE} on the line--a computer--assisted proof},
year = {2017},
url = {http://ww2.ii.uj.edu.pl/~wilczak/papers/kspde/kschaos-main.pdf},
}
@Article{HBA94,
author = {Hakmi, A. and Bosco, F. and Antoniou, I.},
title = {First return map of the periodic {Lorentz} gas},
journal = {Phys. Rev. E},
year = {1995},
volume = {51},
pages = {3952--3956},
doi = {10.1103/PhysRevE.51.3952},
}
@Article{bk,
author = {Berlin, T. H. and Kac, M.},
title = {The spherical model of a ferromagnet},
journal = {Phys. Rev.},
year = {1952},
volume = {86},
pages = {821--835},
doi = {10.1103/PhysRev.86.821},
}
@Book{PJD,
title = {Circulant Matrices},
publisher = {Amer. Math. Soc.},
year = {1979},
author = {P. J. Davis},
isbn = {978-0821891650},
address = {New York},
edition = {2},
doi = {10.2307/2006411},
}
@Article{Guckenheimer70,
author = {Guckenheimer, J.},
title = {Axiom {A + no} cycles {$ \Rightarrow \zeta_f(t)$} rational},
journal = {Bull. Amer. Math. Soc.},
year = {1970},
volume = {76},
pages = {592--594},
doi = {10.1090/S0002-9904-1970-12449-1},
}
@Article{Hadamard98,
author = {Hadamard, J.},
title = {Les surfaces {\`a} courbures oppos{\'e}es et leurs lignes g{\'e}od{\'e}sique},
journal = {J. Math. Pures Appl.},
year = {1898},
volume = {4},
pages = {27--73},
url = {http://sites.mathdoc.fr/JMPA/PDF/JMPA_1898_5_4_A3_0.pdf},
}
@Article{BoVuHe78,
author = {I. B. Bo{\v{z}}ovi{\'c} and M. Vuji{\v{c}}i{\'c} and F. Herbut},
title = {Irreducible representations of the symmetry groups of polymer molecules. {I}},
journal = {J. Phys. A},
year = {1978},
volume = {11},
number = {11},
pages = {2133},
doi = {10.1088/0305-4470/11/11/003},
}
@Book{Landau70,
title = {{Theory of Elasticity}},
publisher = {Pergamon Press},
year = {1970},
author = {L. D. Landau and E. M. Lifshitz},
isbn = {9780080570693},
address = {Oxford},
edition = {3},
url = {https://archive.org/details/TheoryOfElasticity},
}
@Book{Landau59b,
title = {{Mechanics}},
publisher = {Pergamon Press},
year = {1959},
author = {L.D. Landau and E.M. Lifshitz},
isbn = {978-0750628969},
address = {Oxford},
edition = {3},
url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22},
}
@Book{Landau59c,
title = {{Quantum Mechanics: Non-Relativistic Theory}},
publisher = {Pergamon Press},
year = {1959},
author = {L.D. Landau and E.M. Lifshitz},
isbn = {978-0750635394},
address = {Oxford},
url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22},
}
@Book{Landau60,
title = {{Electrodynamics of Continuous Media}},
publisher = {Pergamon Press},
year = {1960},
author = {L.D. Landau and E.M. Lifshitz},
isbn = {978-0750626347},
address = {Oxford},
edition = {2},
url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22},
}
@Book{Landau80a,
title = {{Statistical Physics, Part 1}},
publisher = {Pergamon Press},
year = {1980},
author = {L.D. Landau and E.M. Lifshitz},
isbn = {978-0750633727},
address = {Oxford},
url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22},
}
@Book{Landau80b,
title = {{Statistical Physics, Part 2: Theory of the Condensed State}},
publisher = {Pergamon Press},
year = {1980},
author = {L.D. Landau and E.M. Lifshitz},
isbn = {978-0750626361},
address = {Oxford},
url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22},
}
@Book{LifPit,
title = {{Physical Kinetics}},
publisher = {Elsevier},
year = {1981},
author = {L. P. Pitaevskii, E. M. Lifshitz},
isbn = {9780750626354},
address = {Burlington, MA},
}
@Article{AllBar12,
author = {A. Allahem and T. Bartsch},
title = {Chaotic dynamics in multidimensional transition states},
journal = {J. Chem. Phys.},
year = {2012},
volume = {137},
pages = {214310},
doi = {10.1063/1.4769197},
}
@Misc{KubBoz16,
author = {K{\"u}bra Duru, H. and Bozkurt, D.},
title = {Integer powers of certain complex pentadiagonal 2-{Toeplitz} matrices},
year = {2017},
url = {https://arxiv.org/abs/1708.04121},
}
@Article{TBAMR92,
author = {T.E. Tezduyar, and M. Behr, S.K. Aliabadi, S. Mittal and S.E. Ray},
title = {A new mixed preconditioning method for finite element computations},
