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@Article{AACI,
author = {R. Artuso and E. Aurell and P. Cvitanovi{\'c}},
title = {Recycling of strange sets: {I. Cycle} expansions},
journal = {Nonlinearity},
year = {1990},
volume = {3},
pages = {325--359},
doi = {10.1088/0951-7715/3/2/005},
}
@Article{AACII,
author = {R. Artuso and E. Aurell and P. Cvitanovi{\'c}},
title = {Recycling of strange sets: {II. Applications}},
journal = {Nonlinearity},
year = {1990},
volume = {3},
pages = {361},
doi = {10.1088/0951-7715/3/2/006},
}
@Book{ablowbook,
title = {{Solitions, Nonlinear Evolution Equations and Inverse Scattering}},
publisher = {Cambridge Univ. Press},
year = {1992},
author = {M. J. Ablowitz and P. A. Clarkson},
address = {Cambridge},
}
@Book{AbrMars78,
title = {{Foundations of Mechanics}},
publisher = {Benjamin-Cummings},
year = {1978},
author = {R. Abraham and J. E. Marsden},
address = {Reading, Mass.},
}
@Article{Absh05,
author = {J. Abshagen and J. M. Lopez and F. Marques and G. Pfister},
title = {Mode competition of rotating waves in reflection-symmetric {Taylor-Couette} flow},
journal = {J. Fluid Mech.},
year = {2005},
volume = {540},
pages = {269--300},
doi = {10.1017/s0022112005005811},
}
@Article{Absh05a,
author = {J. Abshagen and J. M. Lopez and F. Marques and G. Pfister},
title = {Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics},
journal = {Phys. Rev. Lett.},
year = {2005},
volume = {94},
pages = {074501},
doi = {10.1103/physrevlett.94.074501},
}
@Book{AbSh92,
title = {{Dynamics - The Geometry of Behavior}},
publisher = {Addison-Wesley},
year = {1992},
author = {R. H. Abraham and C. D. Shaw},
address = {Reading, MA}
}
@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}
}
@Book{Adams:2003wi,
Title = {Sobolev spaces},
Author = {Adams, R. A. and Fournier, J. J. F.},
Publisher = {Academic press},
Year = {2003},
Address = {New York}
}
@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{Afraimovich87,
Title = {On the appearence and the structure of the {Lorenz} attractor},
Author = {V. S. Afraimovich and B. B. Bykov and L. P. Shilnikov},
Journal = {Dokl. Akad. Nauk SSSR},
Year = {1987},
Note = {In Russian},
Pages = {336--339},
Volume = {234},
Keywords = {Lorenz, attractor}
}
@Article{AGHks88,
author = {D. Armbruster and J. Guckenheimer and P. Holmes},
title = {Heteroclinic cycles and modulated travelling waves in systems with {O}(2) symmetry},
journal = {Physica D},
year = {1988},
volume = {29},
pages = {257--282},
doi = {10.1016/0167-2789(88)90032-2},
}
@Article{AGHks89,
author = {D. Armbruster and J. Guckenheimer and P. Holmes},
title = {{Kuramoto-Sivashinsky} dynamics on the center-unstable manifold},
journal = {SIAM J. Appl. Math.},
year = {1989},
volume = {49},
pages = {676--691},
doi = {10.1137/0149039},
}
@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{airPollution,
Title = {Fundamentals of Air Pollution},
Author = {Vallero, D.},
Publisher = {Academic Press},
Year = {2008},
Address = {New York},
Edition = {4\textsuperscript{th}}
}
@Article{AKcgl02,
author = {I. S. Aranson and L. Kramer},
title = {The world of the complex {Ginzburg-Landau} equation},
journal = {Rev. Mod. Phys.},
year = {2002},
volume = {74},
pages = {99--143},
doi = {10.1103/revmodphys.74.99},
}
@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 = {www.math.colostate.edu/emeriti/georg/homExtra.pdf}
}
@Article{AltTel08,
author = {Altmann, E. G. and T{\'e}l, 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{AmbWil08,
Title = {Computation of time-periodic solutions of the {Benjamin-Ono} equation},
Author = {Ambrose, D. M. and Wilkening, J.},
Journal = {J. Nonlinear Science},
Year = {2010},
Pages = {277--308},
Volume = {20},
DOI = {10.1007/s00332-009-9058-x}
}
@Article{AmbWil09,
Title = {Global paths of time-periodic solutions of the {Benjamin-Ono} equation connecting pairs of traveling waves},
Author = {Ambrose, D. M. and Wilkening, J.},
Journal = {Commun. App. Math. and Comp. Sci.},
Year = {2009},
Pages = {177--215},
Volume = {4},
DOI = {10.2140/camcos.2009.4.177}
}
@Article{AMdABH11,
Title = {The onset of turbulence in pipe flow},
Author = {Avila, K. and Moxey, D. and de Lozar, A. and Avila, M. and Barkley, D. and Hof, B.},
Journal = {Science},
Year = {2011},
Pages = {192--196},
Volume = {333},
DOI = {10.1126/science.1203223}
}
@Incollection{ampatt,
Title = {Amplitude equations for pattern forming systems},
Author = {M. van Hecke and P. C. Hohenberg and W. van Saarloos},
Booktitle = {Fundamental Problems in Statistical Mechanics},
Publisher = {North-Holland},
Year = {1994},
Address = {Amsterdam},
Editor = {H. van Beijeren and M. H. Ernst},
Volume = {VIII}
}
@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},
Number = {1},
Pages = {10007},
Volume = {90},
DOI = {10.1209/0295-5075/90/10007}
}
@Book{AnAr88,
title = {{Dynamical systems {I}: {Ordinary} Differential Equations and Smooth Dynamical Systems}},
publisher = {Springer},
year = {1988},
author = {D. V. Anosov and V. I. Arnol'd},
address = {New York},
}
@Article{AndCom07,
Title = {Relativistic fluid dynamics: {Physics} for many different scales},
Author = {N. Andersson and G. L. Comer},
Journal = {Living Rev. Relat.},
Year = {2007},
Volume = {10},
DOI = {10.12942/lrr-2007-1}
}
@Article{andereck86,
author = {C. D. Andereck and S. S. Liu and H. L. Swinney},
title = {Flow regimes in circular {Couette} system with independently rotating cylinders},
journal = {J. Fluid Mech.},
year = {1986},
volume = {164},
pages = {155},
doi = {10.1017/s0022112086002513},
}
@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{AnSo01,
author = {Antoulas, A. C. and Sorensen, D. C.},
title = {{Lyapunov}, {Lanczos}, and inertia},
journal = {Linear Algebra and its Applications},
year = {2001},
volume = {326},
pages = {137--150},
doi = {10.1016/s0024-3795(00)00288-3},
}
@Article{arnold91k,
author = {V. I. Arnold},
title = {Kolmogorov's hydrodynamic attractors},
journal = {Proc. R. Soc. Lond. A},
year = {1991},
volume = {434},
pages = {19--22},
abstract = {A review of Kolmogorov's efforts relating
the Navier-Stokes equation to the theory of dynamical system.
Several interesting questions regarding the connection are exposed.},
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}
}
@Article{ARS,
author = {U. M. Ascher and S. J. Ruuth and R. J. Spiteri},
title = {Implicit-explicit {R}unge-{K}utta methods for time-dependent partial differential equations},
journal = {Appl. Num. Math.},
year = {1997},
volume = {25},
pages = {151--167},
doi = {10.1016/s0168-9274(97)00056-1},
}
@Article{art03int,
author = {R. Artuso and P. Cvitanovi{\'c} and G. Tanner},
title = {Cycle expansions for intermittent maps},
journal = {Proc. Theo. Phys. Supp.},
year = {2003},
volume = {150},
pages = {1--21},
doi = {10.1143/ptps.150.1},
}
@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}
}
@Book{ArWe05,
Title = {Mathematical Methods for Physicists: A Comprehensive Guide},
Author = {G. B. Arfken and H. J. Weber},
Publisher = {Academic Press},
Year = {2005},
Address = {New York},
Edition = {6}
}
@Article{AS87,
Title = {A study of hairpin vortices in a laminar boundary layer},
Author = {M. S. Acarlar and C. R. Smith},
Journal = {J. Fluid Mech.},
Year = {1987},
Pages = {1--41, 45--83},
Volume = {175}
}
@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},
pages = {797--823},
doi = {10.1137/0732037},
}
@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{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{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{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},
}
@Incollection{autod89,
Title = {On Automatic Differentiation},
Author = {A. Griewank},
Booktitle = {Mathematical Programming: Recent Developments and Applications},
Publisher = {Kluwer},
Year = {1989},
Address = {Amsterdam},
Editor = {M. Iri and K. Tanabe},
Pages = {83--108}
}
@Article{ave99,
author = {V. M. Egu{\'\i}luz and P. Alstr{\o}m and E. Hern{\'a}ndez-Garc{\'\i}a and O. Piro},
title = {Average patterns of spatiotemporal chaos: {A} boundary effect},
journal = {Phys. Rev. E},
year = {1999},
volume = {59},
pages = {2822},
doi = {10.1103/physreve.59.2822},
}
@Article{AvHo2013,
Title = {Nature of laminar-turbulence intermittency in shear flows},
Author = {Avila, M. and Hof, B.},
Journal = {Phys. Rev. E},
Year = {2013},
Pages = {063012},
Volume = {87},
DOI = {10.1103/PhysRevE.87.063012},
Publisher = {APS}
}
@Article{avila2008,
author = {Avila, M. and Grimes, M. and Lopez, J. M. and Marques, F.},
title = {Global endwall effects on centrifugally stable flows},
journal = {Phys. Fluids},
year = {2008},
volume = {20},
number = {104104},
doi = {10.1063/1.2996326}
}
@Article{avila2012,
author = {Avila, M.},
title = {Stability and angular-momentum transport of fluid flows between corotating cylinders},
journal = {Phys. Rev. Lett.},
year = {2012},
volume = {108},
pages = {124501},
doi = {10.1103/PhysRevLett.108.124501}
}
@Article{AvMeRoHo13,
Title = {Streamwise-localized solutions at the onset of turbulence in pipe flow},
Author = {Avila, M. and Mellibovsky, F. and Roland, N. and Hof, B.},
Journal = {Phys. Rev. Lett.},
Year = {2013},
Pages = {224502},
Volume = {110},
DOI = {10.1103/PhysRevLett.110.224502}
}
@Article{AVWIHO10,
Title = {On the transient nature of localized pipe flow turbulence},
Author = {Avila, M. and Willis, A. P. and Hof, B.},
Journal = {J. Fluid Mech.},
Year = {2010},
Pages = {127--136},
Volume = {646},
DOI = {10.1017/S0022112009993296}
}
@Incollection{Axen11,
Title = {Non {Hamiltonian} chaos from {Nambu} dynamics of surfaces},
Author = {Axenides, M.},
Booktitle = {{Chaos Theory: Modeling, Simulation and Applications}},
Publisher = {World Scientific},
Year = {2011},
Editor = {Skiadas, C. H. and Dimotikalis, I. and Skiadas, C.},
ISBN = {9789814460477}
}
@Article{AxFl08,
Title = {{Nambu-Lie} 3-algebras on fuzzy 3\mbox{-}{m}anifolds},
Author = {Axenides, M. and Floratos, E.},
Journal = {JHEP},
Year = {2009},
Pages = {39},
Volume = {902},
DOI = {10.1088/1126-6708/2009/02/039}
}
@Article{AxFl09,
Title = {Strange attractors in dissipative {Nambu} mechanics: {Classical} and quantum aspects},
Author = {Axenides, M. and Floratos, E.},
Journal = {JHEP},
Year = {2010},
Pages = {036},
Volume = {1004},
DOI = {10.1007/JHEP04(2010)036}
}
@Article{AxFlNi09,
Title = {{Nambu} quantum mechanics on discrete 3-tori},
Author = {Axenides, M. and Floratos, E.G. and Nicolis, S.},
Journal = {J. Phys. A},
Year = {2009},
Pages = {275201},
Volume = {42},
DOI = {10.1088/1751-8113/42/27/275201}
}
@Article{B84,
Title = {The evolution of disturbances in shear flows at high {R}eynolds numbers},
Author = {D. J. Benney},
Journal = {Stud. Appl. Math.},
Year = {1984},
Pages = {1--19},
Volume = {70}
}
@Article{BabSap16,
Title = {A minimization principle for the description of modes associated with finite-time instabilities},
Author = {Babaee, H. and Sapsis, T. P.},
Journal = {Proc. R. Soc. Lond. A},
Year = {2016},
Pages = {20150779},
Volume = {472},
DOI = {10.1098/rspa.2015.0779}
}
@Article{Bagheri13,
Title = {Koopman-mode decomposition of the cylinder wake},
Author = {Bagheri, S.},
Journal = {J. Fluid Mech.},
Year = {2013},
Pages = {596--623},
Volume = {726},
DOI = {10.1017/jfm.2013.249}
}
@Misc{BaGuGr16,
author = {Barnett, J. and Gurevich, D. R. and Grigoriev, R. O.},
title = {Streamwise localization of traveling wave solutions in channel flow},
year = {2017},
doi = {10.1103/physreve.95.033124},
journal = {Phys. Rev. E},
pages = {033124},
volume = {95},
}
@Article{Bandelow1998,
author = {U. Bandelow, 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},
}
@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{BarChor98,
Title = {New Perspectives in Turbulence: Scaling Laws, Asymptotics, and Intermittency},
Author = {G. I. Barenblatt and A. J. Chorin},
Journal = {SIAM Review},
Year = {1998},
Pages = {265--291},
Volume = {40}
}
@Article{BARK11,
Title = {Simplifying the complexity of pipe flow},
Author = {Barkley, D.},
Journal = {Phys. Rev. E.},
Year = {2011},
Pages = {016309},
Volume = {84},
DOI = {10.1103/PhysRevE.84.016309}
}
@Article{Barkley05,
author = {Barkley, D. and Tuckerman, L. S.},
title = {Computational study of turbulent laminar patterns in {Couette} flow},
journal = {Phys. Rev. Lett.},
year = {2005},
volume = {94},
pages = {014502},
addendum = {\arXiv{physics/0403142}},
doi = {10.1103/physrevlett.94.014502},
}
@Article{Barkley99,
author = {Barkley, D. and {Tuckerman}, L. S.},
title = {Stability analysis of perturbed plane {Couette} flow},
journal = {Phys. Fluids},
year = {1999},
volume = {11},
pages = {1187--1195},
addendum = {\arXiv{physics/0312048}},
doi = {10.1063/1.869987},
}
@Article{BarTuck07,
Title = {Mean flow of turbulent-laminar patterns in plane {Couette} flow},
Author = {D. Barkley and L. S. Tuckerman},
Journal = {J. Fluid Mech.},
Year = {2007},
Pages = {109--138},
Volume = {576},
DOI = {10.1017/S002211200600454X}
}
@Article{Batch46,
Title = {Double velocity correlation function in turbulent motion},
Author = {Batchelor, G. K.},
Journal = {Nature},
Year = {1946},
Pages = {883--884},
Volume = {158}
}
@Book{baumgarten2006mixture,
Title = {Mixture Formation in Internal Combustion Engines},
Author = {Baumgarten, C.},
Publisher = {Springer},
Year = {2006},
Address = {New York}
}
@InProceedings{BayOrt04,
Title = {Lie algebra template tracking},
Author = {E. Bayro-Corrochano and J. Ortegon-Aguilar},
Booktitle = {International Conference on Pattern Recognition},
Year = {2004},
Pages = {56--59},
Volume = {2},
DOI = {10.1109/ICPR.2004.1334036}
}
@Article{BaZeVanH11,
Title = {Time-periodic solitons in a damped-driven nonlinear Schr\"odinger equation},
Author = {Barashenkov, I. V. and Zemlyanaya, E. V. and van Heerden, T. C.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {056609},
Volume = {83},
DOI = {10.1103/PhysRevE.83.056609}
}
@Article{BBJ85,
author = {Bak, P. and Bohr, T. and Jensen, M. H.},
title = {Mode-locking and the transition to chaos in dissipative systems},
journal = {Phys. Scr.},
year = {1985},
volume = {T9},
pages = {50--58},
doi = {10.1088/0031-8949/1985/t9/007},
}
@Article{BC89,
Title = {A mean flow first harmonic theory for hydrodynamic instabilities},
Author = {D. J. Benney and K. A. Chow},
Journal = {Stud. Appl. Math.},
Year = {1989},
Pages = {37--73},
Volume = {80}
}
@Inbook{BC96,
Title = {Waves and Nonlinear Processes in Hydrodynamics},
Author = {F. H. Busse and R. M. Clever},
Chapter = {Bifurcation sequences in problems of thermal convection and of plane {Couette} flow},
Pages = {209--226},
Publisher = {Springer},
Year = {1996},
Address = {New York}
}
@InProceedings{BC96a,
Title = {Bifurcation sequences in fluid flows and coherent structures in the turbulent state},
Author = {Busse, F. H. and Clever, R. M.},
Booktitle = {Advances in Turbulence VI},
Year = {1996},
Editor = {Gavrilakis, S. and Machiels, L. and Monkewitz, P. A.},
Pages = {309--312},
Series = {Proceedings of the Sixth European Turbulence Conference}
}
@Article{BC98,
Title = {Statistical analysis of the transition to turbulence in plane {Couette} flow},
Author = {Bottin, S. and Chat{\'e}, H.},
Journal = {Eur. Phys. J. B},
Year = {1998},
Pages = {143--155},
Volume = {6},
DOI = {10.1007/s100510050536}
}
@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},
DOI = {10.1103/PhysRevLett.101.260603}
}
@Article{BDMD98,
Title = {Discontinuous transition to spatiotemporal intermittency in plane {Couette} flow},
Author = {S. Bottin and F. Daviaud and P. Manneville and O. Dauchot},
Journal = {Europhys. Lett.},
Year = {1998},
Pages = {171--176},
Volume = {43},
DOI = {10.1140/epje/i2014-14034-1}
}
@Incollection{BDMD98a,
Title = {Discontinuous Transition to Spatio-Temporal Intermittency in the Plane {Couette} Flow},
Author = {Bottin, S. and Daviaud, F. and Manneville, P. and Dauchot, O.},
Booktitle = {Advances in Turbulence VII},
Publisher = {Springer},
Year = {1998},
Editor = {Frisch, U.},
Pages = {117--120},
DOI = {10.1007/978-94-011-5118-4_28},
ISBN = {978-94-010-6151-3}
}
@Article{BDS98,
author = {Briggs, K. M. and Dixon, T. W. and Szekeres, G.},
title = {Analytic solutions of the {Cvitanovi{\'c}-Feigenbaum} and {Feigenbaum-Kadanoff-Shenker} equations},
journal = {Int. J. Bif. Chaos},
year = {1998},
volume = {8},
pages = {347--357},
}
@Article{beck2009,
Title = {Snakes, ladders, and isolas of localized patterns},
Author = {Beck, M. and Knobloch, J. and Lloyd, D. J. B. and Sandstede, B. and Wagenknecht, T.},
Journal = {SIAM J. Math. Anal.},
Year = {2009},
Number = {3},
Pages = {936--972},
Volume = {41},
DOI = {10.1137/080713306},
Publisher = {SIAM}
}
@Article{bene80a,
author = {Benettin, G. and Galgani, L. and Giorgilli, A. and Strelcyn, J.M.},
title = {{Lyapunov} characteristic exponents for smooth dynamical systems; a method for computing all of them. {Part 1: Theory}},
journal = {Meccanica},
year = {1980},
volume = {15},
pages = {9--20},
doi = {10.1007/BF02128236},
}
@Article{bene80b,
author = {Benettin, G. and Galgani, L. and Giogilli, A. and Strelcyn, J.M.},
title = {{Lyapunov} characteristic exponents for smooth dynamical systems; a method for computing all of them. {Part 2: Numerical} application},
journal = {Meccanica},
year = {1980},
volume = {15},
pages = {21--30},
doi = {10.1007/BF02128237},
}
@Article{benjamin98-1,
author = {T. B. Benjamin},
title = {Bifurcation phenomena in steady flows of a viscous fluid. {I. Theory}},
journal = {Proc. R. Soc. Lond. A},
year = {1978},
volume = {359},
pages = {1--26},
doi = {10.1098/rspa.1978.0028}
}
@Article{benjamin98-2,
author = {Benjamin, T. B.},
title = {Bifurcation phenomena in steady flows of a viscous fluid. {II. Experiments}},
journal = {Proc. R. Soc. Lond. A},
year = {1978},
volume = {359},
pages = {27--43},
doi = {10.1098/rspa.1978.0030},
eprint = {http://rspa.royalsocietypublishing.org/content/359/1696/27.full.pdf},
issn = {0080-4630},
publisher = {The Royal Society}
}
@Article{benks66,
Title = {Long waves in liquid films},
Author = {D. J. Benney},
Journal = {J. Math. Phys},
Year = {1966},
Pages = {150--155},
Volume = {45}
}
@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},
DOI = {10.1007/978-3-319-01300-8_3},
Editors = {Dieci, L. and Guglielmi, N.}
}
@Article{Berkooz93,
author = {G. Berkooz and P. Holmes and J. L. Lumley},
title = {The proper orthogonal decomposition in the analysis of turbulent flows.},
journal = {Ann. Rev. Fluid Mech.},
year = {1993},
volume = {25},
pages = {539--575},
doi = {10.1146/annurev.fl.25.010193.002543}
}
@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{BerlinPF94,
author = {S. Berlin and A. Lundbladh and D. Henningson},
title = {Spatial simulations of oblique transition in a boundary layer},
journal = {Phys. Fluids},
year = {1994},
volume = {6},
number = {6},
pages = {1949--1951},
month = jun,
doi = {10.1063/1.868200},
}
@Article{Berry84,
author = {Berry, M. V.},
title = {Quantal phase factors accompanying adiabatic changes},
journal = {Proc. R. Soc. Lond. A},
year = {1984},
volume = {392},
pages = {45--57},
doi = {10.1142/9789813221215_0006},
}
@Article{BeSeTh2008,
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,
author = {W.-J. Beyn and V. Th\"ummler},
title = {Freezing solutions of equivariant evolution equations},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2004},
volume = {3},
pages = {85--116},
doi = {10.1137/030600515},
}
@Article{BG81,
Title = {A new mechanism for linear and nonlinear hydrodynamic instability},
Author = {D. J. Benney and L. H. Gustavsson},
Journal = {Stud. Appl. Math.},
Year = {1981},
Pages = {185--209},
Volume = {64}
}
@Article{BGMWW92,
author = {A. Back and J. Guckenheimer and M. R. Myers and F. J. Wicklin and P. A. Worfolk},
title = {DsTool: {Computer} assisted exploration of dynamical systems},
journal = {Notices Amer. Math. Soc.},
year = {1992},
volume = {39},
pages = {303--309},
}
@Book{BH86,
Title = {Asymptotic Expansions of Integrals},
Author = {N. Bleistein and R. A. Handelsman},
Publisher = {Dover},
Year = {1986},
Address = {New York}
}
@Article{biham90c,
author = {O. Biham and W. Wenzel},
title = {Unstable periodic orbits and the symbolic dynamics of the complex {H\'e}non map},
journal = {Phys. Rev. E},
year = {1990},
volume = {42},
pages = {4639},
doi = {10.1103/physreva.42.4639},
abstract = {Previous work is extended to the complex plane so that
2^n complex orbits are found for symbol sequences of length n.},
}
@Article{Birkhoff,
author = {G. D. Birkhoff},
title = {Recent advances in dynamics},
journal = {Science},
year = {1920},
volume = {51},
pages = {51--55},
doi = {10.1126/science.51.1307.51},
}
@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},
ISSN = {0893-9659}
}
@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{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 = {110A}
}
@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},
Volume = {51}
}
@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}
}
@Article{BKRS96,
Title = {Sharp determinants and kneading operators for holomorphic maps},
Author = {Baladi, V. and Kitaev a. and Ruelle, D. and Semmes, S.},
Journal = {Proc. Steklov. Inst. of Math.},
Year = {1997},
Pages = {186--228},
Volume = {216}
}
@Book{bl,
title = {{Introduction to Numerical Analysis}},
publisher = {Springer},
year = {1983},
author = {J. Stoer and R. Bulirsch},
address = {New York}
}
@Article{blackwelder76,
author = {Blackwelder, R. F. and Kaplan, R.},
title = {On the wall structure of the turbulent boundary layer},
journal = {J. Fluid Mech.},
year = {1976},
volume = {76},
pages = {89},
doi = {10.1017/s0022112076003145},
}
@Article{blackwelder87,
author = {Swearingen, J. D. and Blackwelder, R. F.},
title = {The growth and breakdown of streamwise vortices in the presence of a wall},
journal = {J. Fluid Mech.},
year = {1987},
volume = {182},
pages = {255},
doi = {10.1017/s0022112087002337},
}
@Article{BlHaSh13,
Title = {Lower branch equilibria in {Couette} flow: the emergence of canonical states for arbitrary shear flows},
Author = {H. M. Blackburn and P. Hall and S. J. Sherwin},
Journal = {J. Fluid Mech.},
Year = {2013},
Pages = {R2},
Volume = {726},
DOI = {10.1017/jfm.2013.254}
}
@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{BLZ08,
author = {P. Bates and K. Lu, and C. Zeng},
title = {Approximately invariant manifolds and global dynamics of spike states},
journal = {Invent. Math.},
year = {2008},
volume = {55},
pages = {355--433}
}
@Article{BMS71,
author = {N. H. Baker and D. W. Moore and E. A. Spiegel},
title = {Aperiodic behavior of a non-linear oscillator},
journal = {Quatr. J. Mech. and Appl. Math.},
year = {1971},
volume = {24},
pages = {391},
doi = {10.1093/qjmam/24.4.391},
}
@Inproceedings{BodEck11,
author = {E. Bodenschatz and M. Eckert},
title = {Prandtl and the {G\"ottingen School}},
booktitle = {Highlights in the History of Turbulence},
year = {2011},
editor = {P. A. Davidson and Y. Kaneda and H. K. Moffatt and K. R. Sreenivasan},
publisher = {Springer},
addr = {Berlin},
doi = {10.1017/cbo9781139018241.003},
}
@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},
}
@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{borrero10,
author = {D. Borrero-Echeverry and M. F. Schatz and R. Tagg},
title = {Transient turbulence in {Taylor-Couette} flow},
journal = {Phys. Rev. E},
year = {2010},
volume = {81},
pages = {025301},
doi = {10.1103/physreve.81.025301},
}
@PhdThesis{borrero2014,
author = {D. Borrero-Echeverry},
title = {The subcritical transition to turbulence in {Taylor-Couette} flow},
school = {Georgia Institute of Technology},
year = {2014}
}
@Article{Bottin98,
Title = {Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane {Couette} flow},
Author = {Bottin, S. and {Dauchot}, O. and {Daviaud}, F. and {Manneville}, P.},
Journal = {Phys. Fluids},
Year = {1998},
Pages = {2597--2607},
Volume = {10},
DOI = {10.1063/1.869773}
}
@Unpublished{Bouch03,
Title = {The nonlinear {Schr\"odinger} equation},
Author = {E. Bouchbinder},
Note = {Unpublished notes},
Year = {2003},
URL = {http://ChaosBook.org/library/Bouch03.pdf}
}
@Book{bowen,
title = {{Equilibrium States and the Ergodic Theory of {Anosov} Diffeomorphisms}},
publisher = {Springer},
year = {1975},
author = {R. Bowen},
address = {Berlin}
}
@Article{Bowen72,
author = {R. Bowen},
title = {Periodic orbits for hyperbolic flows},
journal = {Amer. J. Math.},
year = {1972},
volume = {94},
pages = {1--30},
doi = {10.2307/2373590},
}
@Article{Bowen73,
author = {R. Bowen},
title = {Symbolic dynamics for hyperbolic flows},
journal = {Amer. J. Math.},
year = {1973},
volume = {95},
pages = {429--460},
doi = {10.2307/2373793},
}
@Book{BoydiP06,
title = {{Elementary Differential Equations and Boundary Value Problems}},
publisher = {Wiley},
year = {2006},
author = {W. E. Boyce and R. C. DiPrima},
address = {New York},
doi = {10.2307/2321040},
}
@Article{BQT91,
author = {K. M. Briggs and G. R. W. Quispel and C. J. Thompson},
title = {Feigenvalues for {Mandelsets}},
journal = {J. Phys. A},
year = {1991},
volume = {24},
pages = {3363--3368},
doi = {10.1088/0305-4470/24/14/023}
}
@Article{BR96,
Title = {Sharp determinants},
Author = {Baladi, V. and Ruelle, D.},
Journal = {Invent. Math.},
Year = {1996},
Pages = {553--574},
Volume = {123},
DOI = {10.1007/s002220050040}
}
@Article{BraGib14,
author = {E. Brand and J.{~}F. Gibson},
title = {A doubly localized equilibrium solution of plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {2014},
volume = {750},
pages = {R3},
doi = {10.1017/jfm.2014.285}
}
@Incollection{brand03,
Title = {Computational aspects of astrophysical {MHD} and turbulence},
Author = {A. Brandenburg},
Booktitle = {Advances in Nonlinear Dynamos},
Publisher = {Taylor \& Francis},
Year = {2003},
Address = {London},
Editor = {A. Ferriz-Mas and M. N\'u\~nez},
Note = {\arXiv{astro-ph/0109497}},
Pages = {269--344}
}
@Misc{Bridges_priv,
Author = {T. J. Bridges},
Note = {private communication}
}
@Article{Bridges08,
Title = {Degenerate relative equilibria, curvature of the momentum map,and homoclinic bifurcation},
Author = {T. J. Bridges},
Journal = {J. Diff. Eqn.},
Year = {2008},
Pages = {1629--1674},
Volume = {244},
Abstract = {A fundamental class of solutions of symmetric Hamiltonian systems
is relative equilibria. In this paper the nonlinear problem near
a degenerate relative equilibrium is considered. The degeneracy creates
a saddle-center and attendant homoclinic bifurcation in the reduced
system transverse to the group orbit. The surprising result is that
the curvature of the pullback of the momentum map to the Lie algebra
determines the normal form for the homoclinic bifurcation. There
is also an induced directional geometric phase in the homoclinic
bifurcation. The backbone of the analysis is the use of singularity
theory for smooth mappings between manifolds applied to the pullback
of the momentum map. The theory is constructive and generalities
are given for symmetric Hamiltonian systems on a vector space of
dimension (2n+2) with an n-dimensional abelian symmetry group. Examples
for n=1,2,3 are presented to illustrate application of the theory.}
}
@Article{Briggs91,
author = {Briggs, K.},
title = {A precise calculation of the {Feigenbaum} constants},
journal = {Math. Computation},
year = {1991},
volume = {57},
pages = {435--439},
doi = {10.2307/2938684},
}
@InProceedings{BrKevr96,
author = {Brown, H. S. and Kevrekidis, I. G.},
title = {Modulated traveling waves for the {Kuramoto-Sivashinsky} equation},
booktitle = {Pattern Formation: Symmetry Methods and Applications},
year = {1996},
editor = {D. Benest and C. Froeschl\'{e}},
volume = {5},
series = {Fields Inst. Commun.},
pages = {45--66},
address = {Providence, RI},
publisher = {AMS},
doi = {10.1090/fic/005/03},
}
@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},
doi = {10.1063/1.870465},
}
@Article{broer97,
author = {H. W. Broer and H. M. Osinga and G. Vegter},
title = {Algorithms for computing {N}ormally {H}yperbolic {I}nvariant {M}anifolds},
journal = {Z. Angew. Math. Phys.},
year = {1997},
volume = {48},
pages = {480},
doi = {10.1007/s000330050044},
}
@Article{bronski2005,
author = {J. C. Bronski and T. N. Gambill},
title = {Uncertainty estimates and {$L_2$} bounds for the {Kuramoto-Sivashinsky} equation},
journal = {Nonlinearity},
year = {2006},
volume = {19},
pages = {2023--2039},
note = {\arXiv{math/0508481}},
doi = {10.1088/0951-7715/19/9/002},
}
@Article{BSMLAH15,
Title = {The rise of fully turbulent flow},
Author = {Barkley, D. and Song, B. and Mukund, V. and Lemoult, G. and Avila, M. and Hof, B.},
Journal = {Nature},
Year = {2015},
Pages = {550--553},
Volume = {526},
DOI = {10.1038/nature15701}
}
@Article{BTAA95,
Title = {An investigation of turbulent plane {Couette} flow at low {R}eynolds numbers},
Author = {K. H. Bech and N. Tillmark and P. H. Alfredsson and H. I. Andersson},
Journal = {J. Fluid Mech.},
Year = {1995},
Pages = {291--325},
Volume = {286}
}
@Article{BTBmaw03,
author = {L. Brusch and A. Torcini and M. B{\"a}r},
title = {Nonlinear analysis of the {E}ckhaus 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,
author = {L. Brusch and A. Torcini and M. van Hecke and M. G. Zimmermann and M. B{\"a}r},
title = {Modulated amplitude waves and defect formation in the one-dimensional complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {2001},
volume = {160},
pages = {127--148},
doi = {10.1016/s0167-2789(01)00355-4},
}
@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},
Note = {\arXiv{1411.3303}},
Pages = {073112},
Volume = {25},
DOI = {10.1063/1.4923742}
}
@Unpublished{Bud15,
Title = {Invariant measurement of torsion within eigenframes of periodic orbits},
Author = {Budanur, N. B.},
Note = {In preparation},
Year = {2015}
}
@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},
Addendum = {\arXiv{1405.1096}},
Pages = {084102},
Volume = {114},
DOI = {10.1103/PhysRevLett.114.084102}
}
@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 = {2017},
volume = {167},
pages = {636--655},
doi = {10.1007/s10955-016-1672-z},
}
@Article{BudHof17,
author = {N. B. Budanur and B. Hof},
title = {Heteroclinic path to spatially localized chaos in pipe flow},
journal = {J. Fluid Mech.},
year = {2017},
volume = {827},
doi = {10.1017/jfm.2017.516},
}
@Article{BudMez12,
Title = {Geometry of the ergodic quotient reveals coherent structures in flows},
Author = {M. Budi\v{s}i\'c and I. Mezi\'c},
Journal = {Physica D},
Year = {2012},
Note = {\arXiv{1204.2050}},
Pages = {1255--1269},
Volume = {241},
Abstract = {The
method we present in this paper uses trajectory averages of scalar
functions on the state space to: (a) identify invariant sets in the state
space, and (b) to form coherent structures by aggregating invariant sets
that are similar across multiple spatial scales. First, we construct the
ergodic quotient, the object obtained by mapping trajectories to the
space of the trajectory averages of a function basis on the state space.