journal = {Comp. Meth. Appl. Mech. Eng.},
year = {1992},
volume = {99},
pages = {27--42},
doi = {10.1016/0045-7825(92)90121-Y},
}
@Book{BoyVan04,
title = {{Convex Optimization}},
publisher = {Cambridge Univ. Press},
year = {2004},
author = {S. Boyd and L. Vandenberghe},
address = {Cambridge},
doi = {10.1017/cbo9780511804441},
}
@Article{Nesterov83,
author = {Y. Nesterov},
title = {A method of solving a convex programming problem with convergence rate {O($1/k^2$)}},
journal = {Sov. Math.-Dokl.},
year = {1983},
volume = {27},
pages = {372--376},
}
@Article{BeTe09,
author = {A. Beck and M. Teboulle},
title = {A fast iterative shrinkage-thresholding algorithm for linear inverse problems},
journal = {SIAM J. Imaging Sci.},
year = {2009},
volume = {2},
pages = {183--202},
doi = {10.1137/080716542},
}
@Article{Glaser70,
author = {J. I. Glaser},
title = {Numerical solution of waveguide scattering problems by finite-difference {Green's} functions},
journal = {IEEE Trans. Microwave Theory Tech.},
year = {1970},
volume = {18},
pages = {436--443},
abstract = {A finite-difference Green's function method for solving time-harmonic wave guide scattering problems involving metallic obstacles of finite size by computer is described. The method is applied to the two-dimensional problem of a TE10 mode impinging on cylindrical metallic posts of arbitrary shape in a rectangular waveguide. The equivalent susceptance of a transverse semidiaphragm computed using a 50 point approximation for the induced current distribution is found to be 1.5 percent less than the exact value. The S matrix of a thin bent window versus wavelength is also presented.},
doi = {10.1109/TMTT.1970.1127265},
}
@Article{SerRok16,
author = {Serkh, K. and Rokhlin, V.},
title = {On the solution of the {Helmholtz} equation on regions with corners},
journal = {Proc. Natl. Acad. Sci. USA},
year = {2016},
volume = {113},
pages = {9171--9176},
doi = {10.1073/pnas.1609578113},
abstract = {In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.},
}
@Inproceedings{dlLlave00,
author = {de la Llave, R.},
title = {Variational methods for quasiperiodic solutions of partial differential equations},
booktitle = {{Hamiltonian Systems and Celestial Mechanics (HAMSYS–98)}},
year = {2000},
editor = {Delgado, J. and Lacomba, E. A. and P{\'e}rez-Chavela, E. and Llibre, J.},
isbn = {9789814492119},
address = {Singapore},
publisher = {World Scientific},
doi = {10.1142/4557},
url = {http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=00-56},
}
@Article{JoTeXi95,
author = {M. S. Jolly and R. T{\'e}mam and C. Xiong},
title = {Convergence of a chaotic attractor with increased spatial resolution of the {Ginzburg-Landau} equation},
journal = {Chaos, Solitons Fractals},
year = {1995},
volume = {5},
pages = {1833--1845},
doi = {10.1016/0960-0779(94)00197-X},
}
@Article{Yang15,
author = {Yang, J.},
title = {A numerical method for computing time-periodic solutions in dissipative wave systems},
journal = {Stud. Appl. Math.},
year = {2015},
volume = {134},
pages = {420--455},
doi = {10.1111/sapm.12071},
}
@Inproceedings{CR93,
author = {Cvitanovi{\'c}, P. and Rosenqvist, P. E.},
title = {A new determinant for quantum chaos},
booktitle = {From Classical to Quantum Chaos},
year = {1993},
editor = {G. F. Dell'Antonio, S. Fantoni and V. R. Manfredi},
volume = {41},
pages = {57--64},
address = {Bologna},
organization = {Soc. Italiana di Fisica Conf. Proceed.},
publisher = {Ed. Compositori},
url = {https://arXiv.org/abs/chao-dyn/9304003},
}
@Book{FetWal03,
title = {{Theoretical Mechanics of Particles and Continua}},
publisher = {Dover},
year = {2003},
author = {Fetter, A. L. and Walecka, J. D.},
isbn = {9780486432618},
address = {New York},
}
@TechReport{Crutchfield18,
author = {J. Crutchfield},
title = {{Roadmap for Natural Computation and Self-Organization}},
institution = {U. California, Davis},
year = {2017},
note = {Physics 256A course},
url = {http://csc.ucdavis.edu/~chaos/courses/ncaso/Lectures/},
}
@Comment{jabref-meta: databaseType:bibtex;}