Second, we endow the ergodic quotient with a metric structure that
successfully captures how similar the invariant sets are in the state
space. Finally, we parametrize the ergodic quotient using intrinsic
diffusion modes on it. By segmenting the ergodic quotient based on the
diffusion modes, we extract coherent features in the state space of the
dynamical system. The algorithm is validated by analyzing the
Arnold-Beltrami-Childress flow, which was the test-bed for
alternative approaches: the Ulam's approximation of the transfer
operator and the computation of Lagrangian Coherent Structures.
Furthermore, we explain how the method extends the Poincar\'e map analysis
for periodic flows. As a demonstration, we apply the method to a
periodically-driven three-dimensional Hill's vortex flow, discovering
unknown coherent structures in its state space.},
DOI = {10.1016/j.physd.2012.04.006}
}
@Article{BuMoMe12,
Title = {{Applied Koopmanism}},
Author = {Budi{\v s}i{\'c}, M. and Mohr, R. M. and Mezi{\'c}, I.},
Journal = {Chaos},
Year = {2012},
Note = {\arXiv{1206.3164}},
Pages = {047510},
Volume = {22},
DOI = {10.1063/1.4772195},
Numpages = {33}
}
@Article{burke2009,
author = {Burke, J. and Houghton, S. M. and Knobloch, E.},
title = {{Swift-Hohenberg} equation with broken reflection symmetry},
journal = {Phys. Rev. E},
year = {2009},
volume = {80},
pages = {036202},
doi = {10.1103/PhysRevE.80.036202}
}
@Article{BurKno06,
Title = {Localized states in the generalized {Swift-Hohenberg} equation},
Author = {Burke, J. and Knobloch, E.},
Journal = {Phys. Rev. E},
Year = {2006},
Pages = {056211},
Volume = {73},
DOI = {10.1103/PhysRevE.73.056211}
}
@Article{BurKno07,
Title = {Homoclinic snaking: structure and stability},
Author = {Burke, J. and Knobloch, E.},
Journal = {Chaos},
Year = {2007},
Pages = {037102},
Volume = {17},
DOI = {10.1063/1.2746816}
}
@Article{Busse04,
Title = {Visualizing the dynamics of the onset of turbulence},
Author = {F. H. Busse},
Journal = {Science},
Year = {2004},
Pages = {1574--1575},
Volume = {305}
}
@Unpublished{ByMaGr14,
Title = {Unstable and marginally stable solutions of reaction diffusion systems with weakly broken continuous symmetries},
Author = {G. Byrne, C. Marcotte and R. O. Grigoriev},
Note = {To be submitted},
Year = {2014}
}
@InProceedings{ByMaGr14a,
author = {G. Byrne and C. D. Marcotte and R. O. Grigoriev},
title = {Exact coherent structures and dynamics of cardiac tissue},
booktitle = {{Proc. of 8\textsuperscript{th} Conference of the European Study Group on Cardiovascular Oscillations, Trento, Italy}},
year = {2014},
publisher = {IEEE},
doi = {10.1109/esgco.2014.6847523},
}
@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},
abstract = {MAWs of various periods P occur in phase chaotic states.
The pair of MAWs cease to exist via a saddle-node bifurcation. For
periods beyond this bifurcation, incoherent near-MAW evolve toward
defects.},
doi = {10.1103/physrevlett.85.86},
}
@Article{C02,
author = {S. J. Chapman},
title = {Subcritical transition in channel flows},
journal = {J. Fluid Mech.},
year = {2002},
volume = {451},
pages = {35--97},
doi = {10.1017/s0022112001006255},
}
@Misc{C77,
Title = {Classical and exceptional {Lie} algebras as invariance algebras},
Author = {P. Cvitanovi\'c},
Note = {({Oxford University} preprint 40/77, unpublished)},
Year = {1977},
URL = {www.nbi.dk/GroupTheory}
}
@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},
Keywords = {VELOCITY; TENSORS; ANALYTICAL SOLUTION; PRESSURE GRADIENTS; STRAIN RATE; TURBULENT FLOW; REYNOLDS NUMBER; NAVIERSTOKES EQUATIONS; KINETIC ENERGY; INCOMPRESSIBLE FLOW; NUMERICAL SOLUTION; ISOTROPY; INITIAL CONDITIONS}
}
@Book{Canuto2006,
Title = {Spectral Methods: Fundamentals in Single Domains},
Author = {C. Canuto and M. Y. Hussaini and A. Quarteroni and T. A. Zang},
Publisher = {Springer},
Year = {2006},
Address = {New York}
}
@Book{Canuto2007,
Title = {Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics},
Author = {C. Canuto and M. Y. Hussaini and A. Quarteroni and T. A. Zang},
Publisher = {Springer},
Year = {2007},
Address = {New York}
}
@Book{Canuto88,
Title = {Spectral Methods in Fluid Dynamics},
Author = {C. Canuto and M. Y. Hussaini and A. Quarteroni and T. A. Zang},
Publisher = {Springer},
Year = {1988},
Address = {New York}
}
@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{CarCha04,
Title = {Covariant analysis of {Newtonian} multi-fluid models for neutron stars {I: Milne-Cartan} structure and variational formulation},
Author = {Carter, B. and Chamel, N.},
Journal = {Int. J. Mod. Phys. D},
Year = {2004},
Note = {\arXiv{astro-ph/0305186}},
Pages = {291--325},
Volume = {13},
DOI = {10.1142/S0218271804004542}
}
@Article{carl97int,
author = {C. P. Dettmann and P. Cvitanovi{\'c}},
title = {Cycle expansions for intermittent diffusion},
journal = {Phys. Rev. E},
year = {1997},
volume = {56},
pages = {6687},
doi = {10.1103/physreve.56.6687},
}
@Article{CarlSchn62,
author = {D. Carlson and H. Schneider},
title = {Inertia theorems for matrices: the semi-definite case},
journal = {Bull. Amer. Math. Soc.},
year = {1962},
volume = {68},
pages = {479--484},
doi = {10.1090/s0002-9904-1962-10784-8},
publisher = {American Mathematical Society ({AMS})},
}
@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}
}
@Article{CB92,
Title = {Three-dimensional convection in a horizontal layer subjected to constant shear},
Author = {Clever, R. M. and {Busse}, F. H.},
Journal = {J. Fluid Mech.},
Year = {1992},
Pages = {511--527},
Volume = {234}
}
@Article{CB97,
author = {Clever, R. M. and Busse, F. H.},
title = {Tertiary and quaternary solutions for plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1997},
volume = {344},
pages = {137--153},
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.},
doi = {10.1017/s0022112097005818},
}
@Incollection{CBconverg,
author = {R. Artuso and H. H. Rugh and P. Cvitanovi{\'c}},
title = {Why does it work?},
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#converg},
}
@Incollection{CBook:appendApplic,
author = {P. Cvitanovi{\'c} and G. Vattay},
title = {Appendix: {Transport of vector fields}},
booktitle = {{Chaos: Classical and Quantum}},
publisher = {Niels Bohr Inst.},
year = {2011},
editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay},
address = {Copenhagen},
url = {http://ChaosBook.org/paper.shtml#appendApplic},
}
@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},
}
@Article{CCKFNRS12,
Title = {Neural population dynamics during reaching},
Author = {Churchland, M. M. and Cunningham, J. P. and Kaufman, M. T. and Foster, J. D. and Nuyujukian, P. and Ryu, S. I. and Shenoy, K. V.},
Journal = {Nature},
Year = {2012},
Pages = {51--56},
Volume = {487},
DOI = {10.1038/nature11129}
}
@Article{CCW05,
Title = {A new property of a class of {J}acobi polynomials},
Author = {G. Csordas and M. Charalambides and F. Waleffe},
Journal = {Proc. Amer. Math. Soc.},
Year = {2005},
Pages = {3551--3560},
Volume = {133}
}
@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{CE91,
author = {P. Cvitanovi{\'c} and B. Eckhardt},
title = {Periodic orbit expansions for classical smooth flows},
journal = {J. Phys. A},
year = {1991},
volume = {24},
pages = {L237},
doi = {10.1088/0305-4470/24/5/005},
}
@Article{CE95,
Title = {Spatially localized two-dimensional finite-amplitude states in plane {Couette} flow},
Author = {A. Cherhabili and U. Ehrenstein},
Journal = {Eur. J. Mech. B Fluids},
Year = {1995},
Pages = {677--696},
Volume = {14},
URL = {http://cat.inist.fr/?aModele=afficheN&cpsidt=2903887}
}
@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},
abstract = {Proved the analyticity of the solution of the KSe on a
periodic interval near the real axis and the width of the region is
estimated. Numerical calculations show that this width should not
depend on the size of the interval.},
doi = {10.1016/0167-2789(93)90168-z},
}
@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},
}
@Book{cellwolf,
Title = {Cellular Automata and Complexity},
Author = {S. Wolfram},
Publisher = {Addison-Wesley},
Year = {1994},
Address = {Reading, MA}
}
@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{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{cgole92,
author = {C. Gol{\'e}},
title = {A new proof of the {Aubry-Mather}'s theorem},
journal = {Math. Z.},
year = {1992},
volume = {210},
pages = {441--448},
doi = {10.1007/bf02571806},
}
@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}
}
@Article{ChaKer12,
Title = {Invariant recurrent solutions embedded in a turbulent two-dimensional {Kolmogorov} flow},
Author = {Chandler, G. J. and Kerswell, R. R.},
Journal = {J. Fluid M.},
Year = {2013},
Note = {\arXiv{1207.4682}},
Pages = {554--595},
Volume = {722},
DOI = {10.1017/jfm.2013.122}
}
@Article{champneys2008,
author = {Champneys, A. R. and Kirk, V. and Knobloch, E. and Oldeman, B. E. and Rademacher, J. D. M.},
title = {Unfolding a tangent equilibrium-to-periodic heteroclinic cycle},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2008},
volume = {8},
pages = {1261--1304},
doi = {10.1137/080734923}
}
@Article{Champneys98,
Title = {Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics},
Author = {Champneys, A. R.},
Journal = {Physica D},
Year = {1998},
Pages = {158--186},
Volume = {112},
DOI = {10.1016/S0167-2789(97)00209-1}
}
@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},
abstract = {Use wavelets to extract local frequencies and use the
major frequencies to identify the characteristics of phase space
motion.},
doi = {10.1016/s0167-2789(03)00117-9},
}
@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}
}
@TechReport{channelflow,
author = {J. F. Gibson},
title = {{Channelflow}: {A} spectral {Navier-Stokes} simulator in {C}++},
institution = {U. New Hampshire},
year = {2017},
note = {{\tt {Channelflow.org}}},
publisher = {J. F. Gibson},
url = {http://Channelflow.org},
}
@Misc{channelflowDat,
Title = {Database of invariant solutions of plane {Couette} flow},
Author = {J. F. Gibson},
Note = {{\tt {Channelflow.org/database}}},
Year = {2013},
Institution = {U. New Hampshire},
Publisher = {J. F. Gibson}
}
@Article{CHASCH14,
author = {Chantry, M. and Schneider, T. M.},
title = {Studying edge geometry in transiently turbulent shear flows},
journal = {J. Fluid Mech.},
year = {2014},
volume = {747},
pages = {506--517},
doi = {10.1017/jfm.2014.150},
}
@Article{chate94,
author = {H. Chat{\'e}},
title = {Spatiotemporal intermittency regimes of the one-dimensional complex {Ginzburg-Landau} equation},
journal = {Nonlinearity},
year = {1994},
volume = {7},
pages = {185--204},
abstract = {In the Benjamin-Feir stable region, spatiotemporal
intermittency regimes are identified which consists of patches of
linearly stale stable plane waves separated by localized objects with
a well defined dynamics. In the transition reginon, asymptotic states
with an irregular, frozen spatial structure are shown to occur. The
bistable region beyond the Benjamin-Feir stable region is of the same
spatiotemporal intermittency type with phase turbulence as the },
doi = {10.1088/0951-7715/7/1/007},
}
@Article{ChaWri81,
Title = {Transitions and distribution functions for chaotic systems},
Author = {Chang, S.-J. and Wright, J.},
Journal = {Phys. Rev. A},
Year = {1981},
Pages = {1419--1433},
Volume = {23},
DOI = {10.1103/PhysRevA.23.1419}
}
@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},
note = {\arXiv{chao-dyn/9905027}},
doi = {10.1063/1.870101},
}
@Article{cherh00,
Title = {Nonlinear equilibrium states in plane {Couette} flow: Continuation from {P}oiseuille flow to {Couette} flow},
Author = {A. Cherhabili},
Journal = {Notes in Numerical Fluid Mechanics},
Year = {2000},
Pages = {69--80},
Volume = {74},
ISSN = {0179-9614}
}
@Article{cherh96,
Title = {Existence and stability of finite-amplitude states in plane {Couette} flow},
Author = {A. Cherhabili and U. Ehrenstein},
Journal = {Fluid Mechanics and its Applications},
Year = {1996},
Pages = {317--320},
Volume = {36},
DOI = {10.1007/978-94-009-0297-8_89}
}
@Article{Cherh97,
author = {Cherhabili, A. and {Ehrenstein}, U.},
title = {Finite-amplitude equilibrium states in plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1997},
volume = {342},
pages = {159--177},
doi = {10.1017/s0022112097005661},
}
@Article{CheSu90,
author = {Cheng, C. Q. and Sun, Y. S.},
title = {Existence of invariant tori in three-dimensional measure-preserving mappings},
journal = {Celestial Mech. Dynam. Astronom.},
year = {1990},
volume = {47},
pages = {275--92},
doi = {10.1007/bf00053456},
}
@Article{chfield,
author = {P. Cvitanovi{\'c}},
title = {Chaotic field theory: {A} sketch},
journal = {Physica A},
year = {2000},
volume = {288},
pages = {61},
note = {\arXiv{nlin.CD/0001034}},
doi = {10.1016/s0378-4371(00)00415-5},
}
@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. Math. Phys.},
year = {1998},
volume = {39},
pages = {3138--3157},
}
@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{choi94,
author = {H. Choi and P. Moin and J. Kim},
title = {Active turbulence control for drag reduction in wall-bounded flows},
journal = {J. Fluid Mech.},
year = {1994},
volume = {262},
pages = {75},
doi = {10.1017/s0022112094000431},
}
@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},
}
@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{ChriPol96,
author = {F. Christiansen and A. Politi},
title = {Symbolic encoding in symplectic maps},
journal = {Nonlinearity},
year = {1996},
volume = {9},
pages = {1623--1640},
doi = {10.1088/0951-7715/9/6/014},
}
@Article{ChriPol97,
author = {F. Christiansen and A. Politi},
title = {Guidelines for the construction 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{Christiansen97,
Title = {Hopf's last hope: {Spatiotempora}l 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{ChrPol95,
author = {F. Christiansen and A. Politi},
title = {A generating partition for the standard map},
journal = {Phys. Rev. E},
year = {1995},
volume = {51},
pages = {3811},
note = {\arXiv{chao-dyn/9411005}},
doi = {10.1103/physreve.51.r3811},
}
@Article{ChSaKa14,
Title = {On the equivalence of dynamically orthogonal and bi-orthogonal methods: {Theory} and numerical simulations},
Author = {M. Choi and T. P. Sapsis and G. E. Karniadakis},
Journal = {J. Comput. Physics},
Year = {2014},
Pages = {1--20},
Volume = {270},
DOI = {10.1016/j.jcp.2014.03.050}
}
@Article{ChTuBa16,
Title = {Turbulent-laminar patterns in shear flows without walls},
Author = {Chantry, M. and Tuckerman, L. S. and Barkley, D.},
Journal = {J. Fluid M.},
Year = {2016},
Pages = {R8},
Volume = {791},
DOI = {10.1017/jfm.2016.92}
}
@Article{ChWiKe14,
Title = {Genesis of streamwise-localized solutions from globally periodic traveling waves in pipe flow},
Author = {Chantry, M. and Willis, A. P. and Kerswell, R. R.},
Journal = {Phys. Rev. Lett.},
Year = {2014},
Pages = {164501},
Volume = {112},
DOI = {10.1103/PhysRevLett.112.164501}
}
@Conference{CKBEG15,
Title = {Experimental observations of direct laminar-turbulent transition in counter-rotating {Taylor}-Couette flow},
Author = {C. Crowley and M. Krygier and D. Borrero-Echeverry and R. Grigoriev and M. Schatz},
Booktitle = {68\textsuperscript{th} Annual Meeting of the APS Division of Fluid Dynamics},
Year = {2015},
Series = {Bull. Am. Phys. Soc},
Volume = {60},
URL = {http://meetings.aps.org/link/BAPS.2015.DFD.D29.2}
}
@Article{Clever74,
author = {R. Clever and F. Busse},
title = {Large wavelength convection rolls in low Prandt number fluids},
journal = {J. Fluid Mech.},
year = {1974},
volume = {65},
pages = {665},
doi = {10.1007/bf01601497},
keywords = {fluid dynamics},
}
@Incollection{CleverBusse00,
Title = {Tertiary and quaternary solutions for plane {Couette} flow with thermal stratification},
Author = {Clever, R. M. and Busse, F. H.},
Booktitle = {Physics of Rotating Fluids},
Publisher = {Springer},
Year = {2000},
Editor = {Egbers, C. and Pfister, G.},
Pages = {399--416},
DOI = {10.1007/3-540-45549-3_22},
ISBN = {978-3-540-67514-3}
}
@Article{CM87tran,
author = {H. Chat{\'e} and P. Manneville},
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},
}
@Misc{CNS,
Note = {Center for Nonlinear Science,\weblink{www.cns.gatech.edu}}
}
@Phdthesis{Coff76,
Title = {{The stability of plane {Couette} flow}},
Author = {Coffee, T. P.},
School = {City Univ. of New York, NY.},
Year = {1976}
}
@Article{cohen72,
author = {B. I. Cohen and J. A. Krommes and W. M. Tang and M. N. Rosenbluth},
title = {Non-linear saturation of the dissipative trapped-ion mode by mode coupling},
journal = {Nucl. Fusion},
year = {1972},
volume = {16},
pages = {971--991},
doi = {10.2172/7189685},
}
@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{collet80,
author = {P. Collet and J.-P. Eckmann and O. E. Lanford},
title = {Universal properties of maps on an interval},
journal = {Commun. Math. Phys.},
year = {1980},
volume = {76},
pages = {211},
doi = {10.1007/bf02193555},
}
@Article{collis04,
author = {S. S. Collis and R. D. Joslin and A. Seifert and V. Theofilis},
title = {Issues in active flow control: {Theory}, control, simulation, and experiment},
journal = {Prog. Aerosp. Sci.},
year = {2004},
volume = {40},
pages = {237},
doi = {10.1016/j.paerosci.2004.06.001},
}
@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}
}
@Article{conjug_Fred,
author = {P. Cvitanovi\'{c} and C. P. Dettmann and R. Mainieri and G. Vattay},
title = {Trace formulae for stochastic evolution operators: {Smooth} conjugation method},
journal = {Nonlinearity},
year = {1999},
volume = {12},
pages = {939},
note = {\arXiv{chao-dyn/9811003}},
doi = {10.1088/0951-7715/12/4/312},
}
@Book{constantin_integral_1989,
Title = {Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations},
Author = {P. Constantin and C. Foias and B. Nicolaenko and R. Temam},
Publisher = {Springer},
Year = {1989},
Address = {New York}
}
@Book{contebook,
Title = {The {P}ainlev{\'e} property: one century later},
Author = {R. Conte},
Publisher = {Springer},
Year = {1999},
Address = {New York}
}
@Book{Cornwell97,
Title = {Group Theory in Physics: An introduction},
Author = {Cornwell, J. F.},
Publisher = {Academic Press},
Year = {1997},
Address = {New York}
}
@Article{CouTre78,
author = {P. Coullet and C. Tresser},
title = {It\'erations d'endomorphismes et groupe de renormalisation},
journal = {J. de Physique Colloque C},
year = {1978},
volume = {39},
pages = {5--25},
doi = {10.1051/jphyscol:1978513},
}
@Article{CouTre78a,
author = {P. Coullet and C. Tresser},
title = {It\'erations d'endomorphismes et groupe de renormalisation},
journal = {C. R. Acad. Sci. Paris A},
year = {1978},
volume = {287},
pages = {577--580},
doi = {10.1051/jphyscol:1978513},
}
@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},
doi = {10.1007/bf00944751},
}
@Article{Cra72,
author = {A. D. D. Craik},
title = {Eigenvalue bounds in linear inviscid stability theory},
journal = {J. Fluid Mech.},
year = {1972},
volume = {53},
pages = {657--670},
abstract = {New eigenvalue bounds are derived for the linear
stability of inviscid parallel flows, both for homogeneous and for
stratified fluids. The usefulness of these bounds, as compared with
that of previous results, is assessed for several examples. For
homogeneous fluids the new upper bounds for the imaginary part ci of
the complex phase velocity are sometimes better than previous
criteria. For both homogeneous and stratified flows, the new upper
bounds for the wave-number ? of neutrally stable disturbances
improve on previous results, giving values within 10% of the known
exact solution in several cases.},
doi = {10.1017/s0022112072000400},
}
@Article{Cra89,
author = {A. D. D. Craik},
title = {The stability of unbounded two- and three-dimensional flows subject to body forces: some exact solutions},
journal = {J. Fluid Mech.},
year = {1989},
volume = {198},
pages = {275--292},
doi = {10.1017/s0022112089000133},
}
@Article{CroDav06,
author = {J. J. Crofts and R. L. Davidchack},
title = {Efficient detection of periodic orbits in chaotic systems by stabilizing transformations},
journal = {SIAM J. Sci. Comp.},
year = {2006},
volume = {28},
pages = {1275--1288},
doi = {10.1137/050623401},
}
@Phdthesis{Crofts07thesis,
Title = {Efficient method for detection of periodic orbits in chaotic maps and flows},
Author = {J. J. Crofts},
School = {Univ. of Leicester},
Year = {2007},
Address = {Leicester, UK},
Note = {\arXiv{nlin.CD/0706.1940}}
}
@Article{cross93,
author = {M. C. Cross and P. C. Hohenberg},
title = {Pattern formation outside of equilibrium},
journal = {Rev. Mod. Phys},
year = {1993},
volume = {65},
doi = {10.1103/revmodphys.65.851},
}
@Article{cross94sp,
author = {M. C. Cross and P. C. Hohenberg},
title = {Spatiotemporal Chaos},
journal = {Science},
year = {1994},
volume = {263},
pages = {1569--1570},
doi = {10.1126/science.263.5153.1569},
abstract = {The phenomena of spatiotermporal chaos are introduced based on both rotating and regular Rayleigh-Bernard convection. The enormous number of available degrees of freedom is a vivid feature. A set of interesting questions have been raised, including how to characterize a spatiotemporal chaotic state. The importance of the study of small subsystems is emphasized.},
}
@Article{CSS85,
Title = {Scaling laws for mode lockings in circle maps},
Author = {P. Cvitanovi\'c and B. Shraiman and B. S\"oderberg},
Journal = {Phys. Scr.},
Year = {1985},
Pages = {263--270},
Volume = {32},
DOI = {10.1088/0031-8949/32/4/003}
}
@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},
note = {\arXiv{chao-dyn/9307012}},
doi = {10.1103/physrevlett.71.4138},
}
@Misc{Cvi07,
author = {P. Cvitanovi{\'c}},
title = {Continuous symmetry reduced trace formulas},
year = {2007},
url = {http://ChaosBook.org/~predrag/papers/Cvi07.pdf},
}
@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}
}
@InProceedings{CviLip12,
Title = {Knowing when to stop: {How} noise frees us from determinism},
Author = {P. Cvitanovi\'c and D. Lippolis},
Booktitle = {Let's Face Chaos through Nonlinear Dynamics},
Year = {2012},
Address = {Melville, New York},
Editor = {M. Robnik and V. G. Romanovski},
Note = {\arXiv{1206.5506}},
Pages = {82--126},
Publisher = {Am. Inst. of Phys.},
DOI = {10.1063/1.4745574}
}
@Article{CvitaEckardt,
author = {P. Cvitanovi{\'c} and B. Eckhardt},
title = {Symmetry decomposition of chaotic dynamics},
journal = {Nonlinearity},
year = {1993},
volume = {6},
pages = {277},
note = {\arXiv{chao-dyn/9303016}},
doi = {10.1088/0951-7715/6/2/008},
}
@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},
}
@Book{cvt89b,
Title = {Universality in Chaos},
Author = {P. Cvitanovi{\'c}},
Publisher = {Adam Hilger},
Year = {1989},
Address = {Bristol}
}
@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 = {J. Wang},
doi = {10.1017/jfm.2013.75},
}
@Article{Da73,
author = {A. Davey},
title = {On the stability of plane {Couette} flow to infinitesimal disturbances},
journal = {J. Fluid Mech.},
year = {1973},
volume = {57},
pages = {369--380},
doi = {10.1017/s0022112073001217},
}
@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{Dang86,
Title = {Steady-state mode interactions in the presence of {0(2)}-symmetry},
Author = {Dangelmayr, G.},
Journal = {Dyn. Sys.},
Year = {1986},
Pages = {159--185},
Volume = {1},
DOI = {10.1080/02681118608806011}
}
@Article{DASB11,
Title = {Optimal transfers between unstable periodic orbits using invariant manifolds},
Author = {Davis, K. E. and Anderson, R. L. and Scheeres, D. J. and Born, G. H.},
Journal = {Celestial Mech. Dynam. Astronom.},
Year = {2011},
Pages = {241--264},
Volume = {109},
DOI = {10.1007/s10569-010-9327-x}
}
@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}
}
@Incollection{DasBuchMirror,
author = {P. Cvitanovi{\'c}},
title = {World in a mirror},
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#discrete},
}
@Article{DauBer12,
Title = {Subcritical transition to turbulence: {What} we can learn from the physics of glasses},
Author = {Dauchot, O. and Bertin, E.},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {036312},
Volume = {86-96},
DOI = {10.1103/PhysRevE.86.036312},
}
@Book{DayanAbbott01,
title = {{Theoretical Neuroscience}},
publisher = {MIT Press},
year = {2001},
author = {Dayan, P. and Abbott, L. F.},
address = {Cambridge, MA}
}
@Incollection{DBD96,
Title = {Pairs of counter-rotating streamwise vortices: {A} finite amplitude solution in plane {Couette} flow},
Author = {Dauchot, O. and Bottin, S. and Daviaud, F.},
Booktitle = {Advances in Turbulence VI},
Publisher = {Springer},
Year = {1996},
Editor = {Gavrilakis, S. and Machiels, L. and Monkewitz, P. A.},
Pages = {329--332},
Volume = {36},
DOI = {10.1007/978-94-009-0297-8_92},
ISBN = {978-94-010-6618-1}
}
@Article{DCTSCD14,
author = {Ding, X. and Chat\'e, H. and Cvitanovi\'c, P. and Siminos, E. and Takeuchi, K. A.},
title = {Estimating the dimension of the inertial manifold from unstable periodic orbits},
journal = {Phys. Rev. Lett.},
year = {2016},
volume = {117},
pages = {024101},
doi = {10.1103/PhysRevLett.117.024101},
}
@Article{DD95,
author = {O. Dauchot and F. Daviaud},
title = {Finite-amplitude perturbation and spots growth mechanism in plane {Couette} flow},
journal = {Phys. Fluids},
year = {1995},
volume = {7},
pages = {335--343},
doi = {10.1063/1.868631},
}
@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{DDM98,
author = {O. Dauchot and F. Daviaud and P. Manneville},
title = {Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane {Couette} flow},
journal = {Phys. Fluids},
year = {1998},
volume = {10},
pages = {2597--2607},
doi = {10.1063/1.869773},
}
@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}
}
@Article{Dea63,
author = {J. W. Deardorff},
title = {On the stability of viscous plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1963},
volume = {15},
pages = {623--630},
doi = {10.1017/s0022112063000495},
}
@Article{DegHaWa13,
author = {K. Deguchi and P. Hall and A. Walton},
title = {The emergence of localized vortex--wave interaction states in plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {2013},
volume = {721},
pages = {58--85},
doi = {10.1017/jfm.2013.27}
}
@Article{deguchi2014,
author = {Deguchi, K. and Hall, P.},
title = {Canonical exact coherent structures embedded in high {Reynolds}S number flows},
journal = {Phil. Trans. Royal Soc. A},
year = {2014},
volume = {372},
number = {2020},
pages = {20130352},
doi = {10.1098/rsta.2013.0352}
}
@Article{deguchi2015,
author = {Deguchi, K.},
title = {Self-sustained states at {Kolmogorov} microscale},
journal = {J. Fluid Mech.},
year = {2015},
volume = {781},
pages = {R6},
doi = {10.1017/jfm.2015.514}
}
@Article{deLMeAvHo12,
Title = {Edge state in pipe flow experiments},
Author = {de Lozar, A. and Mellibovsky, F. and Avila, M. and Hof, B.},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Pages = {214502},
Volume = {108},
DOI = {10.1103/PhysRevLett.108.214502}
}
@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},
}
@Article{DeMeMe14,
Title = {Subcritical equilibria in {Taylor-Couette} flow},
Author = {Deguchi, K. and Meseguer, A. and Mellibovsky, F.},
Journal = {Phys. Rev. Lett.},
Year = {2014},
Pages = {184502},
Volume = {112},
DOI = {10.1103/PhysRevLett.112.184502}
}
@Incollection{DeNa12,
Title = {Exact coherent state with travelling hairpin vortex in plane {Couette} flow},
Author = {Deguchi, K. and Nagata, M.},
Booktitle = {Progress in Turbulence and Wind Energy IV},
Publisher = {Springer},
Year = {2012},
Editor = {Oberlack, M. and Peinke, J. and Talamelli, A. and Castillo, L. and H\"olling, M.},
Pages = {129--134},
Series = {Proceedings in Physics},
Volume = {141},
Addr = {New York},
DOI = {10.1007/978-3-642-28968-2_27}
}
@Book{Dennis96,
Title = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations},
Author = {J.E. Dennis and R.B. Schnabel},
Publisher = {SIAM},
Year = {1996},
Addr = {Philadelphia}
}
@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{DeSo14,
Title = {Distinct organizational states of fully developed turbulent pipe flow},
Author = {Dennis, D. J. C. and Sogaro, F. M.},
Journal = {Phys. Rev. Lett.},
Year = {2014},
Pages = {234501},
Volume = {113},
DOI = {10.1103/PhysRevLett.113.234501}
}
@Article{Deufl84,
author = {P. Deuflhard},
title = {Computation of periodic solutions of nonlinear {ODE}},
journal = {BIT},
year = {1984},
volume = {34},
pages = {456},
doi = {10.1007/bf01934904},
}
@Book{devnmap,
Title = {An Introduction to Chaotic Dynamical systems},
Author = {R. L. Devaney},
Publisher = {Addison-Wesley},
Year = {1989},
Address = {Reading, MA}
}
@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{DHB92,
author = {F. Daviaud and J. Hegseth and P. Berge},
title = {Subcritical transition to turbulence in plane {Couette} flow},
journal = {Phys. Rev. Lett.},
year = {1992},
volume = {69},
pages = {2511--2514},
doi = {10.1103/physrevlett.69.2511},
}
@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{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}
}
@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}
}
@Article{DIAFRE84,
author = {Diaconis, P. and Freedman, D.},
title = {Asymptotics of graphical projection pursuit},
journal = {Ann. Statistics},
year = {1984},
volume = {12},
pages = {793--815},
doi = {10.1214/aos/1176346703},
}
@Article{diag_Fred,
author = {P. Cvitanovi\'{c} and N. S{\o}ndergaard and G. Palla and G. Vattay and C. P. Dettmann},
title = {Spectrum of stochastic evolution operators: {Local} matrix representation approach},
journal = {Phys. Rev. E},
year = {1999},
volume = {60},
pages = {3936},
note = {\arXiv{chao-dyn/9904027}},
doi = {10.1103/physreve.60.3936},
}
@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}
}
@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{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 Contin. Dynam. Systems},
year = {2007},
volume = {9},
pages = {555--580},
doi = {10.3934/dcdsb.2008.9.555},
}
@Unpublished{DKY05,
author = {Hua-Shu Dou and Boo Cheong Kho and Khoon Seng Yeo},
title = {Flow transition in plane {Couette} flow},
note = {\arXiv{nlin.CD/0501048}},
year = {2005},
}
@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: {T}heoretical model and experiments},
journal = {Physica D},
year = {1992},
volume = {55},
pages = {287--308},
doi = {10.1016/0167-2789(92)90061-q},
}
@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{doeb94nls,
author = {H.-D. Doebner and G. A. Goldin},
title = {Properties of nonlinear {Schr\"odinger} equations associated with diffeomorphism group representations},
journal = {J. Phys. A},
year = {1994},
volume = {27},
pages = {1771--1780},
doi = {10.1088/0305-4470/27/5/036},
}
@Article{doelman91n,
author = {A. Doelman},
title = {Finite-dimensional models of the {Ginzburg-Landau} equation},
journal = {Nonlinearity},
year = {1991},
volume = {4},
pages = {231--250},
doi = {10.1088/0951-7715/4/2/003},
}
@Article{doercgl87,
author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko},
title = {Exact {Lyapunov} dimension of the universal attractor for the Complex {Ginzburg-Landau} equation},
journal = {Phys. Rev. Lett.},
year = {1987},
volume = {59},
pages = {2911--2914},
doi = {10.1103/physrevlett.59.2911},
}
@Article{doercgl88,
author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko},
title = {Low-dimensional behaviour in the complex {Ginzburg-Landau} equation},
journal = {Nonlinearity},
year = {1988},
volume = {1},
pages = {279--309},
doi = {10.1088/0951-7715/1/2/001},
}
@Article{Lin2011,
author = {Lin, Z. and Thiffeault, J.-L. and Doering, C. R.},
title = {Optimal stirring strategies for passive scalar mixing},
journal = {J. Fluid Mech.},
year = {2011},
volume = {675},
pages = {465--476},
doi = {10.1017/s0022112011000292},
}
@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{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},
ISSN = {0375-9601}
}
@Article{DOP79,
Title = {Bistability, oscillation, and chaos in an enzyme reaction},
Author = {H. Degn and L. F. Olsen and J. W. Perram},
Journal = {Ann. N. Y. Acad. Sci.},
Year = {1979},
Pages = {623--637},
Volume = {316},
DOI = {10.1111/j.1749-6632.1979.tb29503.x}
}
@Article{DR_prl,
author = {P. Dahlqvist and G. Russberg},
title = {Existence of stable orbits in the $x^{2}y^{2}$ potential},
journal = {Phys. Rev. Lett.},
year = {1990},
volume = {65},
pages = {2837},
doi = {10.1103/physrevlett.65.2837},
}
@Book{DR04,
title = {Hydrodynamic Stability},
publisher = {Cambridge Univ. Press},
year = {2004},
author = {P. Drazin and W. H. Reid},
address = {Cambridge},
edition = {Second},
doi = {10.1017/cbo9780511616938},
}
@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{Dragt05,
author = {Dragt, A. J.},
title = {The symplectic group and classical mechanics},
journal = {Ann. N. Y. Acad. Sci.},
year = {2005},
volume = {1045},
pages = {291--307},
doi = {10.1196/annals.1350.025},
}
@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},
Note = {{www.physics.umd.edu/dsat/dsatliemethods.html}}
}
@Unpublished{DraHab08,
Title = {How {Wigner} functions transform under symplectic maps},
Author = {Dragt, A. J. and Habib, S.},
Note = {\arXiv{quant-ph/9806056}},
Year = {1998}
}
@Book{Drazin02,
title = {Introduction to Hydrodynamic Stability},
publisher = {Cambridge Univ. Press},
year = {2002},
author = {P.G. Drazin},
doi = {10.1017/cbo9780511809064},
}
@Article{DreLau90,
author = {U. Dressler and W. Lauterborn},
title = {Ruelle's rotation frequency for a symplectic chain of dissipative oscillators},
journal = {Phys. Rev. A},
year = {1990},
volume = {41},
pages = {6702},
doi = {10.1103/physreva.41.6702},
}
@Article{DrNeMe99,
Title = {Subharmonic instabilities of {Tollmien-Schlichting} waves in two-dimensional {Poiseuille} flow},
Author = {Drissi, A. and Net, M. and Mercader, I.},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {1781--1791},
Volume = {60},
DOI = {10.1103/PhysRevE.60.1781}
}
@Article{DruCip00,
Title = {Application of {Lie} algebras to visual servoing},
Author = {T. Drummond and R. Cipolla},
Journal = {Intern. J. Computer Vision},
Year = {2000},
Pages = {21--41},
Volume = {37}
}
@Book{DS,
Title = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations},
Author = {Dennis Jr., J. E. and R. B. Schnabel},
Publisher = {SIAM},
Year = {1996},
Address = {Philadelphia}
}
@Book{DS83,
Title = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations},
Author = {Dennis Jr., J. E. and R. B. Schnabel},
Publisher = {Prentice-Hall},
Year = {1983},
Address = {Englewood Cliffs, New Jersey}
}
@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},
abstract = {A quantitative theory has been developed which shows that
each classical closed orbit that begins and ends near the nucleus
contributes an oscillatory term to the average oscillator strength.},
doi = {10.1103/physrevlett.58.1731},
}
@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}
}
@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{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}
}
@Book{DuiKol00,
title = {{Lie Groups}},
publisher = {Springer},
year = {2000},
author = {J. J. Duistermaat and J. A. C. Kolk},
address = {New York},
doi = {10.1007/978-3-642-56936-4},
}
@Misc{DuisterDSsymm,
author = {J. J. Duistermaat},
title = {{Dynamical Systems with Symmetry}}
}
@Book{dummitfoote,
title = {{Abstract Algebra}},
publisher = {Wiley},
year = {2004},
author = {Dummit, D.S. and Foote, R.M.},
}
@Article{DuWiKe10,
author = {Duguet, Y. and Willis, A. P. and Kerswell, R. R.},
title = {Slug genesis in cylindrical pipe flow},
journal = {J. Fluid Mech.},
year = {2010},
volume = {663},
pages = {180--208},
doi = {10.1017/s0022112010003435},
}
@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{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},
DOI = {10.1007/s100510050142}
}
@Unpublished{Viswanath,
author = {D. Viswanath},
title = {An extension of the {Lindstedt-Poincar\'e} algorithm for computing periodic orbits},
note = {Published as SIAM Rev. (2002) 43, 478--496},
doi = {10.1137/S0036144500375292},
}
@Article{EaPoSa10,
author = {J. Early and J. Pohjanpelto and R. Samelson},
title = {Group foliation of equations in geophysical fluid dynamics},
journal = {Discrete Contin. Dynam. Systems},
year = {2010},
volume = {27},
pages = {1571--1586},
doi = {10.3934/dcds.2010.27.1571},
}
@Article{EAS87,
author = {E. A. Spiegel},
title = {Chaos: a mixed metaphor for turbulence},
journal = {Proc. Roy. Soc. A},
year = {1987},
volume = {413},
pages = {87},
doi = {10.1515/9781400860197.87},
}
@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{eck81,
author = {J.-P. Eckmann},
title = {Roads to turbulence in dissipative dynamical systems},
journal = {Rev. Mod. Phys.},
year = {1981},
volume = {53},
pages = {643},
doi = {10.1103/revmodphys.53.643},
}
@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},
}
@Article{eckerg,
author = {J.-P. Eckmann and D. Ruelle},
title = {Ergodic theory of chaos and strange attractors},
journal = {Rev. Mod. Phys.},
year = {1985},
volume = {57},
pages = {617},
doi = {10.1007/978-0-387-21830-4_17},
}
@InCollection{EckhardtFaisst05,
author = {Eckhardt, B. and Faisst, H.},
title = {Dynamical systems and the transition to turbulence},
booktitle = {{IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions}},
publisher = {Springer},
year = {2005},
editor = {Mullin, T. and Kerswell, R.},
volume = {77},
pages = {35--50},
doi = {10.1007/1-4020-4049-0_2},
isbn = {978-1-4020-4048-1}
}
@Article{ecklp88,
author = {J.-P. Eckmann and C. E. Wayne},
title = {Liapunov spectra for infinite chains of nonlinear oscillators},
journal = {J. Stat. Phys.},
year = {1988},
volume = {50},
pages = {853--878},
doi = {10.1007/bf01019144},
}
@Book{eckman80map,
title = {{Iterated Maps on the Interval as Dynamical Systems}},
publisher = {Birkh{\"a}user},
year = {1980},
author = {P. Collet and J.-P. Eckmann},
address = {Boston}
}
@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{Eggels94,
author = {J. G. M. Eggels and F. Unger and M. H. Weiss and J. Westerweel and R. J. Adrian and R. Freidrich and F. T. M. Nieuwstadt},
title = {Fully developed turbulent pipe flow: a comparison between direct numberical simulation and experiment},
journal = {J. Fluid Mech.},
year = {1994},
volume = {268},
pages = {175--209},
doi = {10.1017/s002211209400131x},
}
@Article{egolf00,
Title = {Mechanisms of extensive spatiotemporal chaos in {R}ayleigh-{B\'e}nard convection},
Author = {D. A. Egolf and I. V. Melnikov and W. Pesch and R. E. Ecke},
Journal = {Nature},
Year = {2000},
Pages = {733},
Volume = {404},
}
@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},
doi = {10.1038/369129a0},
}
@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},
doi = {10.1103/physrevlett.80.3228},
}
@Article{EGP70,
author = {T. Ellingsen and B. Gjevik and E. Palm},
title = {On the non-linear stability of plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1970},
volume = {40},
pages = {97--112},
doi = {10.1017/s002211207000006x},
}
@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},
abtract = {For the CGLe on a large periodic interval, the transition from defect to phase turbulence is continuous. The conclusion is based on the calculation of the defect density, Lyapunov dimension density and correlation lengths.},
doi = {10.1103/physrevlett.74.1751},
}
@Article{Ehren08,
author = {Ehrenstein, U. and Nagata, M. and Rincon, F.},
title = {Two-dimensional nonlinear plane {Poiseuille-Couette} flow homotopy revisited},
journal = {Phys. Fluids},
year = {2008},
volume = {20},
pages = {064103},
doi = {10.1063/1.2943675}
}
@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{EKO04,
author = {J. P. England and B. Krauskopf and H. M. Osinga},
title = {Computing one-dimensional stable and unstable sets of planar maps without the inverse},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2004},
volume = {3},
pages = {161--190},
doi = {10.1137/030600131},
}
@Article{EKR87,
author = {Eckmann, J.-P. and Kamphorst, S. O. and Ruelle, D.},
title = {Recurrence plots of dynamical systems},
journal = {Europhys. Lett.},
year = {1987},
volume = {4},
pages = {973},
doi = {10.1209/0295-5075/4/9/004},
}
@Book{ellip,
title = {{Elliptic Functions and Applications}},
publisher = {Springer},
year = {1989},
author = {D. F. Lawden},
address = {New York}
}
@Techreport{Elton08,
Title = {An exploration of moderate {Reynolds} number plane {Couette} turbulence},
Author = {Elton, J. R.},
Institution = {School of Physics, Georgia Inst. of Technology},
Year = {2007},
Note = {{\tt ChaosBook.org/projects}}
}
@Article{EM99,
author = {B. Eckhardt and A. Mersmann},
title = {Transition to turbulence in a shear flow},
journal = {Phys. Rev. E},
year = {1999},
volume = {60},
pages = {509--517},
doi = {10.1103/physreve.60.509},
}
@Book{encDicMath,
title = {{Encyclopedic Dictionary of Mathematics}},
publisher = {MIT Press},
year = {1993},
author = {It{\^o}, K.},
address = {Cambridge, MA}
}
@Article{EnUrRi15,
author = {Engl, T. and Urbina, J. D. and Hummel, Q. and Richter, K.},
title = {Complex scattering as canonical transformation: {A} semiclassical approach in {Fock} space},
journal = {Ann. Phys.},
year = {2015},
volume = {527},
pages = {737--747},
doi = {10.1002/andp.201500151},
}
@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{ErshPot98,
author = {S. V. Ershov and A. B. Potapov},
title = {On the concept of stationary {Lyapunov} basis},
journal = {Physica D},
year = {1998},
volume = {118},
pages = {167--198},
doi = {10.1016/s0167-2789(98)00013-x},
}
@Article{ERTW91,
author = {Ezra, G. S. and Richter, K. and Tanner, G. and Wintgen, D.},
title = {Semiclassical cycle expansion for the helium atom},
journal = {J. Phys. B},
year = {1991},
volume = {24},
pages = {L413--L420},
doi = {10.1088/0953-4075/24/17/001},
}
@Article{ESHW07,
author = {B. Eckhardt and T. M. Schneider and B. Hof and J. Westerweel},
title = {Turbulence transition in pipe flow},
journal = {Ann. Rev. Fluid Mech.},
year = {2007},
volume = {29},
pages = {447--468},
doi = {10.1146/annurev.fluid.39.050905.110308},
}
@Article{ET02,
author = {M. Embree and L. Trefethen},
title = {Generalizing eigenvalue theorems to pseudospectra theorems},
journal = {SIAM J. Sci. Comput.},
year = {2002},
volume = {23},
pages = {83--590},
doi = {10.1137/s1064827500373012},
}
@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},
abstract = {G},
doi = {10.1007/978-3-642-03085-7-17},
}
@Article{ETFS,
author = {W. S. Edwards and L. S. Tuckerman and R. A. Friesner and D. C. Sorensen},
title = {Krylov methods for the incompressible {Navier-Stokes} equations},
journal = {J. Comput. Physics},
year = {1994},
volume = {110},
pages = {82--102},
doi = {10.1006/jcph.1994.1007},
}
@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 = {Cont. Math., AMS},
year = {1988},
volume = {81},
pages = {213--244},
doi = {10.1090/conm/081/986267},
}
@Article{ExpsPCtransition,
author = {N. Tillmark and P. H. Alfredsson},
title = {Experiments on transition in plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1992},
volume = {235},
pages = {89--102},
doi = {10.1017/s0022112092001046},
}
@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}
}
@Article{FAIECK04,
Title = {Sensitive dependence on initial conditions in transition to turbulence},
Author = {Faisst, H. \& Eckhardt, B.},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {343--352},
Volume = {504}
}
@Article{FaisstPRE00,
Title = {Transition from {Couette-Taylor} system to plane {Couette} system},
Author = {H. Faisst and B. Eckhardt},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {7227--7230},
Volume = {61},
DOI = {10.1103/PhysRevE.61.7227}
}
@Article{Faraz15,
author = {Farazmand, M.},
title = {An adjoint-based approach for finding invariant solutions of {Navier-Stokes} equations},
journal = {J. Fluid Mech.},
year = {2016},
volume = {795},
pages = {278--312},
doi = {10.1017/jfm.2016.203},
}
@Misc{farazmand2014coherent,
author = {Farazmand, M. and Haller, G.},
title = {How coherent are the vortices of two-dimensional turbulence?},
year = {2014},
url = {https://arxiv.org/abs/1402.4835},
}
@Article{FarHal13,
Title = {Attracting and repelling {Lagrangian} coherent structures from a single computation},
Author = {M. Farazmand and G. Haller},
Journal = {Chaos},
Year = {2013},
Pages = {023101},
Volume = {23},
DOI = {10.1063/1.4800210}
}
@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{FE03,
author = {H. Faisst and B. Eckhardt},
title = {Traveling waves in pipe flow},
journal = {Phys. Rev. Lett.},
year = {2003},
volume = {91},
pages = {224502},
doi = {10.1103/physrevlett.91.224502},
}
@Article{FeHa82,
Title = {Irrational decimations and path-integrals for external noise},
Author = {M. J. Feigenbaum and B. Hasslacher},
Journal = {Phys. Rev. Lett.},
Year = {1982},
Pages = {605--609},
Volume = {49},
DOI = {10.1103/PhysRevLett.49.605}
}
@Article{feigen78,
author = {M. J. Feigenbaum},
title = {Quantitative universality for a class of nonlinear transformations},
journal = {J. Stat. Phys.},
year = {1978},
volume = {19},
pages = {25--52},
doi = {10.1007/bf01020332},
}
@Article{feigen79,
author = {M. J. Feigenbaum},
title = {The universal metric properties of nonlinear transformations},
journal = {J. Stat. Phys.},
year = {1979},
volume = {21},
pages = {669--706},
note = {Reprinted in \refref{cvt89b}.},
doi = {10.1007/bf01107909},
}
@Article{feigen79scal,
author = {M. J. Feigenbaum},
title = {The onset spectrum of turbulence},
journal = {Phys. Lett. A},
year = {1979},
volume = {74},
pages = {375--378},
doi = {10.1016/0375-9601(79)90227-5},
}
@InProceedings{FeigKen83,
Title = {The onset of chaos},
Author = {M. J. Feigenbaum and R. D. Kenway},
Booktitle = {Statistical and Particle Physics},
Year = {1983},
Address = {Edinburgh},
Editor = {K. C. Bowler and A. J. McKane},
Organization = {Proc. 26\textsuperscript{th} Scottish Universities Summer School in Physics},
Pages = {1--100},
Publisher = {SUSSP Publ.}
}
@Article{Feiste1994,
author = {U. Feiste and D. J. As and A. Erhardt},
title = {18 {GHZ} all-optical frequency locking and clock recovery using a self-pulsating two-section laser},
journal = {IEEE Photon. Technol. Lett.},
year = {1994},
volume = {6},
pages = {106--108},
doi = {10.1109/68.265905},
}
@Article{FeKaSh82,
Title = {Quasiperiodicity in dissipative systems: {A} renormalization group analysis},
Author = {M.J. Feigenbaum and L.P. Kadanoff and S.J. Shenker},
Journal = {Physica D},
Year = {1982},
Pages = {370--386},
Volume = {5},
DOI = {10.1016/0167-2789(82)90030-6}
}
@Article{FelCou98,
Title = {Unified approach to the classical statistical analysis of small signals},
Author = {Feldman, G. J. and Cousins, R. D.},
Journal = {Phys. Rev. D},
Year = {1998},
Pages = {3873--3889},
Volume = {57},
DOI = {10.1103/PhysRevD.57.3873}
}
@Article{FelsOlver98,
Title = {Moving coframes: {I. A} practical algorithm},
Author = {M. Fels and P. J. Olver},
Journal = {Acta Appl. Math.},
Year = {1998},
Pages = {161--213},
Volume = {51}
}
@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}
}
@Techreport{fftwmanual,
Title = {{FFT}W 3.0 User's Manual},
Author = {M. Frigo and S.G. Johnson},
Institution = {fftw.org},
Year = {2006},
Publisher = {M. Frigo and S.G. Johnson},
URL = {http://www.fftw.org/fftw3.pdf}
}
@Article{FiSaScWu96,
author = {B. Fiedler and B. Sandstede and A. Scheel and C. Wulff},
title = {Bifurcation from relative equilibria of noncompact group actions: {Skew} products, meanders, and drifts},
journal = {Doc. Math.},
year = {1996},
volume = {141},
pages = {479--505}
}
@Article{FJolly95,
author = {C. Foias and M. S. Jolly},
title = {On the numerical algebraic approximation of global attractors},
journal = {Nonlinearity},
year = {1995},
volume = {8},
pages = {295--319},
abstract = {An algebraic approximation of the global attractors is
developed for the {Lorenz} and {KS} system.},
doi = {10.1088/0951-7715/8/3/001},
}
@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},
DOI = {10.1016/0022-0396(83)90011-6}
}
@Article{fl92,
author = {C. Falcolini and R. de la Llave},
title = {Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors},
journal = {J. Stat. Phys.},
year = {1992},
volume = {67},
pages = {645--666},
abstract = {Study the complex domains of validity in generalized standard mappings and compare Pad{\'e} methods and periodic orbit methods.},
doi = {10.1007/bf01049723},
}
@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}
}
@Article{Foiasks88,
Title = {{Kuramoto-Sivashinsky} equation},
Author = {C. Foias and B. Nicolaenko and G. R. Sell and R. T{\'e}mam},
Journal = {J. Math. Pures et Appl.},
Year = {1988},
Pages = {197},
Volume = {67}
}
@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{FrankANM03,
author = {J. Frank and W. Hundsdorfer and J.G. Verwer},
title = {On the stability of implicit-explicit linear multistep methods},
journal = {Appl. Num. Math.},
year = {1997},
volume = {25},
pages = {193--205},
doi = {10.1016/s0168-9274(97)00059-7},
}
@Misc{franzosi-2004,
Title = {{Lyapunov} exponents from unstable periodic orbits in the {FPU}-beta model},
Author = {R. Franzosi and P. Poggi and M. Cerruti-Sola},
Note = {\arXiv{nlin/0408056}},
Year = {2004}
}
@Article{FrCv11,
Title = {Reduction of continuous symmetries of chaotic flows by the method of slices},
Author = {Froehlich, S. and Cvitanovi{\'c}, P.},
Journal = {Commun. Nonlinear Sci. Numer. Simul.},
Year = {2012},
Pages = {2074--2084},
Volume = {17},
DOI = {10.1016/j.cnsns.2011.07.007}
}
@InProceedings{Fried87,
Title = {Lefschetz formulas for flows},
Author = {Fried, D.},
Booktitle = {The Lefschetz Centennial Conference},
Year = {1987},
Address = {Providence, RI},
Editor = {D. Sundararaman and A. Verjovsky and S. Gitler},
Pages = {41--43},
Publisher = {AMS},
Volume = {58},
DOI = {10.1090/conm/058.3}
}
@Article{Frigo05,
author = {M. Frigo and S.G. Johnson},
title = {The Design and Implementation of {FFTW3}},
journal = {Proceedings of the IEEE},
year = {2005},
volume = {93},
pages = {216--231},
note = {Special issue on ``Program Generation, Optimization, and Platform Adaptation''},
doi = {10.1109/jproc.2004.840301},
}
@Book{frisch,
Title = {Turbulence},
Author = {U. Frisch},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Address = {Cambridge, UK}
}
@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},
}
@Book{froyland,
title = {Chaos and coherence},
publisher = {Inst. of Phys. Publ.},
year = {1992},
author = {Fr{\o}yland, J.},
address = {Bristol},
}
@Article{froyland_alfsen,
author = {Fr{\o}yland, J. and Alfsen, K. H.},
title = {{Lyapunov}-exponent spectra for the {Lorenz} model},
journal = {Phys. Rev. A},
year = {1984},
volume = {29},
pages = {2928},
doi = {10.1103/physreva.29.2928},
}
@Article{FSTks86,
author = {U. Frisch and Z. S. She and O. Thual},
title = {Viscoelastic behavior of cellular solutions to the {Kuramoto-Sivashinsky} model},
journal = {J. Fluid Mech.},
year = {1986},
volume = {168},
pages = {221--240},
abstract = {The KSe on the periodic interval has stable steady
states of period 2*pi/N. These },
doi = {10.1017/s0022112086000356},
}
@Misc{FWweb,
Title = {Exact coherent structures},
Author = {F. Waleffe},
Year = {2006},
URL = {www.math.wisc.edu/~waleffe/ECS/RRC-data.html}
}
@Article{G00,
Title = {The onset of shear turbulence},
Author = {S. Grossmann},
Journal = {Rev. Mod. Phys.},
Year = {2000},
Pages = {603--618},
Volume = {72}
}
@Article{GaChi88,
author = {Garrison, J. C. and Chiao, R. Y.},
title = {Geometrical phases from global gauge invariance of nonlinear classical field theories},
journal = {Phys. Rev. Lett.},
year = {1988},
volume = {60},
pages = {165--168},
doi = {10.1103/physrevlett.60.165},
}
@Article{Gall69,
author = {A. P. Gallagher},
title = {On a proof by {Petrov} of the stability of plane {Couette} flow and plane {Poiseuille} flow},
journal = {SIAM J. Appl. Math.},
year = {1969},
volume = {17},
pages = {765--768},
doi = {10.1137/0117068},
}
@Article{GallMer62,
author = {Gallagher, A. P. and Mercer, A. McD},
title = {On the behaviour of small disturbances in plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1962},
volume = {13},
pages = {623--631},
doi = {10.1017/s0022112062000531},
}
@Article{GallMer64,
Title = {On the behaviour of small disturbances in plane {Couette} flow. Part 2.The higher eigenvalues},
Author = {Gallagher, A. P. and Mercer, A. McD},
Journal = {J. Fluid Mech.},
Year = {1964},
Pages = {350--350},
Volume = {18}
}
@Book{GaQu95,
Title = {{Lyapunov} Matrix Equation in System Stability and Control},
Author = {Z. Gaji\'c and M. Qureshi},
Publisher = {Academic Press},
Year = {1995},
Address = {New York}
}
@Article{garnier,
Title = {Nonlinear dynamics of waves and modulated waves in 1{D} thermocapillary flows},
Author = {N. Garnier and A. Chiffaudel and F. Daviaud and A. Prigent},
Journal = {Physica D},
Year = {2003},
Pages = {1--29},
Volume = {174}
}
@Article{gasp02,
Title = {Trace formula for noisy flows},
Author = {P. Gaspard},
Journal = {J. Stat. Phys.},
Year = {2002},
Pages = {57},
Volume = {106},
Abstract = {A trace formula is derived for the
FokkerPlanck equation associated with Ito stochastic
differential equations describing noisy time-continuous
nonlinear dynamical systems. In the weak-noise limit, the
trace formula provides estimations of the eigenvalues of
the Fokker-Planck operator on the basis of the
Pollicott-Ruelle resonances of the noiseless
deterministic system, which is assumed to be
non-bifurcating. At first order in the noise amplitude,
the effect of noise on a periodic orbit is given in terms
of the period and the derivative of the period with
respect to the pseudo-energy of the
Onsager-Machlup-Freidlin-Wentzell scheme. },
DOI = {10.1023/A:1013167928166}
}
@Article{gasp95,
Title = {Spectral signature of the pitchfork bifurcation: {Liouville} equation approach},
Author = {P. Gaspard and G. Nicolis and A. Provata and S. Tasaki},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {74--94},
Volume = {51},
Keywords = {dynamical systems, Koopman}
}
@Book{gatermannHab,
Title = {Computer Algebra Methods for Equivariant Dynamical Systems},
Author = {Gatermann, K.},
Publisher = {Springer},
Year = {2000},
Address = {New York}
}
@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},
}
@Unpublished{GGJLF10,
Title = {Connecting curves for dynamical systems},
Author = {R. Gilmore and J.-M. Ginoux and T. Jones and C. Letellier and U. S. Freitas},
Note = {\arXiv{1003.1703}},
Year = {2010}
}
@Unpublished{GHC08a,
Title = {Periodic orbits of plane {Couette} flow},
Author = {Gibson, J. F. and Cvitanovi{\'c}, P.},
Note = {In preparation},
Year = {2010}
}
@Article{GHCV08,
author = {Halcrow, J. and Gibson, J. F. and Cvitanovi{\'c}, P. and Viswanath, D.},
title = {Heteroclinic connections in plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {2009},
volume = {621},
pages = {365--376},
doi = {10.1017/S0022112008005065},
}
@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{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}
}
@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{GiBr13,
Title = {Spanwise-localized solutions of planar shear flows},
Author = {Gibson, J. F. and Brand, E. W.},
Journal = {J. Fluid Mech.},
Year = {2014},
Note = {\arXiv{1304.6323}},
Pages = {25--61},
Volume = {745},
DOI = {10.1017/jfm.2014.89}
}
@Techreport{GibsonMovies,
Title = {Movies of plane {Couette}},
Author = {J. F. Gibson and P. Cvitanovi{\'c}},
Institution = {Georgia Inst. of Technology},
Year = {2015},
Publisher = {Center for Nonlinear Science},
URL = {http://ChaosBook.org/tutorials}
}
@Phdthesis{GibsonPhD,
Title = {Dynamical systems models of wall-bounded, shear-flow turbulence},
Author = {J. F. Gibson},
School = {Cornell University},
Year = {2002}
}
@Article{GiChLiPo12,
Title = {Covariant {Lyapunov} vectors},
Author = {Ginelli, F. and Chat\'{e}, H. and R. Livi and Politi, A.},
Journal = {J. Phys. A},
Year = {2013},
Pages = {254005},
Volume = {46},
DOI = {10.1088/1751-8113/46/25/254005}
}
@Unpublished{GiLe04,
Title = {Existence of relative periodic orbits near relative equilibria},
Author = {Ginzburg, V. and {Lerman}, E.},
Note = {\arXiv{math/0402264}},
Year = {2004}
}
@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{GioAdr98,
Title = {Nonuniform stationary measure of the invariant unstable foliation in {Hamiltonian} and fluid mixing systems},
Author = {M. Giona and A. Adrover},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {3864},
Volume = {81},
DOI = {10.1103/PhysRevLett.81.3864}
}
@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},
note = {\arXiv{0704.3781}},
doi = {10.1103/physreve.79.016305},
}
@Book{glend94,
Title = {Stability, instability and chaos: an introduction to the theory of nonlinear differential equations},
Author = {P. Glendinning},
Publisher = {Cambridge Univ. Press},
Year = {1994},
Address = {Cambridge},
Key = {QA372 1994}
}
@Book{GL-Gil07b,
Title = {The Symmetry of Chaos},
Author = {R. Gilmore and C. Letellier},
Publisher = {Oxford Univ. Press},
Year = {2007},
Address = {Oxford}
}
@Article{GL-Mir93,
author = {R. Miranda and E. Stone},
title = {The proto-{Lorenz} system},
journal = {Phys. Letters A},
year = {1993},
volume = {178},
pages = {105},
doi = {10.1016/0375-9601(93)90735-i},
}
@Article{GLS16,
author = {S. Grossmann and D. Lohse and C. Sun},
title = {High-{Reynolds}-number {Taylor-Couette} turbulence},
journal = {Ann. Rev. Fluid Mech.},
year = {2016},
volume = {48},
pages = {53},
}
@Article{GM00aut,
Title = {Computing periodic orbits and their bifurcations with automatic differentiation},
Author = {J. Guckenheimer and B. Meloon},
Journal = {SIAM J. Sci. Comput.},
Year = {2000},
Pages = {951--985},
Volume = {22}
}
@Book{golubII,
title = {{Singularities and Groups in Bifurcation Theory}},
publisher = {Springer},
year = {1988},
author = {M. Golubitsky and I. Stewart and D. G. Schaeffer},
volume = {2},
isbn = {978-0-387-96652-6},
address = {New York},
doi = {10.1007/978-1-4612-4574-2},
}
@Book{golubitsky2002sp,
Title = {{The symmetry perspective}},
Author = {Golubitsky, M. and Stewart, I.},
Publisher = {Birkh{\"a}user},
Year = {2002},
Address = {Boston}
}
@Article{golubord,
author = {J. P. Gollub},
title = {Order and disorder in fluid motion},
journal = {Proc. Natl. Acad. Sci. USA},
year = {1995},
volume = {92},
pages = {6705},
doi = {10.1073/pnas.92.15.6705},
abstract = {A brief review of experiments on film flows, surface
waves, and thermal convection. In 1-d, the transition from cellular
states to spatiotemporal chaos is described. In 2-d, periodic and
quasiperiodic patterns including defect-mediating ones are discussed.
Statistical emphasis on the transport and mixing phenomena in fluids
is put and some open problems are stated.},
}
@Article{golubsym84,
author = {M. Golubitsky and J. W. Swift and E. Knobloch},
title = {Symmetries and pattern selection in {R}ayleigh-{B}ernard convection},
journal = {Physica D},
year = {1984},
volume = {10},
pages = {249},
doi = {10.1016/0167-2789(84)90179-9},
}
@Book{gottlieb77,
Title = {Numerical analysis of spectral methods: theory and applications},
Author = {D. Gottlieb and S. A. Orszag},
Publisher = {SIAM},
Year = {1977},
Address = {Philadelphia}
}
@Book{GoVanLo96,
Title = {Matrix Computations},
Author = {Golub, G. H. and Van Loan, C. F.},
Publisher = {J. Hopkins Univ. Press},
Year = {1996},
Address = {Baltimore, MD}
}
@Misc{GPLv2,
author = {{Free Software Foundation}},
title = {{GNU General Public License}},
year = {2007},
url = {http://www.gnu.org/licenses/gpl.html},
}
@Article{GraPro83,
author = {Grassberger, P. and Procaccia, I.},
title = {Estimation of the {Kolmogorov} entropy from a chaotic signal},
journal = {Phys. Rev. A},
year = {1983},
volume = {28},
pages = {2591--2593},
doi = {10.1103/physreva.28.2591},
}
@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{GrBaPo88,
author = {P. Grassberger and R. Badii and A. Politi},
title = {Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors},
journal = {J. Stat. Phys.},
year = {1988},
volume = {51},
pages = {135},
doi = {10.1007/bf01015324},
}
@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},
}
@Book{greshosani,
title = {{Incompressible Flow and the Finite Element Method}},
publisher = {Wiley},
year = {2000},
author = {P. M. Gresho and R. L. Sani},
address = {New York},
}
@Article{grigoriev2003,
author = {R. O. Grigoriev},
title = {Contact line instability and pattern selection in thermally driven liquid films},
journal = {Phys. Fluids},
year = {2003},
volume = {15},
pages = {1363--1374}
}
@Article{grigoriev2005,
author = {R. O. Grigoriev},
title = {Transient growth in driven contact lines},
journal = {Physica D},
year = {2005},
volume = {209},
pages = {105}
}
@Article{Groh64,
Title = {Uber das {S}pektrum bei {E}igenschwingungen ebener {L}aminarstromungen},
Author = {Grohne, D.},
Journal = {Z. Angew. Math. Mech.},
Year = {1964},
Pages = {350--352},
Volume = {13}
}
@Article{GroTho77,
Title = {Invariant distributions and stationary correlation functions of one-dimensional discrete processes},
Author = {S. Grossmann and S. Thomae},
Journal = {Z. Naturforsch. A},
Year = {1977},
Pages = {1353--1363},
Volume = {32}
}
@Book{grue_waves_1996,
Title = {Waves and Nonlinear Processes in Hydrodynamics},
Author = {Grue, J. and Gjevik, B. and Weber, J. E.},
Publisher = {Springer},
Year = {1996},
Address = {New York}
}
@Article{Guck92,
Title = {Symmetry properties of confined convective states},
Author = {Guckenheimer, J.},
Journal = {Z. Angew. Math. Phys.},
Year = {1992},
Pages = {422--429},
Volume = {43}
}
@Book{guckb,
Title = {Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields},
Author = {J. Guckenheimer and P. Holmes},
Publisher = {Springer},
Year = {1983},
Address = {New York}
}
@Article{Guckenheimer79b,
Title = {Structural stability of the {L}orenz attractor},
Author = {J. Guckenheimer and R. Williams},
Journal = {Publ. Math. IHES},
Year = {1979},
Pages = {55--72},
Volume = {50},
Keywords = {attractor, Lorenz}
}
@Article{GuHu98,
Title = {A resonance mechanism in plane {Couette} flow},
Author = {L. H. Gustavsson and L. S. Hultgren},
Journal = {J. Fluid Mech.},
Year = {1980},
Pages = {149--159},
Volume = {98},
Annote = {resonant response leading to algebraic growth for small times. It occurs when the eigenvalues of the Orr-Sommerfeld equation coincide with the eigenvalues of the homogeneous operator for the streamwise velocity component. The resonance has been investigated numerically for plane Couette flow. The aspect ratio of the most rapidly growing wave increases with the Reynolds number, with its spanwise wavelength approaching a constant value of about 3 channel heights.}
}
@Book{GuiSte90,
Title = {Symplectic Techniques in Physics},
Author = {V. Guillemin and S. Sternberg},
Publisher = {Cambridge Univ. Press},
Year = {1990},
Address = {Cambridge}
}
@Unpublished{GupThy08,
Title = {Chaotic advection of inertial particles in two dimensional flows},
Author = {N. Gupte and N. N. Thyagu},
Note = {\arXiv{0811.3685}; {(Published in the proceedings of the conference ``Recent Developments in Nonlinear Dynamics'', Bharathidasan University, Thiruchirapalli, India, February 2008)}},
Year = {2008}
}
@Book{gutbook,
Title = {Chaos in Classical and Quantum Mechanics},
Author = {M. C. Gutzwiller},
Publisher = {Springer},
Year = {1990},
Address = {New York}
}
@Article{GutOsi13b,
author = {Gutkin, B. and Osipov, V. Al.},
title = {Universality in spectral statistics of open quantum graphs},
journal = {Phys. Rev. E},
year = {2015},
volume = {91},
pages = {060901},
doi = {10.1103/PhysRevE.91.060901},
}
@Article{GutOsi15,
author = {Gutkin, B. and Osipov, V.},
title = {Classical foundations of many-particle quantum chaos},
journal = {Nonlinearity},
year = {2016},
volume = {29},
pages = {325--356},
doi = {10.1088/0951-7715/29/2/325},
}
@Article{gutzwiller67,
Title = {Phase-integral approximation in momentum space and the bound states of an atom},
Author = {M. C. Gutzwiller},
Journal = {J. Math. Phys.},
Year = {1967},
Pages = {1979--2000},
Volume = {8}
}
@Article{gutzwiller69,
Title = {Phase-integral approximation in momentum space and the bound states of an atom. II},
Author = {M. C. Gutzwiller},
Journal = {J. Math. Phys.},
Year = {1969},
Pages = {1004--1021},
Volume = {10}
}
@Article{gutzwiller70,
Title = {Energy spectrum according to classical mechanics},
Author = {M. C. Gutzwiller},
Journal = {J. Math. Phys.},
Year = {1970},
Pages = {1791--1806},
Volume = {11}
}
@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}
}
@Misc{HaFaHa13,
Title = {Detecting invariant manifolds, attractors, and generalized {KAM} tori in aperiodically forced mechanical systems},
Author = {Hadjighasem, A. and {Farazmand}, M. and {Haller}, G.},
Note = {\arXiv{1302.1732}},
Year = {2013}
}
@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{HaKiWa95,
Title = {Regeneration mechanisms of near-wall turbulence structures},
Author = {J. M. Hamilton and J. Kim and F. Waleffe},
Journal = {J. Fluid Mech.},
Year = {1995},
Pages = {317--348},
Volume = {287},
DOI = {10.1017/S0022112095000978}
}
@Techreport{Halc04,
Title = {Implementation of a {Pressure Poisson Equation} method for plane {Couette} flow},
Author = {Halcrow, J.},
Institution = {School of Physics, Georgia Inst. of Technology},
Year = {2004},
Note = {{\tt ChaosBook.org/projects}}
}
@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},
Note = {{\tt ChaosBook.org/projects/theses.html}}
}
@Book{haledb,
Title = {Dynamics and Bifurcations},
Author = {J. Hale and H. Ko{\c{c}}ak},
Publisher = {Springer},
Year = {1991},
Address = {New York}
}
@Book{haleinf84,
Title = {An Introduction to Infinite Dimensional Systems-Geometric Theory},
Author = {J. K. Hale and L. T. Magalhaes},
Publisher = {Springer},
Year = {1984},
Address = {New York}
}
@Book{haleob,
title = {{Ordinary Differential Equations}},
publisher = {Wiley},
year = {1969},
author = {J. Hale},
address = {New York},
}
@Book{Hall03,
Title = {Lie Groups, {Lie} Algebras, and Representations},
Author = {Hall, B. C},
Publisher = {Springer},
Year = {2003},
Address = {New York}
}
@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{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{hallerAnnRevFluid,
author = {G. Haller},
title = {Lagrangian coherent structures},
journal = {Ann. Rev. Fluid Mech.},
year = {2015},
volume = {47},
pages = {137--161}
}
@Book{halmos:fdvs,
Title = {Finite-Dimensional Vector Spaces},
Author = {Paul R. Halmos},
Publisher = {D. Van Nostrand},
Year = {1958},
Address = {Princeton},
Edition = {Second}
}
@Article{HAMANE05,
Title = {Geometric representation of high dimension, low sample size data},
Author = {Hall, P. and Marron, J.S. and Neeman, A.},
Journal = {J. R. Statist. Soc. B},
Year = {2005},
Pages = {427--444},
Volume = {67}
}
@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}
}
@Book{hamer,
Title = {Group Theory and Its Application to Physical Problems},
Author = {Morton Hamermesh},
Publisher = {Dover},
Year = {1962},
Address = {New York}
}
@Phdthesis{hansen_thesis,
author = {Hansen, K. T.},
title = {Symbolic Dynamics in Chaotic systems},
school = {Univ. of Oslo},
year = {1993},
address = {Oslo, Norway},
url = {http://ChaosBook.org/projects/KTHansen/thesis},
}
@Article{hansen92,
author = {K. T. Hansen},
title = {Remarks on the symbolic dynamics for the {H{\'e}non} map},
journal = {Phys. Lett. A},
year = {1992},
volume = {165},
pages = {100--104},
doi = {10.1016/0375-9601(92)90083-X},
}
@Article{Hansen95,
Title = {Alternative method to find orbits in chaotic systems},
Author = {Hansen, K. T.},
Journal = {Phys. Rev. E},
Year = {1995},
Note = {\arXiv{chao-dyn/9507003}},
Pages = {2388--2391},
Volume = {52},
DOI = {10.1103/PhysRevE.52.2388}
}
@Book{hao90b,
Title = {Chaos {II}},
Author = {B.-L. Hao},
Publisher = {World Scientific},
Year = {1990},
Address = {Singapore}
}
@Book{hao98,
Title = {Applied Symbolic Dynamics and Chaos},
Author = {B.-L. Hao and W.-M. Zheng},
Publisher = {World Scientific},
Year = {1998},
Address = {Singapore}
}
@Article{Harter69,
author = {Harter, W. G.},
title = {Algebraic theory of ray representations of finite groups},
journal = {J. Math. Phys.},
year = {1969},
volume = {10},
pages = {739--752},
doi = {10.1063/1.1664901},
}
@Article{Harter78,
author = {Harter, W. G. and Dos Santos, N.},
title = {Double-group theory on the half-shell and the two-level system. {I. Rotation} and half-integral spin states},
journal = {Am. J. Phys.},
year = {1978},
volume = {46},
pages = {251--263},
doi = {10.1119/1.11134},
}
@Book{Harter93,
title = {{Principles of Symmetry, Dynamics, and Spectroscopy}},
publisher = {Wiley},
year = {1993},
author = {Harter, W. G.},
address = {New York},
}
@Book{hartmanb,
title = {{Ordinary Differential Equations}},
publisher = {Wiley},
year = {1964},
author = {P. Hartman},
address = {New York},
}
@InProceedings{HDB92,
Title = {Intermittent turbulence in plane and circular {Couette} flow},
Author = {J. Hegseth and F. Daviaud and P. Berge},
Booktitle = {Ordered and Turbulent Patterns in Taylor-{Couette} Flow},
Year = {1992},
Address = {New York},
Editor = {C. D. Andereck and F. Hayot},
Pages = {159--166},
Publisher = {Plenum}
}
@Article{Hei24,
Title = {{\"U}ber Stabilit{\"a}t und Turbulenz von Fl{\"a}teitsstr{\"a}ser},
Author = {W. Heisenberg},
Journal = {Ann. Phys. Lpz.},
Year = {1924},
Note = {fix volume number},
Pages = {577},
Volume = {74 44}
}
@Article{Heisen48,
author = {Heisenberg, W.},
title = {{Zur statistischen Theorie der Turbulenz}},
journal = {Z. Phys.},
year = {1948},
volume = {124},
pages = {628--657},
note = {{On the statistical theory of turbulence, translation by M. L. Mahler, National Advisory Committee for Aeronautics, Technical memorandum, no. 1431}},
doi = {10.1007/978-3-642-61659-4_6},
}
@Article{Heisen48a,
Title = {On the theory of statistical and isotropic turbulence},
Author = {Heisenberg, W.},
Journal = {Proc. Roy. Soc. A},
Year = {1948},
Pages = {402--406},
Volume = {195}
}
@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},
Eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S021812740701821X}
}
@Article{HeKaPo08,
author = {E. J. Heller and L. Kaplan and F. Pollmann},
title = {Inflationary dynamics for matrix eigenvalue problems},
journal = {Proc. Natl. Acad. Sci. USA},
year = {2008},
volume = {105},
pages = {7631},
note = {\arXiv{0712.4093}},
doi = {10.1073/pnas.0801047105},
}
@Article{hell78,
author = {R. Helleman and T. Bountis},
title = {Periodic solutions of arbitrary period, variational methods},
journal = {LNP},
year = {1978},
volume = {93},
pages = {353},
doi = {10.1007/bfb0021758},
}
@Article{HenCviLip14,
Title = {Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system},
Author = {J. M. Heninger and D. Lippolis and P. Cvitanovi\'c},
Journal = {Phys. Rev. E},
Year = {2015},
Note = {\arXiv{1507.00462}},
Pages = {062922},
Volume = {92},
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{HenningsonPF94,
author = {D. Henningson and S. Reddy},
title = {On the role of linear mechanisims in transition to turbulence},
journal = {Phys. Fluids},
year = {1994},
volume = {6},
pages = {1396--1398},
doi = {10.1063/1.868251},
}
@Book{henonrtb2,
title = {{Generating Families in the Restricted Three-Body Problem: {II}. Quantitative Study of Bifurcations}},
publisher = {Springer},
year = {2001},
author = {M. H{\'e}non},
address = {New York}
}
@Article{heron87,
author = {J. M. Ghidaglia and B. H{\'e}non},
title = {Dimension of the attractors associated to the {Ginzburg-Landau} partial differential equation},
journal = {Physica D},
year = {1987},
volume = {28},
pages = {282--304},
doi = {10.1016/0167-2789(87)90020-0},
}
@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}
}
@Article{hhrugh92,
author = {H. H. Rugh},
title = {The correlation spectrum for hyperbolic analytic maps},
journal = {Nonlinearity},
year = {1992},
volume = {5},
pages = {1237},
doi = {10.1088/0951-7715/5/6/003},
}
@Article{hhsys,
author = {M. H{\'e}non and C. Heiles},
title = {The applicability of the third integral of motion: {Some} numerical experiments},
journal = {Astron. J.},
year = {1964},
volume = {69},
pages = {73},
doi = {10.1086/109234},
}
@Article{Hilbert93,
Title = {\"Uber 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}
}
@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{HK82,
Title = {Ergodic properties of invariant measures for piecewise monotonic transformations},
Author = {Hofbauer, F. and Keller, G.},
Journal = {Math. Z.},
Year = {1982},
Pages = {119--140},
Volume = {180},
DOI = {10.1007/BF01215004}
}
@Article{HM90,
author = {Huerre, P. and Monkewitz, P. A.},
title = {Local and global instabilities in spatially developing flows},
journal = {Ann. Rev. Fluid Mech.},
year = {1990},
volume = {22},
pages = {473--537},
doi = {10.1146/annurev.fl.22.010190.002353}
}
@Article{HNks86,
author = {J. M. Hyman and B. Nicolaenko},
title = {The {Kuramoto-Sivashinsky} equation: a bridge between {PDE}'s and dynamical systems},
journal = {Physica D},
year = {1986},
volume = {18},
pages = {113--126},
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},
doi = {10.1016/0167-2789(86)90136-3},
}
@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{hof2008,
author = {Hof, B. and De Lozar, A. and Kuik, D.J. and Westerweel, J.},
title = {Repeller or attractor? {Selecting} the dynamical model for the onset of turbulence in pipe flow},
journal = {Phys. Rev. Lett.},
year = {2008},
volume = {101},
pages = {214501},
doi = {10.1103/physrevlett.101.214501},
}
@Book{hoffman:kunze,
title = {{Linear Algebra}},
publisher = {Prentice-Hall},
year = {1971},
author = {K. Hoffman and R. Kunze},
address = {Englewood Cliffs, NJ},
edition = {Second}
}
@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}
}
@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{hopf48,
Title = {A mathematical example displaying features of turbulence},
Author = {E. Hopf},
Journal = {Commun. Pure Appl. Math.},
Year = {1948},
Pages = {303--322},
Volume = {1},
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},
}
@Unpublished{HopKan14,
author = {A. Blum and J. Hopcroft and R. Kannan},
title = {{Foundations of Data Science}},
note = {In preparation},
year = {2017},
url = {https://www.cs.cornell.edu/jeh/book.pdf},
}
@Article{Horiuti,
author = {K. Horiuti},
title = {Comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow},
journal = {J. Comput. Physics},
year = {1987},
volume = {71},
pages = {343--370},
doi = {10.1016/0021-9991(87)90035-0},
}
@Book{hoyll06,
title = {{Pattern Formation: An Introduction to Methods}},
publisher = {Cambridge Univ. Press},
year = {2006},
author = {R. Hoyle},
address = {Cambridge}
}
@Article{HRCLOL11,
author = {J. Herault and F. Rincon and C. Cossu and G. I. Ogilvie and P.-Y. Longaretti},
title = {Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows},
journal = {Phys. Rev. E},
year = {2011},
volume = {84},
pages = {036321},
doi = {10.1103/physreve.84.036321},
}
@Article{HSGsize98,
author = {M. C. Strain and H. S. Greenside},
title = {Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable media},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {80},
pages = {2306--2309},
doi = {10.1103/physrevlett.80.2306},
}
@Article{hughes98,
author = {Hughes, S. and Randriamampianina, A.},
title = {An improved projection scheme applied to pseudospectral methods for the incompressible {Navier-Stokes} equations},
journal = {Int. J. Numer. Meth. Fluids},
year = {1998},
volume = {28},
pages = {501--521},
doi = {10.1002/(SICI)1097-0363(19980915)28:3<501::AID-FLD730>3.0.CO;2-S}
}
@Article{Hurt93,
Title = {Zeta functions and periodic orbit theory: {A} review},
Author = {Hurt, N. E.},
Journal = {Results Math.},
Year = {1993},
Pages = {55--120},
Volume = {23},
DOI = {10.1007/BF03323131}
}
@Article{Hurt93a,
author = {Hurt, N. E.},
title = {Three topics on periodic orbit theory: {A} review},
journal = {Rev. Math. Phys.},
year = {1993},
volume = {5},
pages = {713--733},
doi = {10.1142/s0129055x9300022x},
}
@Article{Hussain83,
author = {Hussain, A. K. M. F.},
title = {Coherent structures---reality and myth},
journal = {Phys. Fluids},
year = {1983},
pages = {2816--2850},
doi = {10.1063/1.864048}
}
@Book{Huyg1673,
title = {{L'Horloge \`a pendule}},
publisher = {Swets \& Zeitlinger},
year = {1673},
author = {C. Huygens},
address = {Amsterdam}
}
@Article{HwWiCo16,
author = {Hwang, Y. and Willis, A. P. and Cossu, C.},
title = {Invariant solutions of minimal large-scale structures in turbulent channel flow for {$Re_{\tau}$} up to 1000},
journal = {J. Fluid Mech.},
year = {2016},
volume = {802},
pages = {R1},
doi = {10.1017/jfm.2016.470}
}
@Book{ince,
title = {{Ordinary Differential Equations}},
publisher = {Dover},
year = {1956},
author = {E. L. Ince},
address = {New York}
}
@Book{infdymnon,
title = {{Infinite-Dimensional Dynamical Systems in Mechanics and Physics}},
publisher = {Springer},
year = {1988},
author = {R. Temam},
address = {New York}
}
@Book{isham99,
title = {{Modern Differential Geometry for Physicists}},
publisher = {World Scientific},
year = {1999},
author = {C. J. Isham},
address = {Singapore}
}
@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},
ISSN = {0022-0396}
}
@Article{IshNak00,
author = {Ishimura, N. and Nakamura, M.},
title = {Nonexistence of monotonic solutions of some third-order {ODE} relevant to the {Kuramoto-Sivashinsky} equation},
journal = {Taiwanese J. Math.},
year = {2000},
volume = {4},
pages = {621--625},
url = {http://journal.tms.org.tw/index.php/TJM/article/view/1296},
}
@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 = {701--714},
doi = {10.1143/jpsj.70.703},
}
@Article{ItGe09,
author = {Itano, T. and Generalis, S. C.},
title = {Hairpin vortex solution in planar {Couette} flow: {A} tapestry of knotted vortices},
journal = {Phys. Rev. Lett.},
year = {2009},
volume = {102},
pages = {114501},
doi = {10.1103/physrevlett.102.114501},
}
@Book{jackson89,
title = {{Perspectives of nonlinear dynamics: Vol. 1 and 2}},
publisher = {Cambridge Univ. Press},
year = {1989},
author = {Jackson, E. A.},
address = {Cambridge}
}
@Article{Javier_shear,
author = {F. J. Beron-Vera and M. J. Olascoaga and M. G. Brown and H. Kocak and I. I. Rypina},
title = {Invariant-tori-like {Lagrangian} coherent structures in geophysical flows},
journal = {Chaos},
year = {2010},
volume = {20},
pages = {017514},
doi = {10.1063/1.3271342},
}
@Article{JBB84,
author = {Jensen, M. H. and Bak, P. and Bohr, T.},
title = {Transition to chaos by interaction of resonances in dissipative systems. {I. Circle} maps},
journal = {Phys. Rev. A},
year = {1984},
volume = {30},
pages = {1960--1969},
doi = {10.1103/physreva.30.1960},
}
@Book{JBG97,
title = {{Poincar{\'e} and the Tree Body Problem}},
publisher = {AMS},
year = {1997},
author = {J. Barrow-Green},
address = {Providence R.I.}
}
@Book{jeffb,
title = {{Methods of Mathematical Physics}},
publisher = {Cambridge Univ. Press},
year = {1999},
author = {H. Jeffreys and B. Jeffreys},
address = {Cambridge}
}
@Article{JeongJFM97,
Title = {Coherent structures near the wall in a turbulent boundary layer},
Author = {J. Jeong and F. Hussain and W. Schoppa and J. Kim},
Journal = {J. Fluid Mech.},
Year = {1997},
Pages = {185--214},
Volume = {332}
}
@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--123},
doi = {10.1017/s0022112086000551},
}
@Book{jhos,
title = {{Oscillations in Nonlinear Systems}},
publisher = {McGraw-Hill},
year = {1963},
author = {J. K. Hale},
address = {New York}
}
@Article{jimenez07,
author = {Jim{\'e}nez, J. and Moser, R. D.},
title = {What are we learning from simulating wall turbulence?},
journal = {Phil. Trans. Royal Soc. A},
year = {2007},
volume = {367},
pages = {715--732},
doi = {10.1098/rsta.2006.1943}
}
@Article{Jimenez2011,
author = {J. Jim{\'e}nez},
title = {Cascades in wall-bounded turbulence},
journal = {Ann. Rev. Fluid Mech.},
year = {2011},
volume = {44},
pages = {27--45},
doi = {10.1146/annurev-fluid-120710-101039}
}
@Article{Jimenez2012,
author = {A. Lozano-Dur{\'a}n and O. Flores and J. Jim{\'e}nez},
title = {The three-dimensional structure of momentum transfer in turbulent channels},
journal = {J. Fluid Mech.},
year = {2012},
volume = {694},
pages = {100--130},
month = mar,
doi = {10.1017/jfm.2011.524}
}
@Article{JimenezJFM01,
author = {J. Jim{\'e}nez and M. P. Simens},
title = {Low-dimensional dynamics of a turbulent wall flow},
journal = {J. Fluid Mech},
year = {2001},
volume = {435},
pages = {81--91},
doi = {10.1017/S0022112001004050}
}
@Article{JKSNS05,
author = {J. Jim{\'e}nez and G. Kawahara and M. P. Simens and M. Nagata and M. Shiba},
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}
}
@Article{JM91,
Title = {The minimal flow unit in near-wall turbulence},
Author = {Jim{\'e}nez, J. and Moin, P.},
Journal = {J. Fluid Mech.},
Year = {1991},
Pages = {213--240},
Volume = {225},
DOI = {10.1017/S0022112091002033}
}
@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. Physics},
year = {2004},
volume = {199},
pages = {221--259},
doi = {10.1016/j.jcp.2004.02.009},
}
@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}
}
@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--148},
doi = {10.1115/1.3630068},
}
@Article{K31,
author = {B. O. Koopman},
title = {Hamiltonian systems and transformations in {Hilbert} space},
journal = {Proc. Natl. Acad. Sci.},
year = {1931},
volume = {17},
pages = {315--318},
doi = {10.1073/pnas.17.5.315},
}
@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},
Volume = {730},
DOI = {10.1007/BFb0064320}
}
@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}},
publisher = {Cambridge Univ. Press},
year = {1995},
author = {A. Katok and B. Hasselblatt},
address = {Cambridge}
}
@Article{KaUhlVeen12,
author = {G. Kawahara and M. Uhlmann and L. van Veen},
title = {The significance of simple invariant solutions in turbulent flows},
journal = {Ann. Rev. Fluid Mech.},
year = {2012},
volume = {44},
pages = {203--225},
doi = {10.1146/annurev-fluid-120710-101228},
}
@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. Comp. Phys.},
year = {2007},
volume = {225},
pages = {382--407},
doi = {10.1016/j.jcp.2006.12.003},
}
@Article{Kaw05,
author = {G. Kawahara},
title = {Laminarization of minimal plane {Couette} flow: {Going} beyond the basin of attraction of turbulence},
journal = {Phys. Fluids},
year = {2005},
volume = {17},
pages = {041702},
doi = {10.1063/1.1890428},
}
@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--300},
abstract = {Two time-periodic solutions are found in a 3-d
constrained plane Couette flow, multishooting method being used.
The turbulent state mainly follows the periodic orbit with strong
variations. The gentle one is related to the bursting behavior of
the system. Heteroclinic orbits between these two periodic orbits
are found.},
doi = {10.1017/s0022112001006243},
}
@Article{KawKida05,
Title = {Elementary coherent structures in turbulent flows},
Author = {G. Kawahara and S. Kida},
Journal = {Parity},
Year = {2005},
Pages = {12},
Volume = {20}
}
@Article{KawKiVeen06,
author = {G. Kawahara and S. Kida and L. van Veen},
title = {Unstable periodic motion in turbulent flows},
journal = {Nonlinear Process in Geophysics},
year = {2006},
volume = {13},
pages = {499--507},
doi = {10.5194/npg-13-499-2006},
}
@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}
}
@Article{Kazantsev01,
author = {Kazantsev, E.},
title = {Sensitivity of the attractor of the barotropic ocean model to external influences: {Approach} by unstable periodic orbits},
journal = {Nonlinear Processes in Geophysics},
year = {2001},
volume = {8},
pages = {281--300},
doi = {10.5194/npg-8-281-2001},
}
@Article{Kazantsev01a,
Title = {Sensitivity of attractor to external influences: {Approach} by unstable periodic orbits},
Author = {Kazantsev, E.},
Journal = {Chaos, Solitons \&\ Fractals},
Year = {2001},
Pages = {1989--2005},
Volume = {12},
DOI = {10.1016/S0960-0779(00)00154-5}
}
@Article{Kazantsev98,
Title = {Unstable periodic orbits and attractor of the barotropic ocean model},
Author = {Kazantsev, E.},
Journal = {Nonlinear Processes in Geophysics},
Year = {1998},
Pages = {193--208},
Volume = {5},
DOI = {10.5194/npg-5-193-1998}
}
@Article{KDKSEH14,
Title = {Complexity of localised coherent structures in a boundary-layer flow},
Author = {Khapko, T. and Duguet, Y. and Kreilos, T. and Schlatter, P. and Eckhardt, B. and Henningson, D. S.},
Journal = {Eur. Phys. J. E},
Year = {2014},
Pages = {32},
Volume = {37},
DOI = {10.1140/epje/i2014-14032-3}
}
@Book{kellbv,
title = {{Numerical Methods for Two-Point Boundary-Value Problems}},
publisher = {Dover},
year = {1992},
author = {H. B. Keller},
address = {New York}
}
@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 Press}
}
@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 Press},
doi = {10.1016/b978-0-12-208360-0.50009-7},
}
@Book{Kelley,
title = {{Solving Nonlinear Equations with {Newton}'s Method}},
publisher = {SIAM},
year = {2003},
author = {C. T. Kelley},
address = {Philadelphia},
isbn = {0898715466},
pages = {118}
}
@Incollection{KerOli11,
Title = {The ever-elusive blowup in the mathematical description of fluids},
Author = {Kerr, R. M. and Oliver, M.},
Booktitle = {An Invitation to Mathematics},
Publisher = {Springer},
Year = {2011},
Address = {New York},
Editor = {Schleicher, D. and Lackmann, M.},
Pages = {137--164},
DOI = {10.1007/978-3-642-19533-4_10},
ISBN = {978-3-642-19532-7}
}
@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}
}
@Article{KeTu06,
Title = {Recurrence of travelling waves in transitional pipe flow},
Author = {Kerswell, R. R. and Tutty, O.R.},
Journal = {J. Fluid Mech.},
Year = {2007},
Pages = {69--102},
Volume = {584},
DOI = {10.1017/S0022112007006301}
}
@Article{kev01ks,
author = {M. E. Johnson and M. S. Jolly and I. G. Kevrekidis},
title = {The {O}seberg transition: visualization of global bifurcations for the {Kuramoto-Sivashinsky} equation},
journal = {Int. J. Bifurc. Chaos},
year = {2001},
volume = {11},
pages = {1--18},
doi = {10.1142/s0218127401001979},
}
@Article{Kim03,
Title = {Control of turbulent boundary layers},
Author = {J. Kim},
Journal = {Phys. Fluids},
Year = {2003},
Pages = {1093--1105},
Volume = {15}
}
@Article{kim10,
author = {J. H. Kim and M. Nishihara and I. V. Adamovich and M. Samimy and S. V. Gorbatov and F. V. Pliavaka},
title = {Development of localized arc-filament {RF} plasma actuators for high-speed and high {Reynolds} number flow control},
journal = {Exp. Fluids},
year = {2010},
volume = {49},
pages = {497--511},
doi = {10.1007/s00348-010-0819-y},
}
@Article{kim99,
author = {K. C. Kim and R. J. Adrian},
title = {Very large-scale motion in the outer layer},
journal = {Phys. Fluids},
year = {1999},
volume = {11},
pages = {417--422},
doi = {10.1063/1.869889},
}
@Article{kirby_reconstructing_1992,
author = {M. Kirby and D. Armbruster},
title = {Reconstructing phase space from {PDE} simulations},
journal = {Z. Angew. Math. Phys.},
year = {1992},
volume = {43},
pages = {999--1022},
abstract = {We propose the {Karhunen-Lo\'eve} {(K-L)} decomposition as a tool
to analyze complex spatio-temporal structures in {PDE} simulations
in terms of concepts from dynamical systems theory. Taking the {Kuramoto-Sivashinsky}
equation as a model problem we discuss the {K-L} decomposition for
4 different values of its bifurcation parameter a. We distinguish
two modes of using the {K-L} decomposition: As an analytic and synthetic
tool respectively. Using the analytic mode we find unstable fixed
points and stable and unstable manifolds in a parameter regime with
structurally stable homoclinic orbits (a=17.75). Choosing the data
for a {K-L} analysis carefully by restricting them to certain burst
events, we can analyze a more complicated intermittent regime at
a=68. We establish that the spatially localized oscillations around
a so called `strange' fixed point which are considered as fore-runners
of spatially concentrated zones of turbulence are in fact created
by a very specific limit cycle (a=83.75) which, for a=87, bifurcates
into a modulated traveling wave. Using the {K-L} decomposition synthetically
by determining an optimal Galerkin system, we present evidence that
the {K-L} decomposition systematically destroys dissipation and leads
to blow up solutions.},
doi = {10.1007/bf00916425},
}
@InProceedings{KK05,
author = {G. Kawahara and S. Kida and M. Nagata},
title = {Unstable periodic motion in plane {Couette} system: {The} skeleton of turbulence},
booktitle = {One hundred years of boundary layer research},
year = {2005},
address = {Dordrecht},
publisher = {Kluwer},
doi = {10.1007/978-1-4020-4150-1_40},
}
@Article{KKR71,
Title = {The production of turbulence near a smooth wall in a turbulent boundary layer},
Author = {Kim, H.T. and Kline, S.J. and Reynolds, W.C.},
Journal = {J. Fluid Mech.},
Year = {1971},
Pages = {133--160},
Volume = {50}
}
@Article{kleinman10,
author = {R. R. Kleinman and D. J. Bodony and J. B. Freund},
title = {Shear-flow excitation mechanisms of recessed localized arc-filament plasma actuators},
journal = {Phys. Fluids},
year = {2010},
volume = {22},
pages = {116103},
doi = {10.1063/1.3507317},
}
@InProceedings{Kleiser80,
author = {L. Kleiser and U. Schumann},
title = {Treatment of incompressibility and boundary conditions in 3-{D} numerical spectral simulations of plane channel flows},
booktitle = {Proc. 3\textsuperscript{rd} 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{klewicki95,
Title = {Viscous sublayer flow visualizations at {$R_{\theta} \sim 1500000$}},
Author = {Klewicki, J. C. and Metzger, M. M. and Kelner, E. and E. M. Thurlow},
Journal = {Phys. Fluids},
Year = {1995},
Pages = {857},
Volume = {7}
}
@Article{KLH94,
author = {G. Kreiss and A. Lundbladh and D. S. Henningson},
title = {Bounds for threshold amplitudes in subcritical shear flows},
journal = {J. Fluid Mech.},
year = {1994},
volume = {270},
pages = {175--198},
doi = {10.1017/s0022112094004234},
}
@Article{KMM87,
Title = {Turbulence statistics in fully developed channel flow at low {Reynolds} number},
Author = {J. Kim and P. Moin and R. Moser},
Journal = {J. Fluid Mech.},
Year = {1987},
Pages = {133--166},
Volume = {177}
}
@Article{knobloch2015,
author = {Knobloch, E.},
title = {Spatial localization in dissipative systems},
journal = {Ann. Math.. Rev. Condens. Matter Phys.},
year = {2015},
volume = {6},
pages = {325--359},
doi = {10.1146/annurev-conmatphys-031214-014514}
}
@Article{KNSks90,
author = {I. G. Kevrekidis and B. Nicolaenko and J. C. Scovel},
title = {Back in the saddle again: a computer assisted study of the {Kuramoto-Sivashinsky} equation},
journal = {SIAM J. Appl. Math.},
year = {1990},
volume = {50},
pages = {760--790},
doi = {10.1137/0150045},
}
@Article{Koch89,
author = {W. Koch},
title = {Direct resonances in {Orr-Sommerfeld} problems},
journal = {Acta Mechanica},
year = {1986},
volume = {59},
pages = {11},
doi = {10.1007/bf01177057},
}
@Article{kolm91,
author = {A. N. Kolmogorov},
title = {The local structure of turbulence in incompressible viscous fluid for very large {Reynolds} numbers},
journal = {Proc. R. Soc. Lond. A},
year = {1991},
volume = {434},
pages = {9--13},
}
@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{kooknewt,
author = {H-T Kook and J. D. Meiss},
title = {Application of {N}ewton's method to {L}agrangian mappings},
journal = {Physica D},
year = {1989},
volume = {36},
pages = {317--326},
abstract = {An algorithm of {N}ewton's method is presented to find
periodic orbits for {L}agrangian mappings. The method is based on
block-diagonalization of the Hessian Matrix of the action function.},
doi = {10.1016/0167-2789(89)90087-0},
}
@InProceedings{KraOsi00,
author = {B. Krauskopf and H. M. Osinga},
title = {Investigating torus bifurcations in the forced {Van der Pol} oscillator},
booktitle = {{Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems}},
year = {2000},
editor = {E. Doedel and L. Tuckerman},
pages = {199--208},
address = {New York},
publisher = {Springer},
isbn = {9781461212089},
}
@Article{Kras04,
author = {I. Krasikov and G. J. Rodgers and C. E. Tripp},
title = {Growing random sequences},
journal = {J. Phys. A},
year = {2004},
volume = {37},
pages = {2365--2370},
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.},
doi = {10.1088/0305-4470/37/6/026},
}
@Article{KreEck12,
Title = {Periodic orbits near onset of chaos in plane {Couette} flow},
Author = {T. Kreilos and B. Eckhardt},
Journal = {Chaos},
Year = {2012},
Pages = {047505},
Volume = {22},
DOI = {10.1063/1.4757227}
}
@PhdThesis{Kreilos14,
author = {Kreilos, T.},
title = {{Turbulence Transition in Shear Flows and Dynamical Systems Theory}},
school = {Philipps-Universit{\"a}t Marburg},
year = {2014},
note = {http://archiv.ub.uni-marburg.de/diss/z2014/0356/pdf/dtk.pdf}
}
@Article{KrGiSc16,
Title = {Localized travelling waves in the asymptotic suction boundary layer},
Author = {T. Kreilos and J. F. Gibson and T. M. Schneider},
Journal = {J. Fluid Mech.},
Year = {2016},
Pages = {R3},
Volume = {795},
DOI = {10.1017/jfm.2016.242}
}
@Article{KRSR67,
author = {Kline, S. J. and {R}eynolds, W. C. and Schraub, F. A. and Runstadler, P. W.},
title = {The structure of turbulent boundary layers},
journal = {J. Fluid Mech.},
year = {1967},
volume = {30},
pages = {741--773},
doi = {10.1017/s0022112067001740},
}
@Article{kruskal62,
author = {M. Kruskal},
title = {Asymptotic theory of {Hamiltonian} and other systems with all solutons nearly periodic},
journal = {J. Math. Phys.},
year = {1962},
volume = {3},
pages = {806},
abstract = {Asymptotic expansion to all orders. A systematic way to construct the adiabatic invariants.},
doi = {10.1063/1.1724285},
}
@Article{kruskal65,
author = {N. J. Zabusky and M. D. Kruskal},
title = {Interaction of ``solitons'' in a collisionless plasma and the recurrence of initial states},
journal = {Phys. Rev. Lett.},
year = {1965},
volume = {15},
pages = {240--243},
doi = {10.1103/PhysRevLett.15.240}
}
@Article{KrVeSchEck12,
Title = {Edge states for the turbulence transition in the asymptotic suction boundary layer},
Author = {Kreilos, T. and Veble, G. and Schneider, T. M. and Eckhardt, B.},
Journal = {J. Fluid M.},
Year = {2013},
Note = {\arXiv{1209.0593}},
Pages = {100--122},
Volume = {726},
DOI = {10.1017/jfm.2013.212}
}
@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{ks04com,
author = {A.-K. Kassam and L. N. Trefethen},
title = {Fourth-order time stepping for stiff {PDE}s},
journal = {SIAM J. Sci. Comp.},
year = {2005},
volume = {26},
pages = {1214--1233},
abstract = {A contour integral method is presented to evaluate
accurately the matrix functions with removable singularities.},
doi = {10.1137/s1064827502410633},
}
@Article{kschang86,
author = {H.-C. Chang},
title = {Travelling waves on fluid interfaces: {N}ormal form analysis of the {K}uramoto-{S}ivashisky equation},
journal = {Phys. Fluids},
year = {1986},
volume = {29},
pages = {3142},
abstract = {The lowest order normal form analysis is give to the KSe and the approximate analytical wavelength-amplitude and wavespeed-amplitude relation are given. They agree quite well with the numerical calculations.},
doi = {10.1063/1.865965},
}
@Article{ksgreene88,
author = {J. M. Greene and J.-S. Kim},
title = {The steady states of the {Kuramoto-Sivashinsky} equation},
journal = {Physica D},
year = {1988},
volume = {33},
pages = {99--120},
doi = {10.1016/s0167-2789(98)90013-6},
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.},
}
@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},
DOI = {10.1016/0167-2789(91)90177-B}
}
@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{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}
}
@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{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},
Abstract = {For c=1, the existence of two periodic orbits and two
heteroclinic orbits are proved and suggestions for
proving the existence of more complicated orbits are
given.},
DOI = {10.1016/0022-0396(89)90134-4}
}
@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},
Abstract = {For small c>0, at least one odd periodic solution
exists. For any c>0, there existes no monotone bounded
travelling wave solution. The normal form analysis may
not be able to give correct results to all orders.},
DOI = {10.1016/0022-0396(92)90143-B}
}
@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{KT84,
author = {L. Kadanoff and C. Tang},
title = {Escape rate from strange repellers},
journal = {Proc. Natl. Acad. Sci. USA},
year = {1984},
volume = {81},
pages = {1276--1279},
doi = {10.1073/pnas.81.4.1276},
}
@Article{ku,
author = {Y. Kuramoto and T. Tsuzuki},
title = {Persistent propagation of concentration waves in dissipative media far from thermal equilibrium},
journal = {Progr. Theor. Phys.},
year = {1976},
volume = {55},
pages = {365},
abstract = {The KSe is derived through the CGLe near the bifurcation
point. Some scaling argument is used to sort out the domiant terms.},
doi = {10.1143/ptp.55.356},
}
@Article{KuKuKnMo04,
Title = {Catastrophe theoretic classification of nonlinear oscillators},
Author = {A. Yu. Kuznetsova and A. P. Kuznetsov and C. Knudsen and E. Mosekilde},
Journal = {Int. J. Bif. Chaos},
Year = {2004},
Pages = {1241--1266},
Volume = {14},
DOI = {10.1142/S0218127404009995}
}
@Book{kura84tur,
Title = {Chemical Oscillations, Waves and Turbulence},
Author = {Y. Kuramoto},
Publisher = {Springer},
Year = {1984},
Address = {Berlin}
}
@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},
}
@Article{KZ,
author = {L. Kleiser and T. A. Zang},
title = {Numerical simulation of transition in wall-bounded shear flows},
journal = {Ann. Rev. Fluid Mech.},
year = {1991},
volume = {23},
pages = {495--537},
doi = {10.1146/annurev.fluid.23.1.495},
}
@Book{Lax02,
title = {{Functional Analysis}},
publisher = {Wiley},
year = {2002},
author = {P. D. Lax},
address = {New York},
isbn = {9781118626740},
}
@Article{Lagha07,
Title = {Modeling of plane {Couette} flow. {II. On} the spreading of a turbulent spot},
Author = {Lagha, M.},
Journal = {Phys. Fluids},
Year = {2007},
Pages = {4108},
Volume = {19},
DOI = {10.1063/1.2793143}
}
@Article{Lagha07b,
Title = {Modeling transitional plane {Couette} flow},
Author = {M. Lagha and P. Manneville},
Journal = {Eur. Phys. J. B},
Year = {2007},
Pages = {433--447},
Volume = {58},
DOI = {10.1140/epjb/e2007-00243-y}
}
@Article{LagMann07,
Title = {Modeling of plane {Couette} flow. {I. Large} scale flow around turbulent spots},
Author = {Lagha, M. and {Manneville}, P.},
Journal = {Phys. Fluids},
Year = {2007},
Pages = {4105},
Volume = {19},
DOI = {10.1063/1.2768946}
}
@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{lamb98,
author = {J. S. W. Lamb and J. A. G. Roberts},
title = {Time reversal symmetry in dynamical systems: {A} survey},
journal = {Physica D},
year = {1998},
volume = {112},
pages = {1},
doi = {10.1016/s0167-2789(97)00199-1},
}
@Article{lanCvit07,
Title = {Unstable recurrent patterns in {Kuramoto-Sivashinsky} dynamics},
Author = {Lan, Y. and Cvitanovi{\'c}, P.},
Journal = {Phys. Rev. E},
Year = {2008},
Addendum = {\arXiv{0804.2474}},
Pages = {026208},
Volume = {78},
DOI = {10.1103/PhysRevE.78.026208}
}
@Article{landau44,
author = {L. D. Landau},
title = {On the problem of turbulence},
journal = {Akad. Nauk. Doklady},
year = {1944},
volume = {44},
pages = {339},
doi = {10.1016/b978-0-08-010586-4.50057-2},
}
@Book{Landau59c,
Title = {Quantum Mechanics},
Author = {L.D. Landau and E.M. Lifshitz},
Publisher = {Pergamon Press},
Year = {1959},
Address = {Oxford}
}
@Article{lanmaw03,
author = {Y. Lan and N. Garnier and P. Cvitanovi{\'c}},
title = {Stationary modulated-amplitude waves in the 1{D} complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {2004},
volume = {188},
pages = {193--212},
doi = {10.1016/s0167-2789(03)00289-6},
}
@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},
Note = {{\tt ChaosBook.org/projects/theses.html}}
}
@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},
note = {\arXiv{nlin.CD/0308008}},
doi = {10.1103/physreve.69.016217},
}
@Book{lapack,
Title = {{LAPACK} Users' Guide},
Author = {Anderson, E. and Bai, Z. and Bischof, C. and Blackford, S. and Demmel, J. and Dongarra, J. and Du Croz, J. and Greenbaum, A. and Hammarling, S. and McKenney, A. and Sorensen, D.},
Publisher = {Society for Industrial and Applied Mathematics},
Year = {1999},
Address = {Philadelphia},
Edition = {Third},
ISBN = {0-89871-447-8 (paperback)}
}
@Article{laquey74,
author = {R. E. La Quey 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},
}
@Article{lathrop92,
author = {D. P. Lathrop and J. Fineberg and H. L. Swinney},
title = {Transition to shear-driven turbulence in {Couette-Taylor} flow},
journal = {Phys. Rev. A.},
year = {1992},
volume = {46},
pages = {6390},
doi = {10.1103/physreva.46.6390},
}
@Book{latt,
Title = {Quantum Fields on the Computer},
Author = {M. Creutz},
Publisher = {World Scientific},
Year = {1992},
Address = {Singapore}
}
@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 = {42E},
pages = {C735--C751},
abstract = {A lattice refinement scheme is proposed based on the
linear approximation of a given map. Jacobian matrix is not
calculated directly but inferred from the neighboring points.},
doi = {10.21914/anziamj.v42i0.619},
}
@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}
}
@Article{lau92,
Title = {The cocoon bifurcations in three-dimensional systems with two fixed points},
Author = {Y.-T. Lau},
Journal = {Int. J. Bifur. Chaos},
Year = {1992},
Pages = {543--558},
Volume = {2},
DOI = {10.1142/S0218127492000690}
}
@Incollection{lauw86,
Title = {Two-dimensional iterative maps},
Author = {H. A. Lauwerier},
Booktitle = {Chaos},
Publisher = {Princeton Univ. Press},
Year = {1986},
Address = {Princeton},
Editor = {V. Holden},
Pages = {58--96},
ISBN = {9780691610535}
}
@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},
Note = {\arXiv{nlin.CD/0508026}},
Pages = {046206},
Volume = {74}
}
@Article{lee01,
author = {K. Lee and L. Cortelezzi and J. Kim and J. L. Speyer},
title = {Application of reduced order controller to turbulent flows for drag reduction},
journal = {Phys. Fluids},
year = {2001},
volume = {13},
pages = {1321},
doi = {10.1063/1.1359420},
}
@Article{Lega:holes,
author = {J. Lega},
title = {Traveling hole solutions of the complex {Ginzburg Landau} equation: a review},
journal = {Physica D},
year = {2001},
volume = {269},
pages = {152--153},
doi = {10.1016/s0167-2789(01)00174-9},
}
@Article{levenberg44,
author = {Levenberg, K},
title = {A method for the solution of certain non-linear problems in least squares},
journal = {Quart. Appl. Math.},
year = {1944},
volume = {2},
number = {2},
pages = {164--168},
doi = {10.1090/qam/10666},
}
@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},
note = {\arXiv{chao-dyn/9810022}},
doi = {10.1103/physrevlett.81.4349},
}
@Incollection{LHR94,
Title = {Threshold amplitudes for transition in channel flows},
Author = {A. Lundbladh and and S. Henningson and S. C. Reddy},
Booktitle = {Turbulence and Combustion},
Publisher = {Kluwer},
Year = {1994},
Address = {Dordrecht},
Editor = {Hussaini, M.Y. and Gatski, T.B. and Jackson, T.L.}
}
@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},
}
@Book{liede,
Title = {Applications of {Lie} Groups to Differential Equations},
Author = {P. J. Olver},
Publisher = {Spring-Verlag},
Year = {1998},
Address = {New York},
Series = {GTM},
Volume = {107}
}
@Misc{LiHuCa10,
author = {Libert, A.-S. and Hubaux, C. and Carletti, T.},
title = {Symplectic integration of deviation vectors and chaos determination. Application to the {H\'enon-Heiles} model and to the restricted three-body problem},
year = {2010},
url = {https://arxiv.org/abs/1005.5611},
}
@Article{LiMa83,
Title = {Analysis methods for results in gamma-ray astronomy},
Author = {Li, T.-P. and Ma, Y.-Q.},
Journal = {Astrophys. J.},
Year = {1983},
Pages = {317--324},
Volume = {272},
DOI = {10.1086/161295}
}
@Article{LiMoRo01,
author = {Lim, C. and Montaldi, J. and {Roberts}, M.},
title = {Relative equilibria of point vortices on the sphere},
journal = {Physica D},
year = {2001},
volume = {148},
pages = {97--135},
doi = {10.1016/s0167-2789(00)00167-6},
}
@Book{Lin55,
Title = {The Theory of Hydrodynamic Stability},
Author = {Lin, C. C.},
Publisher = {Cambridge Univ. Press},
Year = {1955},
Address = {Cambridge}
}
@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, 2011}
}
@Article{LipCvi08,
Title = {How well can one resolve the state space of a chaotic map?},
Author = {D. Lippolis and P. Cvitanovi\'c},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Note = {\arXiv{0902.4269}},
Pages = {014101},
Volume = {104},
DOI = {10.1103/PhysRevLett.104.014101}
}
@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 = {https://arxiv.org/abs/math/0502549},
}
@Article{lixigraham06,
author = {W. Li and L. Xi and M.D. Graham},
title = {Nonlinear travelling waves as a framework for understanding turbulent drag reduction},
journal = {J. Fluid Mech},
year = {2006},
volume = {565},
pages = {353--362},
doi = {10.1017/s0022112006002138},
}
@Article{lixigraham07,
author = {W. Li and M.D. Graham},
title = {Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow},
journal = {Phys. Fluids},
year = {2007},
volume = {19},
number = {083101},
pages = {1--15},
doi = {10.1063/1.2748443},
}
@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},
Language = {English}
}
@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}
}
@Book{LM94,
Title = {Chaos, Fractals, and Noise; Stochastic Aspects of Dynamics},
Author = {A. Lasota and M. MacKey},
Publisher = {Springer},
Year = {1994},
Address = {Berlin}
}
@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{lop05rel,
Title = {Relative periodic solutions of the {Complex Ginzburg-Landau} equation},
Author = {V. L{\'o}pez and P. Boyland and M. T. Heath and R. D. Moser},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2006},
Note = {\arXiv{nlin/0408018}},
Pages = {1042--1075},
Volume = {4},
DOI = {10.1137/040618977}
}
@Article{lopez98,
author = {Lopez, J. M. and Shen, J.},
title = {An efficient spectral-projection method for the {Navier-Stokes} equations in cylindrical geometries {I}. {Axisymmetric} cases},
journal = {J. Comput. Physics},
year = {1998},
volume = {139},
pages = {308--326},
doi = {S10.1006/jcph.1997.5872}
}
@Article{LopMar00,
Title = {Determining the self-rotation number following a {Neimark-Sacker} bifurcation in the periodically forced {Taylor-Couette} flow},
Author = {Lopez, J. M. and Marques, F.},
Journal = {Z. Angew. Math. Phys.},
Year = {2000},
Pages = {61--74},
Volume = {51},
DOI = {10.1007/PL00001507},
Keywords = {Key words. Floquet theory, self-rotation number, parametric excitation, quasiperiodic flow, Taylor--Couette flow.}
}
@Article{LopMarq05,
author = {J. M. Lopez and F. Marques},
title = {Finite aspect ratio {Taylor-Couette} flow: {Shil'nikov} dynamics of 2-tori},
journal = {Physica D},
year = {2005},
volume = {211},
pages = {168--191},
doi = {10.1016/j.physd.2005.08.011},
}
@Article{LorentzDiff,
Title = {Transport properties of the {Lorentz} gas in terms of periodic orbits},
Author = {Cvitanovi\'c, P. and Eckmann, J.-P. and Gaspard, P.},
Journal = {Chaos Solit. Fract.},
Year = {1995},
Note = {\arXiv{chao-dyn/9312003}},
Pages = {113--120},
Volume = {6},
DOI = {10.1016/0960-0779(95)80018-C}
}
@Article{lorenz63,
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{LoTh10,
Title = {Computing stochastic travelling waves},
Author = {G. J. Lord and V. Th{\"u}mmler},
Journal = {SIAM J. Sci. Comput.},
Year = {2012},
Addendum = {\arXiv{1006.0428}},
Pages = {B24--B43},
Volume = {34},
DOI = {10.1137/100784734}
}
@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{LSAJAH16,
author = {Lemoult, G. and Shi, L. and Avila, K. and Jalikop, S. V. and Avila, M. and Hof, B.},
title = {Directed percolation phase transition to sustained turbulence in {Couette} flow},
journal = {Nature Phys.},
year = {2016},
volume = {12},
pages = {254--258},
doi = {10.1038/nphys3675},
}
@Article{Luce95,
author = {B. P. Luce},
title = {Homoclinic explosions in the complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {1995},
volume = {84},
pages = {553--581},
doi = {10.1016/0167-2789(95)00047-8},
}
@Article{LucKer12,
Title = {Spatiotemporal dynamics in {2D Kolmogorov} flow over large domains},
Author = {Lucas, D. and Kerswell, R. R.},
Journal = {J. Fluid Mech.},
Year = {2014},
Note = {\arXiv{1308.3356}},
Pages = {518--554},
Volume = {750},
DOI = {10.1017/jfm.2014.270}
}
@Article{LucKer14,
Title = {Recurrent flow analysis in spatiotemporally chaotic 2-dimensional {Kolmogorov} flow},
Author = {Lucas, D. and Kerswell, R. R.},
Journal = {Phys. Fluids},
Year = {2015},
Note = {\arXiv{1406.1820}},
Pages = {518--554},
Volume = {27},
DOI = {10.1063/1.4917279}
}
@Proceedings{Lumley_1989,
Title = {Whither Turbulence? Turbulence at the Crossroads: Proceedings, Workshop Cornell U., {March} 22-24, 1989},
Year = {1990},
Address = {New York},
Editor = {Lumley, J. L.},
Publisher = {Springer},
Volume = {357},
DOI = {10.1007/3-540-52535-1}
}
@Article{lumley67,
author = {{Bakewell}, P. and {Lumley}, J. L.},
title = {Viscous sublayer and adjacent wall region in turbulent pipe flow},
journal = {Phys. Fluids},
year = {1967},
volume = {10},
pages = {1880},
doi = {10.1063/1.1762382},
}
@Article{lumley98,
author = {Lumley, J. L. and Blossey, P.},
title = {Control of turbulence},
journal = {Ann. Rev. Fluid Mech.},
year = {1998},
volume = {30},
pages = {311},
doi = {10.1146/annurev.fluid.30.1.311},
}
@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}
}
@Article{lvov-2007,
author = {V. S. L'vov and I. Procaccia and O. Rudenko},
title = {Universal model of finite {Reynolds} number turbulent flow in channels and pipes},
journal = {Phys. Rev. Lett.},
year = {2008},
volume = {100},
pages = {054504},
doi = {10.1103/PhysRevLett.100.054504},
}
@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 Liyapunov vectors are well defined a.e.}
}
@Article{Lyons13,
Title = {{Bayes and Frequentism}: a particle physicist's perspective},
Author = {Lyons, L.},
Journal = {Contemporary Physics},
Year = {2013},
Pages = {1--16},
Volume = {54},
Abstract = { In almost every scientific field, an experiment involves
collecting data and then analysing it. The analysis stage will often
consist in trying to extract some physical parameter and estimating
its uncertainty; this is known as Parameter Determination. An example
would be the determination of the mass of the top quark, from data
collected from high energy proton--proton collisions. A different aim
is to choose between two possible hypotheses. For example, are data
on the recession speed s of distant galaxies proportional to their
distance d, or do they fit better to a model where the expansion of
the Universe is accelerating? There are two fundamental approaches to
such statistical analyses -- Bayesian and Frequentist. This article
discusses the way they differ in their approach to probability, and
then goes on to consider how this affects the way they deal with
Parameter Determination and Hypothesis Testing. The examples are
taken from everyday life and from particle physics. },
DOI = {10.1080/00107514.2012.756312}
}
@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{M86,
author = {S. A. Maslowe},
title = {Critical layers in shear flows},
journal = {Ann. Rev. Fluid Mech.},
year = {1986},
volume = {18},
pages = {405--432},
doi = {10.1146/annurev.fluid.18.1.405},
}
@Article{Ma02,
Title = {A low-dimensional model for simulating 3-dimensional cylinder flow},
Author = {X. Ma and G.E. Karniadakis},
Journal = {J. Fluid Mech.},
Year = {2002},
Pages = {181--190},
Volume = {458}
}
@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}
}
@Book{mallet02,
Title = {Geomodeling},
Author = {Mallet, J.-L.},
Publisher = {Oxford Univ. Press},
Year = {2002},
Address = {Oxford}
}
@Book{man90b,
Title = {Dissipative structures and weak turbulence},
Author = {P. Manneville},
Publisher = {Academic Press},
Year = {1990},
Address = {Boston}
}
@Book{mandel,
Title = {The Fractal Geometry of Nature},
Author = {B. B. Mandelbrot},
Publisher = {WH Freeman Co.},
Year = {1982},
Address = {New York},
ISBN = {9780716711865}
}
@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{Mann08,
Title = {Understanding the sub-critical transition to turbulence in wall flows},
Author = {P. Manneville},
Journal = {Pramana},
Year = {2008},
Pages = {1009--1021},
Volume = {70},
DOI = {10.1007/s12043-008-0105-1}
}
@Unpublished{Mann14,
Title = {On the transition to turbulence of wall-bounded flows in general, and plane {Couette} flow in particular},
Author = {Manneville, P.},
Note = {\arXiv{1403.6374}},
Year = {2014}
}
@Article{marcio03,
Title = {Topological characterization of spatial-temporal chaos},
Author = {M. Gameiro and W. Kalies and K. Mischaikow},
Journal = {Phys. Rev. E},
Year = {2004},
Pages = {035203},
Volume = {70},
Abstract = {Use the Betti number to characterize the spatiotemporal
dynamics of a system. A lyapunov exponent is suggested to measure the
space as well as temporal complexity of the evolution.},
DOI = {10.1103/PhysRevE.70.035203}
}
@PhdThesis{Marcotte2016,
author = {C. D. Marcotte},
title = {Understanding sustained spiral chaos using non-chaotic solutions of a simple model of atrial excitation},
school = {Georgia Institute of Technology},
year = {2016}
}
@Article{Marcus84,
Title = {Simulation of {Taylor-Couette} flow. {Part} 1. {Numerical} methods and comparison with experiment},
Author = {Marcus, P. S.},
Journal = {J. Fluid Mech.},
Year = {1984},
Pages = {45--64},
Volume = {146},
DOI = {10.1017/S0022112084001762}
}
@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{MarRat99,
Title = {Introduction to Mechanics and Symmetry},
Author = {Marsden, J. E. and Ratiu, T. S.},
Publisher = {Springer},
Year = {1999},
Address = {New York}
}
@Book{Marsd92,
Title = {Lectures on Mechanics},
Author = {Marsden, J. E.},
Publisher = {Cambridge Univ. Press},
Year = {1992},
Address = {Cambridge}
}
@Book{marsdenbb,
Title = {The {H}opf Bifurcation and its Applications},
Author = {J. E. Marsden and M. McCracken},
Publisher = {Springer},
Year = {1976}
}
@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},
abstract = {local frequency analysis is used and action-angle
coordinate is parametrized by the frequency ratio. The transport
zones and partial barriers are identified according to the },
doi = {10.1016/0009-2614(87)80655-3},
}
@Article{Marw08,
Title = {A historical review of recurrence plots},
Author = {N. Marwan},
Journal = {Eur. Phys. J. Spec. Top.},
Year = {2008},
Pages = {3--12},
Volume = {164},
DOI = {10.1140/epjst/e2008-00829-1}
}
@Article{MaSiRo73,
Title = {Statistical mechanics of classical systems},
Author = {P. C. Martin and E. D. Siggia and H. A. Rose},
Journal = {Phys. Rev. A},
Year = {1973},
Pages = {423--437},
Volume = {8}
}
@Article{Mather91,
author = {J. N. Mather},
title = {Variational construction of orbits of twist difeomorphisms},
journal = {J. Am. Math. Soc.},
year = {1991},
volume = {4},
pages = {207--263},
doi = {10.2307/2939275},
}
@Book{MathWalk73,
Title = {Mathematical Methods of Physics},
Author = {J. Mathews and R. L. Walker},
Publisher = {W. A. Benjamin},
Year = {1970},
Address = {Reading, MA},
ISBN = {9780805370027}
}
@Article{May76,
author = {R. May},
title = {Simple mathematical models with very complicated dynamics},
journal = {Nature},
year = {1976},
volume = {261},
pages = {459--467},
doi = {10.1038/261459a0},
}
@Article{MC96pha,
author = {P. Manneville and H. Chat{\'e}},
title = {Phase turbulence in the two-dimensional complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {1996},
volume = {96},
pages = {30--46},
abtract = {instability of plane waves},
doi = {10.1016/0167-2789(96)00045-0},
}
@Article{McKean74,
author = {McKean, H. P.},
title = {Selberg's trace formula as applied to a compact {Riemann} surface},
journal = {Commun. Pure Appl. Math.},
year = {1972},
volume = {25},
pages = {225--246},
doi = {10.1002/cpa.3160250302},
}
@Article{McKeon04,
Title = {Further observations on the mean velocity in fully-developed pipe flow},
Author = {B. J. McKeon and J. Li and W. Jiang and J. F. Morrison and A. J. Smits},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {135--147},
Volume = {501}
}
@Article{Mcoh03,
author = {M. van Hecke},
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},
abstract = {Give an overview of the most important properties of the
coherent structures and address the question how such structures may
be identified in the experimental space-time data set.},
doi = {10.1016/s0167-2789(02)00687-5},
}
@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}
}
@Book{Mees81,
title = {{Dynamics of Feedback Systems}},
publisher = {Wiley},
year = {1981},
author = {Mees, A. I.},
address = {New York},
}
@Article{MEF04,
author = {J. Moehlis and B. Eckhardt and H. Faisst},
title = {Fractal lifetimes in the transition to turbulence},
journal = {Chaos},
year = {2004},
volume = {14},
pages = {S11},
doi = {10.1063/1.1821751},
}
@Article{Mehta05,
author = {Mehta, P. G. and Healey, T. J.},
title = {On steady solutions of symmetry-preserving perturbations of the two-dimensional {Couette} flow problem},
journal = {Phys. Fluids},
year = {2005},
volume = {17},
pages = {4108},
doi = {10.1063/1.2059571},
}
@Article{mellibovsky11,
author = {Mellibovsky, F. and Eckhardt, B.},
title = {{Takens--Bogdanov} bifurcation of travelling-wave solutions in pipe flow},
journal = {J. Fluid Mech.},
year = {2011},
volume = {670},
pages = {96--129},
doi = {10.1017/s0022112010005239},
}
@Article{mellibovsky12,
author = {Mellibovsky, F. and Eckhardt, B.},
title = {From travelling waves to mild chaos: {A} supercritical bifurcation cascade in pipe flow},
journal = {J. Fluid Mech.},
year = {2012},
volume = {709},
pages = {149--190},
doi = {10.1017/jfm.2012.326},
}
@Article{MelMes15,
Title = {A mechanism for streamwise localisation of nonlinear waves in shear flows},
Author = {F. Mellibovsky and A. Meseguer},
Journal = {J. Fluid Mech.},
Year = {2015},
Pages = {R1},
Volume = {779},
DOI = {10.1017/jfm.2015.440}
}
@Article{mercader2010,
author = {Mercader, I. and Batiste, O. and Alonso, A.},
title = {An efficient spectral code for incompressible flows in cylindrical geometries},
journal = {Computers \& Fluids},
year = {2010},
volume = {39},
pages = {215--224},
doi = {10.1016/j.compfluid.2009.08.003}
}
@Article{Meseguer2009,
Title = {Families of subcritical spirals in highly counter-rotating {Taylor-Couette} flow},
Author = {Meseguer, A. and Mellibovsky, F. and Avila, M. and Marques, F.},
Journal = {Phys. Rev. E},
Year = {2009},
Pages = {036309},
Volume = {79},
DOI = {10.1103/PhysRevE.79.036309}
}
@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. Num. Math.},
year = {2007},
volume = {57},
pages = {920--938},
doi = {10.1016/j.apnum.2006.09.002},
}
@Article{MesTre03,
author = {Meseguer, A and Trefethen, L. N},
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{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{Mezic05,
author = {Mezi\'c, I.},
title = {Spectral properties of dynamical systems, model reduction and decompositions},
journal = {Nonlinear Dyn.},
year = {2005},
volume = {41},
pages = {309--325},
doi = {10.1007/s11071-005-2824-x},
}
@Article{MFE04,
author = {J. Moehlis and H. Faisst and B. Eckhardt},
title = {A low-dimensional model for turbulent shear flows},
journal = {New Journal of Physics},
year = {2004},
volume = {6},
pages = {56},
doi = {10.1088/1367-2630/6/1/056},
}
@Article{Mathew07,
author = {Mathew, G. and Mezi{\'C}, I. and Grivopoulos, S. and Vaidya, U. and Petzold, L.},
title = {Optimal control of mixing in {Stokes} fluid flows},
journal = {J. Fluid Mech.},
year = {2007},
volume = {580},
pages = {261--281},
doi = {10.1017/s0022112007005332},
}
@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. Sys.},
Year = {2005},
Pages = {352--376},
Volume = {4},
DOI = {10.1137/040606144}
}
@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{MFKM10,
author = {Morita, Y. and Fujiwara, N. and Kobayashi, M. U. and Mizuguchi, T.},
title = {Scytale decodes chaos: {A} method for estimating unstable symmetric solutions},
journal = {Chaos},
year = {2010},
volume = {20},
pages = {013126},
abstract = {A method for estimating a period of unstable periodic solutions
is suggested in continuous dissipative chaotic dynamical
systems. The measurement of a minimum distance between a
reference state and an image of transformation of it exhibits a
characteristic structure of the system, and the local minima of
the structure give candidates of period and state of
corresponding symmetric solutions. Appropriate periods and
initial states for the Newton method are chosen efficiently by
setting a threshold to the range of the minimum distance and
the period.},
doi = {10.1063/1.3365053},
}
@Book{MH,
title = {{Introduction to Hamiltonian Dynamical Systems and the {N}-body Problem}},
publisher = {Springer},
year = {1992},
author = {K. R. Meyer and G. R. Hall},
address = {New York}
}
@Article{MHMwind96,
author = {R. Montagne and E. Hern{\'a}ndez-Garc{\'\i}a and M. S. Miguel},
title = {Winding number instability in the phase-turbulence regime of the complex {Ginzburg-Landau} equation},
journal = {Phys. Rev. Lett.},
year = {1996},
volume = {77},
pages = {267},
abstract = {There exist a band of winding numbers associated with
stable states in the phase turbulent regime. The states with large
winding numbers decay to the ones with smaller winding numbers.
Defect chaos happens when the range of stable winding numbers
vanishes.},
doi = {10.1103/physrevlett.77.267},
}
@Article{michsiv77,
author = {D. M. Michelson and G. I. Sivashinsky},
title = {Nonlinear analysis of hydrodynamic instability in laminar flames - {II. Numerical} experiments},
journal = {Acta Astronaut.},
year = {1977},
volume = {4},
pages = {1207--1221},
abstract = {Consider the effect of hydrodynamics instability and diffusion thermal instability through the numerical calculation of the KSe.},
doi = {10.1016/0094-5765(77)90097-2},
}
@Misc{MiPlSt11,
author = {Mini\'c, Dj. and Pleimling, M. and Staples, A. E.},
title = {On the steady state distributions for turbulence},
year = {2011},
url = {https://arxiv.org/abs/1105.2941},
}
@Book{MiraGum80,
title = {{Recurrances and Discrete Dynamical Systems}},
publisher = {Springer},
year = {1980},
author = {I. Gumowski and C. Mira},
address = {Berlin}
}
@Article{mis01ks,
author = {P. Zgliczynski and K. Mischaikow},
title = {Rigorous numerics for partial differential equations: the {Kuramoto-Sivashinsky} equation},
journal = {Found. Comp. Math},
year = {2001},
volume = {1},
pages = {255--288},
doi = {10.1007/s002080010010},
}
@Article{misdis,
author = {K. Mischaikow and M. Mrozek and J. Reiss and A. Szymczak},
title = {Construction of symbolic dynamics from experimental time series},
journal = {Phys. Rev. Lett.},
year = {1999},
volume = {82},
pages = {1144},
doi = {10.1103/physrevlett.82.1144},
}
@Article{mislor1,
author = {K. Mischaikow and M. Mrozek},
title = {Chaos in the {Lorenz} equations: {A} computer assisted proof {Part II}: {Details}},
journal = {Math. Comp.},
year = {1998},
volume = {67},
pages = {1023--1046},
doi = {10.1090/s0025-5718-98-00945-4},
}
@Phdthesis{MitchellThesis13,
Title = {Transition to turbulence and mixing in a quasi-two-dimensional {Lorentz} force-driven {Kolmogorov} flow},
Author = {Mitchell Jr., R.},
School = {School of Physics, Georgia Inst. of Technology},
Year = {2013},
Address = {Atlanta},
Note = {{\tt ChaosBook.org/projects/theses.html}}
}
@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{MM,
author = {P. Moin and K. Mahesh},
title = {Direct numerical simulation: a tool in turbulence research},
journal = {Ann. Rev. Fluid Mech.},
year = {1998},
volume = {30},
pages = {539--78},
doi = {10.1146/annurev.fluid.30.1.539},
}
@Article{MMAM09,
Title = {Instability mechanisms and transition scenarios of spiral turbulence in {Taylor-Couette} flow},
Author = {A. Meseguer and F. Mellibovsky and Avila, M. and Marques, F.},
Journal = {Phys. Rev. E},
Year = {2009},
Pages = {046315},
Volume = {80},
DOI = {10.1103/PhysRevE.80.046315}
}
@Article{MMG95,
author = {S. Malerud and K. J. M\aa{}l\o{}y and W. I. Goldburg},
title = {Measurements of turbulent velocity fluctuations in a planar {Couette} cell},
journal = {Phys. Fluids},
year = {1995},
volume = {7},
pages = {1949--1955},
doi = {10.1063/1.868509},
}
@Article{Moffatt69,
author = {Moffatt, H. K.},
title = {The degree of knottedness of tangled vortex lines},
journal = {J. Fluid Mech},
year = {1969},
volume = {35},
pages = {117--129},
doi = {10.1017/s0022112069000991},
}
@InProceedings{Moffatt90,
author = {H. K. Moffatt},
title = {Fixed points of turbulent dynamical systems and suppression of nonlinearity, {Comment} 1},
booktitle = {Whither Turbulence? Turbulence at the Crossroads},
year = {1990},
editor = {J. L. Lumley},
pages = {250--257},
address = {New York},
publisher = {Springer},
doi = {10.1007/3-540-52535-1_47},
}
@Article{MoMeCa84,
author = {P. J. Morrison and J. D. Meiss and J. R. Cary},
title = {Scattering of regularized-long-wave solitary waves},
journal = {Physica D},
year = {1984},
volume = {11},
pages = {324--336},
abstract = {The Lagrangian density for the regularized-long-wave equation
(also known as the BBM equation) is presented. Using the trial
function technique, ordinary differential equations that describe
the time dependence of the position of the peaks, amplitudes,
and widths for the collision of two solitary waves are obtained.
These equations are analyzed in the Born and ``equal-width''
approximations and compared with numerical results obtained
by direct integration utilizing the split-step fast Fourier-transform
method. The computations show that collisions are inelastic and
that production of solitary waves may occur.},
doi = {10.1016/0167-2789(84)90014-9},
}
@Book{MonYag71,
title = {{Statistical Fluid Mechanics}},
publisher = {MIT Press},
year = {1971},
author = {Monin, A.S. and Yaglom, A.M.},
address = {Cambridge}
}
@Book{Moon87,
title = {{Chaotic Vibrations: An Introduction for Applied Scientists and Engineers}},
publisher = {Wiley},
year = {1987},
author = {F. C. Moon},
address = {New York}
}
@InProceedings{Morkovin69,
Title = {On the many faces of transition},
Author = {M. V Morkovin},
Booktitle = {Viscous Drag Reduction},
Year = {1969},
Address = {New York},
Editor = {C. S. Wells},
Pages = {1--31},
Publisher = {Plenum}
}
@Article{MoRo99,
author = {Montaldi, J. A. and {Roberts}, R. M.},
title = {Relative equilibria of molecules},
journal = {J. Nonlinear Science},
year = {1999},
volume = {9},
pages = {53--88},
doi = {10.1007/s003329900064},
}
@Article{MoRoSt88,
author = {Montaldi, J. A. and {Roberts}, R. M. and {Stewart}, I. N.},
title = {Periodic solutions near equilibria of symmetric {Hamiltonian} systems},
journal = {Phil. Trans. Royal Soc. A},
year = {1988},
volume = {325},
pages = {237--293},
doi = {10.1098/rsta.1988.0053},
}
@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{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{Moser83,
Title = {A spectral method for the {Navier-Stokes} equations with applications to {Taylor-Couette} flow},
Author = {R. Moser and P. Moin and A. Leonard},
Journal = {J. Comp. Phys.},
Year = {1983},
Pages = {524--544},
Volume = {52}
}
@Article{moser96,
Title = {A rapidly converging iteration method and nonlinear partial differential equations},
Author = {J. Moser},
Journal = {Ann. Scuola Norm. Super. Pisa},
Year = {1966},
Pages = {265--315},
Volume = {20}
}
@Article{moser96a,
Author = {J. Moser},
Journal = {Ann. Scuola Norm. Super. Pisa},
Year = {1966},
Pages = {499--535},
Volume = {20}
}
@Article{MoserPF99,
Title = {Direct numerical simulation of turbulent channel flow up to {$Re_{\tau} = 590$}},
Author = {R. Moser and J. Kim and N. N. Mansour},
Journal = {Phys. Fluids},
Year = {1999},
Pages = {943--946},
Volume = {11}
}
@Book{mosersr,
title = {{Stable and Random Motions in Dynamical Systems}},
publisher = {Princeton Univ. Press},
year = {1973},
author = {J. Moser},
address = {Princeton}
}
@Article{Mostow57,
Title = {Equivariant embeddings in {Euclidean} space},
Author = {G. D. Mostow},
Journal = {Ann. Math.},
Year = {1957},
Pages = {432--446},
Volume = {65}
}
@Book{mpc,
title = {{Model Predictive Control}},
publisher = {Springer},
year = {2004},
author = {E. F. Camacho and C. Bordons},
address = {New York}
}
@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}
}
@Article{MS51,
author = {D. Meksyn and J. T. Stuart},
title = {Stability of viscous motion between parallel planes for finite disturbances},
journal = {Proc. Roy. Soc. A},
year = {1951},
volume = {208},
pages = {517},
doi = {10.1098/rspa.1951.0177},
}
@Article{MS66,
author = {D. W. Moore and E. A. Spiegel},
title = {A thermally excited nonlinear oscillator},
journal = {Astrophys. J.},
year = {1966},
volume = {143},
pages = {871},
doi = {10.1086/148562},
}
@Book{MuKe05,
title = {{Non-uniqueness of Solutions to the Navier-Stokes Equations and their Connection with Laminar-Turbulent Transition}},
publisher = {Kluwer},
year = {2005},
author = {T. Mullin and R. R. Kerswell},
address = {Dordrecht}
}
@Article{Mul10,
Title = {Experimental studies of transition to turbulence in a pipe},
Author = {Mullin, T.},
Journal = {Ann. Rev. Fluid Mech.},
Year = {2011},
Pages = {1--24},
Volume = {43}
}
@Incollection{MuPe06,
Title = {Recent observations of the transition to turbulence in a pipe},
Author = {T. Mullin and J. Peixinho},
Booktitle = {IUTAM Symposium on Laminar-Turbulent Transition},
Publisher = {Springer},
Year = {2006},
Address = {New York},
Editor = {Govindarajan, R.},
Pages = {45--55},
Series = {Fluid Mechanics and Its Applications},
Volume = {78},
DOI = {10.1007/1-4020-4159-4_5}
}
@Article{MvH98,
author = {M. van Hecke},
title = {Building blocks of spatiotemporal intermittency},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {80},
pages = {1896},
doi = {10.1103/physrevlett.80.1896},
}
@Article{MvHhole01,
author = {M. van Hecke and M. Howard},
title = {Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex {Ginzburg-Landau} equation},
journal = {Phys. Rev. Lett.},
year = {2001},
volume = {86},
pages = {2018},
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{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{N96,
Title = {Nonlinear solutions of modified plane {Couette} flow in the presence of a transverse magnetic field},
Author = {M. Nagata},
Journal = {J. Fluid Mech.},
Year = {1996},
Pages = {231--243},
Volume = {307}
}
@Article{N97,
Title = {Three-dimensional traveling-wave solutions in plane {Couette} flow},
Author = {Nagata, M.},
Journal = {Phys. Rev. E},
Year = {1997},
Pages = {2023--2025},
Volume = {55}
}
@Article{NaBu83,
Title = {Three-dimensional tertiary motions in a plane shear layers},
Author = {Nagata, M. and Busse, F. H.},
Journal = {J. Fluid Mech.},
Year = {1983},
Pages = {1--26},
Volume = {135}
}
@Article{NagDeg13,
Title = {Mirror-symmetric exact coherent states in plane {Poiseuille} flow},
Author = {Nagata, M. and Deguchi, K.},
Journal = {J. Fluid Mech.},
Year = {2013},
Volume = {735},
DOI = {10.1017/jfm.2013.515}
}
@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}
}
@Incollection{Narasimha89,
Title = {The utility and drawbacks of traditional approaches},
Author = {R. Narasimha},
Booktitle = {Whither Turbulence? Turbulence at the Cross-Road},
Publisher = {Springer},
Year = {1989},
Address = {Berlin},
Editor = {J. Lumley},
Pages = {13--48}
}
@Article{Navier1823,
Title = {M{\'e}moire sur les lois du mouvement des fluides},
Author = {Navier, C. L. M. H.},
Journal = {M{\'e}moires de l'Acad{\'e}mie Royale des Sciences de l'Institut de France},
Year = {1823},
Pages = {389--440},
Volume = {6}
}
@Article{Neimark59,
Title = {On some cases of periodic motions depending on parameters},
Author = {Neimark, J.},
Journal = {Dokl. Akad. Nauk SSSR},
Year = {1959},
Pages = {736--739},
Volume = {129}
}
@Article{newcgl1,
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 = {XLIV}
}
@Article{newcgl2,
Title = {Instabilities of {Ginzburg-{L}andau} equation: secondary bifurcation},
Author = {P. K. Newton and L. Sirovich},
Journal = {Quart. Appl. Math.},
Year = {1986},
Pages = {367--374},
Volume = {XLIV}
}
@Article{newenv74,
Title = {Envelope equations},
Author = {A. C. Newell},
Journal = {Lect. Appl. Math.},
Year = {1974},
Pages = {157--163},
Volume = {15}
}
@Book{newton1687pnpm,
title = {{Philosophiae Naturalis Principia Mathematica}},
year = {1687},
author = {Newton, I.}
}
@Article{nhouse78,
Title = {Occurrence of strange {A}xiom {A} attractors near quasi-periodic flows on ${T}^m(m=3$ or more)},
Author = {S. E. Newhouse and D. Ruelle and F. Takens},
Journal = {Commun. Math. Phys.},
Year = {1978},
Pages = {35},
Volume = {64}
}
@Article{NiHa91,
Title = {Phase anholonomy in dissipative optical-systems with periodic oscillations},
Author = {Ning, C. Z. and Haken, H.},
Journal = {Phys. Rev. A},
Year = {1991},
Pages = {6410--6413},
Volume = {43},
DOI = {10.1103/PhysRevA.43.6410}
}
@Article{NiHa92,
Title = {An invariance property of the geometrical phase and its consequence in detuned lasers},
Author = {Ning, C. Z. and Haken, H.},
Journal = {Z. Phys. B},
Year = {{1992}},
Pages = {261--262},
Volume = {{89}},
Abstract = {We show that the geometrical phase defined for the dissipative systems
[1] is invariant under a unitary transformation. This implies for
lasers an invariance of the geometrical phase for different choices
of the reference frequency.},
DOI = {10.1007/BF01318153}
}
@Article{NiHa92a,
Title = {Geometrical phase and amplitude accumulations in dissipative systems with cyclic attractors},
Author = {C. Z. Ning and H. Haken},
Journal = {Phys. Rev. Lett.},
Year = {1992},
Pages = {2109--2112},
Volume = {68},
Abstract = {We show that the geometrical {(Berry)} phases discovered in Hamiltonian
systems can also be defined as resulting from parallel transportation
of vectors for nonlinear dissipative systems with cyclic attractors.
If the nonlinear dissipative systems possess a certain kind of asymptotic
solution defined in this Letter, the phase and amplitude accumulation
of a geometrical type can be defined. Detuned one- and two-photon
lasers showing periodic intensity pulsations are taken as examples
of such systems.}
}
@Article{NingHakenCLE90,
Title = {Detuned lasers and the complex {Lorenz} equations: {Subcritical} and supercritical {Hopf} bifurcations},
Author = {Ning, C. Z. and Haken, H.},
Journal = {Phys. Rev.},
Year = {1990},
Pages = {3826},
Volume = {41},
DOI = {10.1103/PhysRevA.41.3826}
}
@Article{NISHI08,
Title = {Laminar-to-turbulent transition of pipe flows through puffs and slugs},
Author = {Nishi, M. and B\"{u}lent, \"{U}. and Durst, F. and Biswas, G.},
Journal = {J. Fluid Mech.},
Year = {2008},
Pages = {425--446},
Volume = {614}
}
@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}
}
@InProceedings{NK04,
Title = {Three-dimensional periodic solutions in rotating/non-rotating plane {Couette} flow},
Author = {M. Nagata and G. Kawahara},
Booktitle = {Advances in Turbulence X},
Year = {2004},
Editor = {H. I. Andersson and P.-A. Krogstad},
Organization = {CIMNE},
Series = {Proceedings of the Tenth European Turbulence Conference}
}
@Article{NLSmal91,
author = {B. A. Malomed and L. Stenflo},
title = {Modulational instabilities and soliton solutions of a generalized nonlinear {Schr\"odinger} equation},
journal = {J. Phys. A},
year = {1991},
volume = {24},
pages = {L1149--L1153},
doi = {10.1088/0305-4470/24/19/006},
}
@Article{NLSper77,
Title = {Nonlinear {{Schr\"odinger}} equation including growth and damping},
Author = {N. R. Pereira and L. Stenflo},
Journal = {Phys. Fluid},
Year = {1977},
Pages = {1733--1734},
Volume = {20},
Abstract = {A nonlinear {Schr\"odinger} equation is found with growth and damping terms in the weakly nonlinear regime. An exact solitary solution is found for the equation.}
}
@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},
abstract = {Under the external driving force, an oscillon solutions is found.},
doi = {10.1063/1.1555625},
}
@Article{noack03,
Title = {A hierarchy of low-dimensional models for the transient and post-transient cylinder wake},
Author = {B. R. Noack and K. Afanasiev and M. Morzynski and F. Thiele},
Journal = {J. Fluid Mech.},
Year = {2003},
Pages = {335--363},
Volume = {497}
}
@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{noisy_Fred,
author = {P. Cvitanovi\'{c} and C. P. Dettmann and R. Mainieri and G. Vattay},
title = {Trace formulas for stochastic evolution operators: {Weak} noise perturbation theory},
journal = {J. Stat. Phys.},
year = {1998},
volume = {93},
pages = {981},
note = {\arXiv{chao-dyn/9807034}},
doi = {10.1023/b:joss.0000033173.38345.f9},
}
@Article{nongal89,
author = {M. Martine and R. Temam},
title = {Nonlinear {G{\"a}lerkin} methods},
journal = {SIAM J. Numer. Anal.},
year = {1989},
volume = {26},
pages = {1139--1157},
doi = {10.1137/0726063},
}
@Article{NP,
Title = {An adaptive {Newton-Picard} algorithm with subspace iteration for computing periodic solutions},
Author = {K. Lust and D. Roose},
Journal = {SIAM J. Sci. Comput.},
Year = {1998},
Pages = {1188--1209},
Volume = {19},
DOI = {10.1137/S1064827594277673}
}
@Book{nrc,
title = {Physics in a New Era},
publisher = {The National Academies Press},
year = {2001},
author = {National Research Council, report},
}
@Book{ns,
title = {{Numerical Partial Differential Equations}},
publisher = {Spring-Verlag},
year = {1995},
author = {J. W. Thomas},
address = {New York}
}
@Article{NSTks85,
author = {B. Nicolaenko and B. Scheurer and R. Temam},
title = {Some global dynamical properties of the {Kuramoto-Sivashinsky} equations: nonlinear stability and attractors},
journal = {Physica D},
year = {1985},
volume = {16},
pages = {155--183},
}
@Techreport{octave,
Title = {{GNU Octave}: a high-level language for numerical computation},
Author = {J. Eaton},
Institution = {University of Wisconsin},
Year = {2007},
Publisher = {J. Eaton},
URL = {http://www.octave.org}
}
@Article{OK96,
author = {S. A. Orszag and L. C. Kells},
title = {Transition to turbulence in plane {Poiseuille} and plane {Couette} flow},
journal = {J. Fluid Mech.},
year = {1980},
volume = {96},
pages = {159--205},
doi = {10.1017/s0022112080002066},
}
@Book{OlverInv,
title = {{Classical Invariant Theory}},
publisher = {Cambridge Univ. Press},
year = {1999},
author = {P. J. Olver},
address = {Cambridge}
}
@Book{OlvSha06,
title = {{Applied Linear Algebra}},
publisher = {Prentice-Hall},
year = {2006},
author = {Olver, P. J. and Shakiban, C.},
address = {Upper Saddle River, NJ}
}
@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}
}
@TechReport{openpipeflow,
author = {Willis, A. P.},
title = {{Openpipeflow}: {Pipe} flow code for incompressible flow},
institution = {U. Sheffield},
year = {2017},
note = {{\tt {Openpipeflow.org}}},
publisher = {A. P. Willis},
url = {http://Openpipeflow.org},
}
@Article{optp1,
Title = {Optimal periodic orbits of chaotic systems},
Author = {B. R. Hunt and E. Ott},
Journal = {Phys. Rev. Lett.},
Year = {1996},
Pages = {2254},
Volume = {76}
}
@Article{optp2,
author = {T.-H. Yang and B. R. Hunt and E. Ott},
title = {Optimal periodic orbits of continuous time chaotic systems},
journal = {Phys. Rev. E},
year = {2000},
volume = {62},
pages = {1950},
doi = {10.1103/physreve.62.1950},
}
@Article{Orr1907,
Title = {The stability or instability of the steady motions of a liquid. {Part II: A} viscous liquid},
Author = {Orr, W. M. F.},
Journal = {Proc. Roy. Irish Acad. A},
Year = {1907},
Pages = {69--138},
Volume = {27}
}
@Article{Orszag71,
author = {S. A. Orszag},
title = {Accurate solution of the {Orr-Sommerfeld} stability equation},
journal = {J. Fluid Mech.},
year = {1971},
volume = {50},
pages = {689--703},
}
@Article{Orszag86,
author = {S. A. Orszag and M. Israeli and M. Deville},
title = {Boundary conditions for incompressible flows},
journal = {J. Sci. Comput.},
year = {1986},
volume = {1},
pages = {75--111},
doi = {10.1007/bf01061454},
}
@Article{OsSchn62,
author = {A. Ostrowski and H. Schneider},
title = {Some theorems on the inertia of general matrices},
journal = {J. Math. Anal. Appl.},
year = {1962},
volume = {4},
pages = {72--84},
doi = {10.1007/978-3-0348-9355-8_37},
}
@Article{ott90a,
Title = {Controlling chaos},
Author = {E. Ott and C. Grebogi and J. A. Yorke},
Journal = {Phys. Rev. Lett},
Year = {1990},
Pages = {1196},
Volume = {64}
}
@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}
}
@Article{Palacios07,
Title = {Heteroclinic cycles},
Author = {A. Palacios},
Journal = {Scholarpedia},
Year = {2007},
Pages = {2352},
Volume = {2}
}
@Book{Pan96,
title = {{Incompressible Flow}},
publisher = {Wiley},
year = {1996},
author = {R. L. Panton},
address = {New York},
}
@Book{Pan97,
Title = {Self-sustaining mechanisms of wall turbulence},
Editor = {R. L. Panton},
Publisher = {Computational Mechanics Publications},
Year = {1997},
Address = {Southhampton}
}
@Article{ParLau86,
Title = {Resonances and torsion numbers of driven dissipative nonlinear oscillators},
Author = {U. Parlitz and W. Lauterborn},
Journal = {Z. Naturforsch. A},
Year = {1986},
Number = {4},
Pages = {605--614},
Volume = {41}
}
@Article{ParLau87,
Title = {Period-doubling cascades and devil's staircases of the driven {van der Pol} oscillator},
Author = {U. Parlitz and W. Lauterborn},
Journal = {Phys. Rev. A},
Year = {1987},
Pages = {1428},
Volume = {36}
}
@Article{Pasq87,
author = {F. Pasquarelli and A. Quarteroni and G. Sacchi-Landriani},
title = {Spectral approximations of the {Stokes} problem by divergence-free functions},
journal = {J. Comp. Sci.},
year = {1987},
volume = {2},
pages = {195--226},
doi = {10.1007/bf01061110},
}
@Article{PC88,
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}
}
@Article{PCar,
Title = {Group theory for {Feynman} diagrams in non-{Abelian} gauge theories},
Author = {Cvitanovi\'c, P.},
Journal = {Phys. Rev. D},
Year = {1976},
Pages = {1536--1553},
Volume = {14},
DOI = {10.1103/PhysRevD.14.1536}
}
@Book{PCgr,
title = {{Group Theory} - {Birdtracks}, {Lie}'s, and {Exceptional Groups}},
publisher = {Princeton Univ. Press},
year = {2008},
author = {P. Cvitanovi\'c},
address = {Princeton},
doi = {10.1515/9781400837670},
note = {{\tt birdtracks.eu}},
}
@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 = {23},
Volume = {58},
Abstract = {Use near recurrence to extract periodic orbits
and their stability eigenvalues.}
}
@Misc{pcopencourse,
author = {Cvitanovi\'c, P.},
title = {Nonlinear dynamics 1 \& 2: {Geometry} of chaos},
url = {http://chaosbook.org/course1/about.html}
}
@Article{PeaHal13,
Title = {Lagrangian coherent structures: {The} hidden skeleton of fluid flows},
Author = {T. Peacock and G. Haller},
Journal = {Physics Today},
Year = {2013},
Number = {2},
Pages = {41--47},
Volume = {66},
DOI = {10.1063/PT.3.1886}
}
@Article{peckham90,
Title = {The necessity of the {Hopf} bifurcation for periodically forced oscillators},
Author = {Peckham, B. B.},
Journal = {Nonlinearity},
Year = {1990},
Pages = {261},
Volume = {3}
}
@Article{PenDai07,
Title = {A potential-flow, deformable-body model for fluid-structure interactions with compact vorticity: application to animal swimming measurements},
Author = {J. Peng and J. O. Dabiri},
Journal = {Experiments in Fluids, to appear},
Year = {2007},
URL = {http://dabiri.caltech.edu/people/dabiri.html}
}
@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}
}
@Article{percgl,
author = {A. V. Porubov and M. G. Velarde},
title = {Exact periodic solutions of the complex {Ginzburg-Landau} equation},
journal = {J. Math. Phys.},
year = {1999},
volume = {40},
pages = {884},
doi = {10.1063/1.532692},
}
@Book{perg,
Title = {An introduction to ergodic theory},
Author = {P. Walters},
Publisher = {Speringer-Verlag},
Year = {1981},
Address = {New York}
}
@Book{perkob,
Title = {Differential Equations and Dynamical Systems},
Author = {L. Perko},
Publisher = {Springer},
Year = {1991},
Address = {New York}
}
@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}
}
@Article{Peterhof1999,
Title = {All-optical clock recovery using multisection distributed-feedback lasers},
Author = {D. Peterhof and B. Sandstede},
Journal = {J. Nonlinear Sci.},
Year = {1999},
Pages = {575--613},
Volume = {9}
}
@Article{Petr40,
Title = {Application of {Galerkin}'s method to the problem of the stability of the flow of a viscous fluid},
Author = {Petrov, G.I.},
Journal = {Prikl. Mat. Mekh.},
Year = {1940},
Pages = {3--12},
Volume = {4}
}
@InProceedings{petsc-efficient,
Title = {Efficient management of parallelism in object oriented numerical software libraries},
Author = {S. Balay and W. D. Gropp and L. C. McInnes and B. F. Smith},
Booktitle = {Modern Software Tools in Scientific Computing},
Year = {1997},
Editor = {E. Arge and A. M. Bruaset and H. P. Langtangen},
Pages = {163--202},
Publisher = {Birkh{\"{a}}user Press}
}
@Techreport{petsc-user-ref,
Title = {{PETS}c Users Manual},
Author = {S. Balay and K. Buschelman and V. Eijkhout and W. D. Gropp and D. Kaushik and M. G. Knepley and L. C. McInnes and B. F. Smith and H. Zhang},
Institution = {Argonne National Laboratory},
Year = {2004},
Number = {ANL-95/11 - Revision 2.1.5}
}
@Misc{petsc-web-page,
Title = {{PETSc} web page},
Author = {S. Balay and K. Buschelman and W. D. Gropp and D. Kaushik and M. G. Knepley and L. C. McInnes and B. F. Smith and H. Zhang},
Note = {www.mcs.anl.gov/petsc},
Year = {2001}
}
@Article{PexMull06,
Title = {Decay of turbulence in pipe flow},
Author = {J. Peixinho and T. Mullin},
Journal = {Phys. Rev. Lett.},
Year = {2006},
Pages = {094501},
Volume = {96}
}
@Article{PexMull07,
Title = {Finite-amplitude thresholds for transition in pipe flow},
Author = {J. Peixinho and T. Mullin},
Journal = {J. Fluid Mech.},
Year = {2007},
Pages = {169--178},
Volume = {582}
}
@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}
}
@Book{PG97,
Title = {Chaos, Scattering and Statistical Mechanics},
Author = {P. Gaspard},
Publisher = {Cambridge Univ. Press},
Year = {1997},
Address = {Cambridge}
}
@Article{PhysToday04,
Title = {New experiments set the scale for the onset of turbulence in pipe flow},
Author = {R. Fitzgerald},
Journal = {Physics Today},
Year = {2004},
Number = {2},
Pages = {21--23},
Volume = {57}
}
@Article{PhysWorld04,
Title = {Turbulent transition for fluids},
Author = {C. Barenghi},
Journal = {Physics World},
Year = {2004},
Number = {12},
Volume = {17}
}
@Article{pimsimp,
author = {P. Moresco and S. P. Dawson},
title = {The {PIM}-simplex method: an extension of the {PIM}-triple method to saddles with an arbitrary number of expanding directions},
journal = {Physica D},
year = {1999},
volume = {126},
pages = {38},
abstract = {They generalized the PIM method to treat the chaotic
saddle with more than one unstable direction by introducing a
simplex to cross the stable manifolds. Combining with one method for
finding local extremum in a simplex, the authors do essentially the
same job as in the simple PIM method.},
doi = {10.1016/s0167-2789(98)00234-6},
}
@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},
abstract = {This is a statistical extension of the PIM method. Here,
the representative points are selected according to the so-called
Exponential Stagger Distribution about the current point, instead of
the points on the line or vertices of a simplex. This is a brutal
force method while the authors claim that it is quite efficient.},
doi = {10.1103/physrevlett.86.2261},
}
@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},
Volume = {36},
Abstract = {{PIM} (proper interior maximum) method is proposed to
find chaotic trajectories on a nonattracting set with one-d unstable
manifold. By partitioning a straight line straddling the stable
manifolds, the point with longer and longer escaping time is found
in a sequel until a sufficiently small interval is reached when the
point is considered to be very close to the stable manifolds. After
that, evolving and restraining the line element results in a
NUMERICAL orbit is obtained.}
}
@Article{pizza2012chaotic,
Title = {Chaotic dynamics in premixed hydrogen/air channel flow combustion},
Author = {Pizza, G. and Frouzakis, C. E. and Mantzaras, J.},
Journal = {Combustion Theory and Modelling},
Year = {2012},
Pages = {275--299},
Volume = {16}
}
@Article{PlSiFi91,
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}
}
@Article{PoBaGr88,
author = {A. Politi and R. Badii and P. Grassberger},
title = {On the geometric structure of non-hyperbolic attractors},
journal = {J. Phys. A},
year = {1988},
volume = {15},
pages = {L763},
doi = {10.1088/0305-4470/21/15/004},
}
@Article{Poinc1896,
Title = {Sur les solutions p\'eriodiques et le principe de moindre action},
Author = {H. Poincar\'e},
Journal = {C. R. Acad. Sci. Paris},
Year = {1896},
Pages = {915--918},
Volume = {123}
}
@Book{poincare,
Title = {Les m{\'e}thodes nouvelles de la m{\'e}chanique c{\'e}leste},
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 \refref{JBG97}.}
}
@Book{poinper,
Title = {New Methods in Celestial Mechanics},
Author = {H. Poincar{\'e}},
Publisher = {Springer},
Year = {1992},
Address = {New York},
Series = {History of Modern Physics and Astronomy},
Volume = {13}
}
@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.},
Year = {1840},
Pages = {961},
Volume = {11}
}
@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{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}
}
@Book{popebook,
Title = {Turbulent Flows},
Author = {S. B. Pope},
Publisher = {Cambridge Univ. Press},
Year = {2000},
Address = {Cambridge}
}
@Article{postgal89,
author = {B. Garc{\'\i}a-Archilla and J. Novo and E. S. Titi},
title = {Postprocessing the {G \"alerkin} method: a novel approach to approximate inertial manifolds},
journal = {SIAM J. Numer. Anal.},
year = {1998},
volume = {35},
pages = {941--972},
doi = {10.1137/s0036142995296096},
}
@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}
}
@Article{PP90,
Title = {Zeta functions and the periodic orbit structure of hyperbolic dynamics},
Author = {W. Parry and M. Pollicott},
Journal = {Ast\'erisque},
Year = {1990},
Pages = {268},
Volume = {187-188}
}
@Article{Prants14,
Title = {Chaotic {Lagrangian} transport and mixing in the ocean},
Author = {Prants, S. V.},
Journal = {Eur. Phys. J. Spec. Top.},
Year = {2014},
Pages = {2723--2743},
Volume = {223},
DOI = {10.1140/epjst/e2014-02288-5}
}
@Article{PrBrPo93,
author = {Price, T. and Brachet, M. and Pomeau, Y.},
title = {Numerical characterization of localized solutions in plane {Poiseuille} flow},
journal = {Phys. Fluids A},
year = {1993},
volume = {5},
pages = {762--764},
doi = {10.1063/1.858659}
}
@Article{pre88top,
author = {P. Cvitanovi\'{c} and G. H. Gunaratne and I. Procaccia},
title = {Topological and metric properties of {H\'enon}-type strange attractors},
journal = {Phys. Rev. A},
year = {1988},
volume = {38},
pages = {1503},
doi = {10.1103/physreva.38.1503},
}
@Book{Press:96,
Title = {Numerical Recipes in Fortran},
Author = {W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Address = {Cambridge}
}
@Article{Pringle07,
author = {Pringle, C. C. T. and Kerswell, R. R.},
title = {Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {99},
pages = {074502},
doi = {10.1103/physrevlett.99.074502},
}
@Article{Pringle09,
author = {Pringle, C. C. T. and Duguet, Y. and Kerswell, R. R.},
title = {Highly symmetric travelling waves in pipe flow},
journal = {Phil. Trans. Royal Soc. A},
year = {2009},
volume = {367},
pages = {457--472},
doi = {10.1098/rsta.2008.0236},
}
@Article{Pringle2010,
Title = {Using nonlinear transient growth to construct the minimal seed for shear flow turbulence},
Author = {Pringle, C. C. T. and Kerswell, R. R.},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {154502},
Volume = {105},
DOI = {10.1103/PhysRevLett.105.154502}
}
@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},
Pages = {026214},
Volume = {64},
Abstract = {Change the stability of the fixed points on the
Poincar{\'e} section to find periodic orbits.}
}
@Article{PSDB00,
Title = {Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems},
Author = {D. Pingel and P. Schmelcher and F. K. Diakonos and O. Biham},
Journal = {Phys. Rev. E},
Year = {2000},
Note = {\arXiv{nlin.CD/0006011}},
Pages = {2119},
Volume = {62}
}
@Article{pugh67cl,
author = {C. Pugh},
title = {An improved closing lemma and a general density theorem},
journal = {Amer. J. Math.},
year = {1967},
volume = {89},
doi = {10.2307/2373414},
}
@Article{PWK15,
author = {Pringle, C.C.T. and Willis, A.P. and Kerswell, R.R.},
title = {Fully localised nonlinear energy growth optimals in pipe flow},
journal = {Phys. Fluids},
year = {2015},
volume = {27},
pages = {064102},
doi = {10.1063/1.4922183},
}
@Article{PXBFB14,
Title = {Redistribution of kinetic energy in turbulent flows},
Author = {Pumir, A. and Xu, H. and Boffetta, G. and Falkovich, G. and Bodenschatz, E.},
Journal = {Phys. Rev. X},
Year = {2014},
Pages = {041006},
Volume = {4},
DOI = {10.1103/PhysRevX.4.041006}
}
@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 = {174},
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 = {186},
pages = {123--161},
doi = {10.1098/rspl.1894.0075},
}
@Article{RaCoRi14,
Title = {Relative periodic orbits in plane {Poiseuille} flow},
Author = {S. Rawat and C. Cossu and F. Rincon},
Journal = {Compt. Rend. M\'ecanique},
Year = {2014},
Pages = {485--489},
Volume = {342},
DOI = {10.1016/j.crme.2014.05.008}
}
@Article{rademacher2005,
author = {Rademacher, J. D. M.},
title = {Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit},
journal = {J. Diff. Eqn.},
year = {2005},
volume = {218},
pages = {390--443},
doi = {10.1016/j.jde.2005.03.016},
}
@Article{Radziunas2006,
author = {M. Radziunas},
title = {Numerical bifurcation analysis of the traveling wave model of multisection semiconductor lasers},
journal = {Physica D},
year = {2006},
volume = {213},
pages = {98--112},
doi = {10.1016/j.physd.2005.11.003},
}
@Article{RaHaAb96,
author = {Rauh, A. and Hannibal, L. and Abraham, N. B.},
title = {Global stability properties of the complex {Lorenz} model},
journal = {Physica D},
year = {1996},
volume = {99},
pages = {45--58},
doi = {10.1016/s0167-2789(96)00129-7},
}
@Article{Rand82,
author = {Rand, D.},
title = {Dynamics and symmetry - predictions for modulated waves in rotating fluids},
journal = {Arch. Rational Mech. Anal.},
year = {1982},
volume = {79},
pages = {1--3},
doi = {10.1007/bf02416564},
}
@Article{RaOsSeSi82,
Title = {Universal transition from quasiperiodicity to chaos in dissipative systems},
Author = {D. Rand and S. Ostlund and J. Sethna and E. Siggia},
Journal = {Phys. Rev. Lett.},
Year = {1982},
Pages = {132--135},
Volume = {49},
DOI = {10.1103/PhysRevLett.49.132}
}
@Article{RCHR15,
Title = {On the self-sustained nature of large-scale motions in turbulent {Couette} flow},
Author = {Rawat, S. and Cossu, C. and Hwang, Y. and Rincon, F.},
Journal = {J. Fluid Mech.},
Year = {2015},
Pages = {515--540},
Volume = {782},
DOI = {10.1017/jfm.2015.550}
}
@Article{Recke1998,
author = {L. Recke and D. Peterhof},
title = {Abstract forced symmetry breaking and forced frequency locking of modulated waves},
journal = {J. Diff. Eqn.},
year = {1998},
volume = {144},
pages = {233--262},
doi = {10.1006/jdeq.1997.3379},
}
@Article{Recke1998a,
author = {L. Recke},
title = {Forced frequency locking of rotating waves},
journal = {Ukrain. Math. J.},
year = {1998},
volume = {50},
pages = {94--101},
doi = {10.1007/bf02514692},
}
@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 Contin. Dynam. Systems},
year = {2011},
volume = {31},
pages = {847--875},
note = {\arXiv{1108.5990}},
doi = {10.3934/dcds.2011.31.847},
}
@Article{reimann1,
author = {P. Reimann},
title = {Noisy one-dimensional maps near a crisis 1: {Weak {Gauss}ian} white and colored noise},
journal = {J. Stat. Phys.},
year = {1996},
volume = {82},
pages = {1467--1501},
doi = {10.1007/bf02183392},
}
@Article{reimann2,
author = {P. Reimann},
title = {Noisy one-dimensional maps near a crisis 2: {General} uncorrelated weak noise},
journal = {J. Stat. Phys.},
year = {1996},
volume = {85},
pages = {403--425},
doi = {10.1007/bf02174212},
}
@Article{Rem03,
author = {D. Rempfer},
title = {Low-dimensional modeling and numerical simulation of transition in simple shear flows},
journal = {Review of Fluid Mechanics},
year = {2003},
volume = {35},
pages = {229},
doi = {10.1146/annurev.fluid.35.030602.113908},
}
@Article{Rem06,
Title = {On boundary conditions for incompressible {Navier-Stokes} problems},
Author = {Rempfer, D.},
Journal = {Appl. Mech. Rev.},
Year = {2006},
Pages = {107--125},
Volume = {59},
DOI = {10.1115/1.2177683}
}
@Misc{ReSaTkYa11,
author = {Recke, L. and {Samoilenko}, A. and {Tkachenko}, V. and {Yanchuk}, S.},
title = {Frequency locking by external forcing in systems with rotational symmetry},
year = {2011},
note = {\arXiv{1108.5990}},
doi = {10.1137/110846750},
}
@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{RiMeAv16,
Title = {Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow},
Author = {P. Ritter and F. Mellibovsky and M. Avila},
Journal = {New J. Phys.},
Year = {2016},
Pages = {083031},
Volume = {18},
DOI = {10.1088/1367-2630/18/8/083031}
}
@Article{Rincon07,
author = {Rincon, F.},
title = {On the existence of two-dimensional nonlinear steady states in plane {Couette} flow},
journal = {Phys. Fluids},
year = {2007},
volume = {19},
pages = {4105},
note = {\arXiv{0706.1165}},
abstract = {It is not possible to obtain the nonlinear plane
Couette flow solutions reported by Cherhabili and
Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using
their Poiseuille-Couette homotopy. We also demonstrate that
the steady solutions obtained by Mehta and Healey [Phys.
Fluids 17, 094108 (2005)] for small symmetry-preserving
perturbations are influenced by an artefact of the modified
system of equations used in their paper.},
doi = {10.1063/1.2753982},
}
@Book{Risken96,
Title = {The {F}okker-{P}lanck Equation},
Author = {H. Risken and H. Haken},
Publisher = {Springer},
Year = {1996},
Address = {New York}
}
@Incollection{RMChaosHist,
author = {R. Mainieri and P. Cvitanovi{\'c}},
title = {A brief history of chaos},
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#appendHist},
}
@Article{Robinson91,
author = {S. K. Robinson},
title = {{Coherent motions in the turbulent boundary layer}},
journal = {Ann. Rev. Fluid Mech.},
year = {1991},
volume = {23},
pages = {601--639},
doi = {10.1146/annurev.fluid.23.1.601},
}
@Techreport{Robinson91b,
Title = {The Kinematics of turbulent boundary layer structure},
Author = {S. K. Robinson},
Institution = {NASA},
Year = {1991},
Note = {103859}
}
@Article{ROC07,
author = {F. Rincon and G. I. Ogilvie and C. Cossu},
title = {On self-sustaining processes in {Rayleigh}-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks},
journal = {Astron. Astrophys.},
year = {2007},
volume = {463},
pages = {817--832},
doi = {10.1051/0004-6361:20066544},
}
@Article{Rolland14,
author = {Rolland, J.},
title = {Turbulent spot growth in plane {Couette} flow: statistical study and formation of spanwise vorticity},
journal = {Fluid Dyn. Res.},
year = {2014},
volume = {46},
pages = {015512},
note = {\arXiv{1401.3586}},
doi = {10.1088/0169-5983/46/1/015512},
}
@Article{Romanov73,
author = {V. A. Romanov},
title = {Stability of plane-parallel {Couette} flow},
journal = {Functional Anal. Applics.},
year = {1973},
volume = {7},
pages = {137--146},
doi = {10.1007/bf01078886},
}
@Article{Rome69,
author = {Rome, H.},
title = {A direct solution to the linear variance equation of a time-invariant linear system},
journal = {IEEE Trans. Automatic Control},
year = {1969},
volume = {14},
pages = {592--593},
doi = {10.1109/tac.1969.1099271},
}
@Article{RoSa00,
author = {Roweis, S. T. and Saul, L. K.},
title = {Nonlinear dimensionality reduction by locally linear embedding},
journal = {Science},
year = {2000},
volume = {290},
pages = {2323--2326},
doi = {10.1126/science.290.5500.2323},
}
@Article{ross,
author = {O. E. R{\"{o}}ssler},
title = {An equation for continuous chaos},
journal = {Phys. Lett. A},
year = {1976},
volume = {57},
pages = {397},
doi = {10.1016/0375-9601(76)90101-8},
}
@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},
}
@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},
note = {\arXiv{1110.0766}},
doi = {10.1088/1751-8113/45/19/195101},
}
@Article{RP67,
author = {W. C. Reynolds and M. C. Potter},
title = {Finite-amplitude instability of parallel shear flows},
journal = {J. Fluid Mech.},
year = {1967},
volume = {27},
pages = {465},
doi = {10.1017/s0022112067000485},
}
@Article{RPM,
Title = {Stabilization of unstable procedures: the recursive projection method},
Author = {G. M. Shroff and H. B. Keller},
Journal = {SIAM J. Numer. Anal.},
Year = {1993},
Pages = {1099--1120},
Volume = {30},
DOI = {10.1137/0730057},
}
@Article{RSBH98,
Title = {On stability of streamwise streaks and transition thresholds in plane channel flows},
Author = {S. C. Reddy and P. J. Schmid and J. S. Baggett and D. S. Henningson},
Journal = {J. Fluid Mech.},
Year = {1998},
Pages = {269--303},
Volume = {365}
}
@Book{rtb,
Title = {Theory of Orbits},
Author = {V. Szebehely},
Publisher = {Academic Press},
Year = {1967},
Address = {New York}
}
@Article{rue04ne,
author = {D. Ruelle},
title = {Conversations on nonequilibrium physics with an extraterrestrial},
journal = {Physics Today},
year = {2004},
volume = {57},
number = {5},
pages = {48--53},
abstract = {New ideas of nonequilibrium physics are introduced. Emphasize the SRB measure approach and energy fluctuation theorem.},
doi = {10.1063/1.1768674},
}
@Article{ruelext,
author = {D. Ruelle},
title = {Large volume limit of the distribution of characteristic exponents in turbulence},
journal = {Commun. Math. Phys.},
year = {1982},
volume = {87},
pages = {287--302},
doi = {10.1007/bf01218566},
}
@Article{ruell71,
author = {D. Ruelle and F. Takens},
title = {On the nature of turbulence},
journal = {Commun. Math. Phys.},
year = {1971},
volume = {20},
pages = {167},
doi = {10.1007/bf01893621},
}
@Book{ruelle,
Title = {Statistical Mechanics, Thermodynamic Formalism},
Author = {D. Ruelle},
Publisher = {Addison-Wesley},
Year = {1978},
Address = {Reading, MA}
}
@Article{Ruelle76,
author = {D. Ruelle},
title = {Zeta-functions for expanding maps and {Anosov} flows},
journal = {Inv. Math.},
year = {1976},
volume = {34},
pages = {231--242},
doi = {10.1007/bf01403069},
}
@Article{ruelle86,
author = {D. Ruelle},
title = {Locating resonances for {Axiom A} dynamical systems},
journal = {J. Stat. Phys.},
year = {1986},
volume = {44},
pages = {281--292},
abstract = {For a class of differentiable dynamical systems (called Axiom
A systems) it has been shown by Pollicott and the author that correlation
functions have Fourier transforms which are meromorphic in a strip. The
poles (or resonances) are, however, not easy to locate. This note reviews
the results which are known and discusses a simple model where the
position of resonances can be estimated. The effect of noise is also
discussed.},
doi = {10.1007/bf01011300},
}
@Article{ruelle86a,
author = {D. Ruelle},
title = {Resonances of chaotic dynamical systems},
journal = {Phys. Rev. Lett.},
year = {1986},
volume = {56},
pages = {405--407},
doi = {10.1103/physrevlett.56.405},
}
@Techreport{Ruelle95,
author = {Ruelle, D.},
title = {Functional determinants related to dynamical systems and the thermodynamic formalism},
institution = {Inst. Hautes Etud. Sci.},
year = {1995},
number = {IHES-P-95-30},
address = {Bures-sur-Yvette},
url = {http://cds.cern.ch/record/281769},
}
@Article{RVVCMG97,
Title = {Review article: {The} dynamics of optically pumped molecular lasers. {On} its relation with the {Lorenz - Haken model}},
Author = {Rold{\'a}n , E. and {de Valc{\'a}rcel}, G. J. and {Vilaseca}, R. and {Corbal{\'a}n}, R. and {Mart{\'{\i}}nez}, V. J. and {Gilmore}, R.},
Journal = {Quantum Semiclass. Opt.},
Year = {1997},
Pages = {R1},
Volume = {9},
DOI = {10.1088/1355-5111/9/1/001}
}
@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{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}
}
@Article{saka90br,
author = {H. Sakaguchi},
title = {Breakdown of the phase dynamics},
journal = {Prog. Ther. Phys.},
year = {1990},
volume = {84},
pages = {792--800},
doi = {10.1143/ptp.84.792},
}
@Article{Sakhr1,
Title = {Amplitude ordering of the trace formula for the two-particle disk billiard},
Author = {Sakhr, J.},
Journal = {Phys. Rev. A},
Year = {2001},
Pages = {044102},
Volume = {64},
DOI = {10.1103/PhysRevA.64.044102}
}
@Article{SalEck15,
Title = {Turbulent states in plane {Couette} flow with rotation},
Author = {Salewski, M. and Eckhardt, B.},
Journal = {Phys. Fluids},
Year = {2015},
Pages = {045109},
Volume = {27},
DOI = {10.1063/1.4917281}
}
@Article{SALOHO11,
author = {Samanta, D. and De Lozar, A. and Hof, B.},
title = {Experimental investigation of laminar turbulent intermittency in pipe flow},
journal = {J. Fluid Mech.},
year = {2011},
volume = {681},
pages = {193--204},
doi = {10.1017/jfm.2011.189},
}
@Article{Samoilenko2005,
author = {A. M. Samoilenko and L. Recke},
title = {Conditions for synchronization of one oscillation system},
journal = {Ukrain. Math. J.},
year = {2005},
volume = {57},
pages = {1089--1119},
doi = {10.1007/s11253-005-0250-3},
}
@Article{SaOuGoHa11,
Title = {Neutrally buoyant particle dynamics in fluid flows: {Comparison} of experiments with {Lagrangian} stochastic models},
Author = {T. P. Sapsis and N. T. Ouellette and J. P. Gollub and G. Haller},
Journal = {Phys. Fluids},
Year = {2011},
Pages = {093304},
Volume = {23},
DOI = {10.1063/1.3632100}
}
@Article{SapLerm09,
Title = {Dynamically orthogonal field equations for continuous stochastic dynamical systems},
Author = {Sapsis, T. P. and Lermusiaux, P. F. J.},
Journal = {Phys. D},
Year = {2009},
Pages = {2347--2360},
Volume = {238},
DOI = {10.1016/j.physd.2009.09.017}
}
@Article{SapMaj13,
Title = {Blending modified {Gaussian} closure and non-{Gaussian} reduced subspace methods for turbulent dynamical systems},
Author = {Sapsis, T. P. and Majda, A. J.},
Journal = {J. Nonlinear Sci.},
Year = {2013},
Pages = {1039--1071},
Volume = {23},
DOI = {10.1007/s00332-013-9178-1}
}
@Article{SapMajMQDPhysD,
Title = {A statistically accurate modified quasilinear {Gauss}ian closure for uncertainty quantification in turbulent dynamical systems},
Author = {Sapsis, T. P. and Majda, A. J.},
Journal = {Phys. D},
Year = {2013},
Pages = {34--45},
Volume = {252},
DOI = {10.1016/j.physd.2013.02.009}
}
@Article{SapMajPhysD13,
Title = {Blending reduced subspace algorithms for uncertainty quantification of quadratic systems with a stable mean state},
Author = {Sapsis, T. P. and Majda, A. J.},
Journal = {Phys. D},
Year = {2013},
Pages = {61--76},
Volume = {258},
DOI = {10.1016/j.physd.2013.05.004}
}
@Article{Sapsis13,
Title = {Attractor local dimensionality, nonlinear energy transfers and finite-time instabilities in unstable dynamical systems with applications to two-dimensional fluid flows},
Author = {Sapsis, T. P.},
Journal = {Proc. R. Soc. Lond. A},
Year = {2013},
Volume = {469},
DOI = {10.1098/rspa.2012.0550}
}
@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}
}
@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{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 Letters, 34},
Year = {1998},
Pages = {1664--1665}
}
@Article{SB95,
author = {R. Sureshkumar and A. Beris},
title = {Linear stability analysis of viscoelastic {P}oiseuille flow using an {A}rnoldi-based orthogonalization algorithm},
journal = {J. Non-Newton. Fluid Mech.},
year = {1995},
volume = {56},
pages = {151--182},
doi = {10.1016/0377-0257(94)01279-q},
}
@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},
}
@Unpublished{SCD09b,
Title = {Recurrent spatio-temporal structures of translationally invariant {Kuramoto-Sivashinsky} flow},
Author = {Siminos, E. and Cvitanovi{\'c}, P. and Davidchack, R. L.},
Note = {In preparation},
Year = {2011}
}
@Article{SchEck06,
Title = {Edge of chaos in pipe flow},
Author = {T. M. Schneider and B. Eckhardt},
Journal = {Chaos},
Year = {2006},
Pages = {041103},
Volume = {16}
}
@Article{SchEckVoll07,
Title = {Statistical analysis of coherent structures in transitional pipe flow},
Author = {Schneider, T. M. and Eckhardt, B. and Vollmer, J.},
Journal = {Phys. Rev. E},
Year = {2007},
Pages = {066313},
Volume = {75}
}
@Article{SchEckYor07,
author = {T. M. Schneider and B. Eckhardt and J. Yorke},
title = {Turbulence, transition, and the edge of chaos in pipe flow},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {99},
pages = {034502},
doi = {10.1103/PhysRevLett.99.034502},
}
@Book{SchGer00,
title = {{Boundary-Layer Theory}},
publisher = {Springer},
year = {2000},
author = {Schlichting, H. and Gersten, K.},
address = {New York},
keywords = {Boundary-Layer Theory}
}
@Phdthesis{Schmi99,
Title = {Transition to turbulence in linearly stable shear flows},
Author = {A. Schmiegel},
School = {Philipps-Universit{\"a}t Marburg},
Year = {1999},
Note = {Available on {\tt archiv.ub.uni-marburg.de/diss/z2000/0062}}
}
@Article{Schmid10,
Title = {Dynamic mode decomposition of numerical and experimental data},
Author = {P. J. Schmid},
Journal = {J. Fluid Mech.},
Year = {2010},
Pages = {5--28},
Volume = {656},
DOI = {10.1017/S0022112010001217},
Numpages = {24}
}
@Article{Schneider2005,
author = {K. R. Schneider},
title = {Entrainment of modulation frequency: {A} case study},
journal = {Int. J. Bifurc. Chaos},
year = {2005},
volume = {15},
pages = {3579--3588},
doi = {10.1142/s0218127405014234},
}
@Book{Schouten89,
title = {{Tensor Analysis for Physicists}},
publisher = {Dover},
year = {1989},
author = {Schouten, J. A.},
address = {New York}
}
@Book{Schutz80,
title = {{Geometrical Methods of Mathematical Physics}},
publisher = {Cambridge Univ. Press},
year = {1980},
author = {Schutz, B. F.},
address = {Cambridge}
}
@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},
Abstract = {Transition to turbulence in pipe flow is one of the most
fundamental and longest-standing problems in fluid dynamics.
Stability theory suggests that the flow remains laminar for all flow
rates, but in practice pipe flow becomes turbulent even at moderate
speeds. This transition drastically affects the transport efficiency
of mass, momentum, and heat. On the basis of the recent discovery of
unstable traveling waves in computational studies of the
Navier-Stokes equations and ideas from dynamical systems theory, a
model for the transition process has been suggested. We report
experimental observation of these traveling waves in pipe flow,
confirming the proposed transition scenario and suggesting that the
dynamics associated with these unstable states may indeed capture the
nature of fluid turbulence.},
DOI = {10.1126/science.1100393}
}
@Article{ScMaEc10,
author = {Schneider, T. M. and Marinc, D. and Eckhardt, B.},
title = {Localized edge states nucleate turbulence in extended plane {Couette} cells},
journal = {J. Fluid Mech.},
year = {2010},
volume = {646},
pages = {441--451},
address = {Cambridge, UK},
day = {10},
doi = {10.1017/S0022112009993144}
}
@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},
Volume = {57},
Abstract = {Change stability of maps to locate periodic orbits.}
}
@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}
}
@Article{SE97,
author = {A. Schmiegel and B. Eckhardt},
title = {Fractal stability border in plane {Couette} flow},
journal = {Phys. Rev. Lett.},
year = {1997},
volume = {79},
pages = {5250},
}
@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{semwogerere04,
Title = {Secondary instabilities of hexagonal patterns in a {B}enard-{M}arangoni convection experiment},
Author = {D. Semwogerere and M. F. Schatz},
Journal = {Phys. Rev. Lett.},
Year = {2004},
Pages = {124502},
Volume = {93}
}
@Article{SeOsRaSi83,
Title = {Universal properties of the transition from quasi-periodicity to chaos in dissipative systems},
Author = {Sethna, J. and Ostlund, S. and Rand, D. A. and Siggia, E.},
Journal = {Physica D},
Year = {1983},
Pages = {303},
Volume = {8}
}
@Book{seydel,
Title = {From equilibrium to chaos: {Practical} bifurcation and stability analysis},
Author = {R. Seydel},
Publisher = {Elsevier},
Year = {1988},
Address = {New York}
}
@Article{SGB10,
Title = {Snakes and ladders: {Localized} solutions of plane {Couette} flow},
Author = {T. M. Schneider and J. F. Gibson and J. Burke},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {104501},
Volume = {104},
DOI = {10.1103/PhysRevLett.104.104501}
}
@Article{SGLDE08,
author = {T. M. Schneider and J. F. Gibson and M. Lagha and F. De Lillo and B. Eckhardt},
title = {Laminar-turbulent boundary in plane {Couette} flow},
journal = {Phys. Rev. E.},
year = {2008},
volume = {78},
pages = {037301},
note = {\arXiv{0805.1015}},
doi = {10.1103/physreve.78.037301},
}
@Article{SHcgl90,
author = {W. van Saarloos and P. C. Hohenberg},
title = {Pulses and fronts in the complex {Ginzburg-Landau} equation near a subcritical bifurcation},
journal = {Phys. Rev. Lett.},
year = {1990},
volume = {64},
pages = {749},
doi = {10.1103/physrevlett.64.749},
}
@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 = {1--7},
Volume = {121},
Abstract = {Fast Lyapunov indicator method is used to identify the
chaotic and regular regions in the phase space. Periodic orbits are
determined to characterized the resonance properties of these
regions.}
}
@Article{SHcoh92,
author = {W. van Saarloos and P. C. Hohenberg},
title = {Fronts, pulses, sources and sinks in generalized complex {Ginzburg-Landau} equations},
journal = {Physica D},
year = {1992},
volume = {56},
pages = {303--367},
abstract = {Propose the concept of coherent structures and study the
competition between them in chaotic dynamics. Specifically, the
invasion of front to another state is discussed.},
doi = {10.1016/0167-2789(92)90175-m},
}
@Article{shearless,
author = {M. Farazmand and D. Blazevski and G. Haller},
title = {Shearless transport barriers in unsteady two-dimensional flows and maps},
journal = {Physica D},
year = {2014},
volume = {278-279},
pages = {44--57},
doi = {10.1016/j.physd.2014.03.008},
}
@Article{ShenKad82,
author = {S. J. Shenker and L. P. Kadanoff},
title = {Critical behavior of a {KAM} surface: {I. Empirical} results},
journal = {J. Stat. Phys.},
year = {1982},
volume = {27},
pages = {631},
doi = {10.1007/bf01013439},
}
@Article{Shenker82,
Title = {Scaling behavior in a map of a circle onto itself: {Empirical} results},
Author = {S.J. Shenker},
Journal = {Physica D},
Year = {1982},
Pages = {405--411},
Volume = {5},
DOI = {10.1016/0167-2789(82)90033-1}
}
@Article{ShHsGo15,
author = {Shih, Hong-Yan and Hsieh, Tsung-Lin and Goldenfeld, Nigel},
title = {Ecological collapse and the emergence of travelling waves at the onset of shear turbulence},
journal = {Nature Physics},
year = {2015},
doi = {10.1038/nphys3548},
}
@Article{shi2013,
author = {Shi, L. and Avila, M. and Hof, B.},
title = {Scale invariance at the onset of turbulence in {Couette} flow},
journal = {Phys. Rev. Lett.},
year = {2013},
volume = {110},
pages = {204502},
doi = {10.1103/PhysRevLett.110.204502}
}
@Misc{ShiAvHof2015,
author = {Shi, L. and {Lemoult}, G. and {Avila}, K. and {Jalikop}, S. and {Avila}, M. and {Hof}, B.},
title = {The universality class of the transition to turbulence},
year = {2015},
url = {https://arxiv.org/abs/1504.03304},
}
@Article{Shte69,
Title = {Stability of plane {Couette} flow},
Author = {Shtern, V. N.},
Journal = {J. Appl. Mechanics and Tech. Physics},
Year = {1969},
Pages = {793--796},
Volume = {10}
}
@Article{ShWi06,
Title = {Geometry of self-propulsion at low {Reynolds} number},
Author = {Shapere, A. and Wilczek, F.},
Journal = {J. Fluid Mech.},
Year = {2006},
Pages = {557},
Volume = {198}
}
@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{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}
}
@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}
}
@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}
}
@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}
}
@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}
}
@Article{siegel42,
Title = {Iteration of analytic functions},
Author = {C. L. Siegel},
Journal = {Ann. Math.},
Year = {1942},
Pages = {607--612},
Volume = {43}
}
@Article{SieStei90,
Title = {Classical and quantum mechanics of a strongly chaotic billiard system},
Author = {Sieber, M. and Steiner, F.},
Journal = {Physica D},
Year = {1990},
Pages = {248--266},
Volume = {44},
DOI = {10.1016/0167-2789(90)90058-W}
}
@Article{SieStei91,
Title = {Quantization of chaos},
Author = {Sieber, M. and Steiner, F.},
Journal = {Phys. Rev. Lett.},
Year = {1991},
Pages = {1941--1944},
Volume = {67}
}
@PhdThesis{SiminosThesis,
author = {Siminos, E.},
title = {{Recurrent Spatio-temporal Structures in Presence of Continuous Symmetries}},
school = {School of Physics, Georgia Inst. of Technology},
year = {2009},
address = {Atlanta},
note = {\\ \wwwcb{/projects/theses.html}}
}
@InProceedings{simo89,
Title = {On the analytical and numerical approximation of invariant manifolds},
Author = {C. Simo},
Booktitle = {Les M\'{e}thodes Modernes de la M\'{e}canique C\'{e}leste (Goutelas '89)},
Year = {1989},
Address = {Gif-sur-Yvette},
Editor = {D. Benest and C. Froeschl\'{e}},
Pages = {285--329},
Publisher = {Editions Frontieres}
}
@Article{sinai,
Title = {Gibbs measures in ergodic theory},
Author = {Ya. G. Sinai},
Journal = {Russian Mathematical Surveys},
Year = {1972},
Pages = {21},
Volume = {166}
}
@Book{sinai76,
title = {{Introduction to Ergodic Theory}},
publisher = {Princeton Univ. Press},
year = {1976},
author = {Ya. G. Sinai},
address = {Princeton}
}
@Article{SipGol11,
Title = {Directed percolation describes lifetime and growth of turbulent puffs and slugs},
Author = {Sipos, M. and Goldenfeld, N.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {035304},
Volume = {84},
DOI = {10.1103/PhysRevE.84.035304}
}
@Article{sirovcgl90,
author = {J. D. Rodriguez and L. Sirovich},
title = {Low-dimensional dynamics for the complex {Ginzburg-Landau} equation},
journal = {Physica D},
year = {1990},
volume = {43},
pages = {77--86},
doi = {10.1016/0167-2789(90)90017-j},
}
@Article{Sirovich87,
author = {Sirovich, L.},
title = {Turbulence and the dynamics of coherent structures part {I:} coherent structures},
journal = {Quart. Appl. Math.},
year = {1987},
volume = {45},
pages = {561--571},
url = {http://www.jstor.org/stable/43637457}
}
@Article{Sirovich94,
Title = {Reply to ``{O}bservations regarding '{C}oherence and chaos in a model of turbulent boundary layer' by {X}. {Z}hou and {L}. {S}irovich''},
Author = {L. Sirovich and X. Zhou},
Journal = {Phys. Fluids},
Year = {1994},
Pages = {1579--1582},
Volume = {6}
}
@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},
Volume = {4},
Abstract = {A integro-differential equation (KSe) is derived directly from the flame propagation equations near the bifurcation point.}
}
@Article{sivmich80,
Title = {On irregular wavy flow of a liquid down a vertical plane},
Author = {G. I. Sivashinsky and D. M. Michelson},
Journal = {Progr. Theor. Phys. Suppl.},
Year = {1980},
Pages = {2112--2114},
Volume = {66},
DOI = {On irregular wavy flow of a liquid down a vertical plane}
}
@Article{skeleton,
author = {P. Cvitanovi{\'c}},
title = {Periodic orbits as the skeleton of classical and quantum chaos},
journal = {Physica D},
year = {1991},
volume = {51},
pages = {138},
doi = {10.1016/0167-2789(91)90227-z},
}
@Phdthesis{Skuf05,
Title = {Understanding the chaotic saddle with focus on a 9-variable model of planar {Couette} flow},
Author = {J. D. Skufca},
School = {U. Maryland},
Year = {2005},
URL = {https://drum.umd.edu/dspace/handle/1903/2897}
}
@Article{SM,
Title = {The study of hairpin vortices in a laminar boundary layer},
Author = {C. R. Smith and S. P. Metzler},
Journal = {J. Fluid Mech.},
Year = {1983},
Pages = {27},
Volume = {129}
}
@Article{SM83,
author = {Smith, CR and Metzler, SP},
title = {The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer},
journal = {J. Fluid Mech.},
year = {1983},
volume = {129},
pages = {27--54},
doi = {10.1017/s0022112083000634},
}
@Article{smale,
author = {S. Smale},
title = {Differentiable dynamical systems},
journal = {Bull. Amer. Math. Soc.},
year = {1967},
volume = {73},
pages = {747--817},
doi = {10.1142/9789812792822_0021},
}
@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}
}
@Article{Smale70I,
author = {S. Smale},
title = {Topology and mechanics, {I}.},
journal = {Invent. Math.},
year = {1970},
volume = {10},
pages = {305--331},
doi = {10.1142/9789812792822_0039},
}
@Article{Smale70II,
author = {S. Smale},
title = {Topology and mechanics, {II}.},
journal = {Invent. Math.},
year = {1970},
volume = {11},
pages = {45--64},
doi = {10.1007/bf01389805},
}
@Book{Smale80,
title = {{The Mathematics of Time}},
publisher = {Springer},
year = {1980},
author = {S. Smale},
address = {New York},
annote = {Subtitle: Essays on Dynamical Systems, Economic Processes and related topics},
isbn = {9781461381013}
}
@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},
}
@Article{SMH05,
author = {T. R. Smith and J. Moehlis and P. Holmes},
title = {Low-dimensional models for turbulent plane {Couette} flow in a minimal flow unit},
journal = {J. Fluid Mech.},
year = {2005},
volume = {538},
pages = {71--110},
doi = {10.1017/s0022112005005288},
}
@Article{smith2005POD,
author = {Smith, T. R. and Moehlis, J. and Holmes, P.},
title = {Low-dimensional modelling of turbulence using the proper orthogonal decomposition: a tutorial},
journal = {Nonlinear Dynamics},
year = {2005},
volume = {41},
pages = {275--307},
doi = {10.1007/s11071-005-2823-y},
}
@Article{SNGS,
author = {J. Sanche\'{z} and M. Net and B. Gar{\'c}ia-Archilla and C. Sim{\'o}},
title = {{Newton-Krylov} continuation of periodic orbits for {Navier-Stokes} flows},
journal = {J. Comput. Physics},
year = {2004},
volume = {201},
pages = {13--33},
doi = {10.1016/j.jcp.2004.04.018},
}
@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}},
publisher = {Birkh\"auser},
year = {1997},
author = {J.-M. Souriau},
address = {Boston},
doi = {10.1007/978-1-4612-0281-3},
}
@Article{Spalart91,
author = {P. R. Spalart and R. D. Moser and M. M. Rogers},
title = {Spectral methods for the {Navier-Stokes} equations with one infinite and two periodic directions},
journal = {J. Comp. Phys.},
year = {1991},
volume = {96},
pages = {297--324},
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},
Abstract = {A brief survey of modelling equations of fully developed
homogeneous turbulence. Kolmogorov's original paper is translated.}
}
@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{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},
Volume = {66}
}
@Book{spfunc1,
title = {Special functions: an introduction to the classical functions of mathematical physics},
publisher = {Wiley},
year = {1996},
author = {N. M. Temme},
address = {New York},
}
@Techreport{SpiekerBlog,
Title = {{Gone fishin' - a research blog on fluid flows}},
Author = {Spieker, D. W.},
Institution = {School of Physics, Georgia Inst. of Technology},
Year = {2009},
Note = {{\tt Channelflow.org/dokuwiki/doku.php/gtspring2009:spieker\_blog}}
}
@Article{spotspreading,
author = {N. Tillmark},
title = {On the spreading mechanisms of a turbulent spot in plane {Couette} flow},
journal = {Europhys. Lett.},
year = {1995},
volume = {32},
pages = {481--485},
doi = {10.1209/0295-5075/32/6/004},
}
@Article{Spruill07,
author = {Spruill, M. C.},
title = {Asymptotic distribution of coordinates on high dimensional spheres},
journal = {Elect. Commun. in Probab.},
year = {2007},
volume = {12},
pages = {234--247},
doi = {10.1214/ecp.v12-1294},
}
@Article{SPScgl92,
Title = {Spatiotemporal chaos in the one-dimensional complex {Ginzburg-Landau} equation},
Author = {B. I. Shraiman and A. Pumir and W. van Saarloos and P. C. Hohenberg and H. Chat{\'e} and M. Holen},
Journal = {Physica D},
Year = {1992},
Pages = {241--248},
Volume = {57}
}
@Article{Sq33,
Title = {On the stability of three-dimensional distribution of viscous fluid between parallel walls},
Author = {H. B. Squire},
Journal = {Proc. Roy. Soc. A},
Year = {1933},
Pages = {621},
Volume = {142}
}
@Article{SS86,
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{stabpcgl,
author = {B. J. Matkowsky and V. Volpert},
title = {Stability of plane wave solutions of complex {Ginzburg-Landau} equations},
journal = {Quart. Appl. Math.},
year = {1993},
volume = {LI},
pages = {265--281},
doi = {10.1090/qam/1218368},
}
@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{SteLar91,
author = {C. G. Steinmetz and R. Larter},
title = {The quasiperiodic route to chaos in a model of the peroxidase--oxidase reaction},
journal = {J. Chem. Phys},
year = {1991},
volume = {94},
pages = {1388--1396},
doi = {10.1063/1.459996},
}
@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},
abstract = {A nonlinear equation of the plasma surface is derived for the small deformation. Possible solitary solutions are discussed.},
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},
doi = {10.1063/1.873038},
}
@Article{sternb57,
author = {S. Sternberg},
title = {Local contractions and a theorem of {Poincar\'e}},
journal = {Amer. J. Math.},
year = {1957},
volume = {79},
pages = {809--824},
doi = {10.2307/2372437}
}
@Article{sternb58,
author = {S. Sternberg},
title = {On the structure of local homeomorphisms of {Euclidean} n-space, {II}},
journal = {Amer. J. Math.},
year = {1958},
volume = {80},
pages = {623--631},
doi = {10.2307/2372774}
}
@Article{sternb59,
author = {S. Sternberg},
title = {The structure of local homeomorphisms},
journal = {Amer. J. Math.},
year = {1959},
volume = {81},
pages = {578},
doi = {10.2307/2372915}
}
@Book{StGo09,
Title = {Mathematics for Physics: A Guided Tour for Graduate Students},
Author = {M. Stone and P. Goldbart},
Publisher = {Cambridge Univ. Press},
Year = {2009},
Address = {Cambridge}
}
@Article{STMEG15,
Title = {Velocity profile in a two-layer {Kolmogorov}-like flow},
Author = {Suri, B. and Tithof, J. and Mitchell, R. and R. Grigoriev and M. Schatz},
Journal = {Phys. Fluids},
Year = {2014},
Pages = {053601},
Volume = {26},
DOI = {10.1063/1.4873417}
}
@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},
abstract = {Singular perturbation method. Through scaling
transformation, a small parameter is introduced such that when it is
equal to zero, the map becomes simple and controlable though
non-deterministic. The symbolic dynamics is easy to build and the AI
limit orbit can be extended in a unique way to the small parameter
case when the AI limit is nondegenerate. {H}{\'e}non map is used to
demonstrate the idea.},
doi = {10.1016/s0375-9601(98)00094-2},
}
@Article{Stokes1845,
author = {Stokes, G. G.},
title = {On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids},
journal = {Trans. Cambridge Philosophical Soc.},
year = {1845},
volume = {8},
pages = {287--319},
doi = {10.1017/cbo9780511702242.005},
}
@Conference{STPGS15,
Title = {Experimental Observation of Exact Coherent Structures in a Weakly Turbulent Quasi-Two-Dimensional Flow},
Author = {B. Suri and J. Tithof and R. K. Pallantla and R. Grigoriev and M. Schatz},
Booktitle = {68\textsuperscript{th} Annual Meeting of the APS Division of Fluid Dynamics},
Year = {2015},
Series = {Bull. Am. Phys. Soc},
Volume = {60},
URL = {http://meetings.aps.org/link/BAPS.2015.DFD.D29.2}
}
@Book{strogb,
Title = {Nonlinear Dynamics and Chaos},
Author = {S. H. Strogatz},
Publisher = {Perseus Books},
Year = {2000},
Address = {Cambridge, MA}
}
@Article{StrWan02,
Title = {Instability of traveling waves of the {Kuramoto-Sivashinsky} equation},
Author = {Strauss, W. and Wang, G.},
Journal = {Chin. Ann. Math.},
Year = {2002},
Number = {02},
Pages = {267--276},
Volume = {23},
DOI = {10.1142/S0252959902000250},
Eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0252959902000250}
}
@InProceedings{sunil_ahuja_template-based_2006,
Title = {Template-based stabilization of relative equilibria},
Author = {S. Ahuja and {I.G.} Kevrekidis and {C.W.} Rowleym},
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{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 = {2016},
volume = {118},
pages = {114501},
doi = {10.1103/physrevlett.118.114501},
}
@Article{SW60,
Title = {On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows},
Author = {J. T. Stuart and J. Watson},
Journal = {J. Fluid Mech.},
Year = {1960},
Pages = {353--370, 371--389},
Volume = {9}
}
@Article{SWG02,
author = {P. A. Stone and F. Waleffe and M. D. Graham},
title = {Toward a structural understanding of turbulent drag reduction: {Nonlinear} coherent states in viscoelastic shear flows},
journal = {Phys. Rev. Lett.},
year = {2002},
volume = {89},
pages = {20831},
doi = {10.1103/physrevlett.89.208301},
}
@Article{SwinneyPhysD83,
author = {H. L. Swinney},
title = {Observations of order and chaos in nonlinear systems},
journal = {Physica D},
year = {1983},
volume = {7},
pages = {3--15},
doi = {10.1016/0167-2789(83)90111-2},
}
@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{Sylvester1852,
Title = {A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares},
Author = {Sylvester, J. J.},
Journal = {Philos. Mag.},
Year = {1852},
Pages = {138--142},
Volume = {4}
}
@Article{symmcgl,
author = {A. Doelman},
title = {Breaking the hidden symmetry in the {Ginzburg-Landau} equation},
journal = {Physica D},
year = {1996},
volume = {97},
pages = {398--428},
doi = {10.1016/0167-2789(95)00303-7},
}
@Article{TaGiCh09,
author = {Takeuchi, K. A. and Ginelli, F. and Chat\'{e}, H.},
title = {{Lyapunov} analysis captures the collective dynamics of large chaotic systems},
journal = {Phys. Rev. Lett.},
year = {2009},
volume = {103},
pages = {154103},
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{tajima02,
author = {S. Tajima and H. S. Greenside},
title = {Microextensive chaos of a spatially extended system},
journal = {Phys. Rev. E},
year = {2002},
volume = {66},
pages = {017205},
doi = {10.1103/physreve.66.017205},
}
@Article{Takh93,
Title = {On foundation of the generalized {Nambu} mechanics},
Author = {Takhtajan, L.},
Journal = {Commun. Math. Phys.},
Year = {1994},
Note = {\arXiv{hep-th/9301111}},
Pages = {295--316},
Volume = {160},
DOI = {10.1007/BF02103278}
}
@Article{TakOon84,
Title = {Towards the statistical mechanics of chaos},
Author = {Takahashi, Y. and Oono, Y.},
Journal = {Prog. Theor. Phys},
Year = {1984},
Pages = {851--854},
Volume = {71},
DOI = {10.1143/PTP.71.851}
}
@Book{Taub61,
Title = {{John von Neumann}: Collected Works. {Volume II}: {Operators}, Ergodic Theory and Almost Periodic Functions in a Group},
Editor = {A. H. Taub},
Publisher = {Pergamon Press},
Year = {1961},
Address = {New York}
}
@Article{Taylor23,
author = {Taylor, G. I.},
title = {Stability of a viscous liquid contained between two rotating cylinders},
journal = {Phil. Trans. Royal Soc. A},
year = {1923},
volume = {223},
pages = {289--343},
doi = {10.1098/rspa.1923.0013},
}
@Article{Taylor38,
Title = {The spectrum of turbulence},
Author = {Taylor, G. I.},
Journal = {Proc. R. Soc. Lond. A},
Year = {1938},
Pages = {476--490},
Volume = {164},
DOI = {10.1098/rspa.1938.0032}
}
@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},
Volume = {217}
}
@Book{TE05,
Title = {Spectra and pseudospectra: the behavior of nonnormal matrices and operators},
Author = {L. N. Trefethen and M. Embree},
Publisher = {Princeton Univ. Press},
Year = {2005},
Address = {Princeton}
}
@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{temam91edd,
author = {R. Temam},
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},
}
@Article{tenenbaum2000,
author = {Tenenbaum, J. B. and Silva, V. de and Langford, J. C.},
title = {A global geometric framework for nonlinear dimensionality reduction},
journal = {Science},
year = {2000},
volume = {290},
pages = {2319--2323},
doi = {10.1126/science.290.5500.2319},
}
@Book{Tennekes72,
Title = {A First Course in Turbulence},
Author = {H. Tennekes and J.L. Lumley},
Publisher = {MIT Press},
Year = {1972},
Addr = {Cambridge, MA}
}
@Article{teramura2014,
author = {Teramura, T. and Toh, S.},
title = {Damping filter method for obtaining spatially localized solutions},
journal = {Phys. Rev. E},
year = {2014},
volume = {89},
pages = {052910},
doi = {10.1103/physreve.89.052910},
}
@Article{TFGphase97,
Title = {Studies of phase turbulence in the one dimensional complex {Ginzburg-Landau} equation},
Author = {A. Torcini und H. Frauenkron and P. Grassberger},
Journal = {Phys. Rev. E},
Year = {1997},
Pages = {5073},
Volume = {55},
Abstract = {The phase gradient is used as an order parameter.
Different states are identified. In the PT region, a modified KSe
rules the phase dynamics of the CGLe.}
}
@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},
pages = {16--28},
note = {\arXiv{physics/0009017}},
abstract = {Constraints are found on the spatial variation of finite-time Lyapunov
exponents of two and three-dimensional systems of ordinary differential
equations. In a chaotic system, finite-time Lyapunov exponents describe
the average rate of separation, along characteristic directions,
of neighboring trajectories. The solution of the equations is a coordinate
transformation that takes initial conditions (the Lagrangian coordinates)
to the state of the system at a later time (the Eulerian coordinates).
This coordinate transformation naturally defines a metric tensor,
from which the Lyapunov exponents and characteristic directions are
obtained. By requiring that the Riemann curvature tensor vanish for
the metric tensor (a basic result of differential geometry in a flat
space), differential constraints relating the finite-time Lyapunov
exponents to the characteristic directions are derived. These constraints
are realized with exponential accuracy in time. A consequence of
the relations is that the finite-time Lyapunov exponents are locally
small in regions where the curvature of the stable manifold is large,
which has implications for the efficiency of chaotic mixing in the
advection-diffusion equation. The constraints also modify previous
estimates of the asymptotic growth rates of quantities in the dynamo
problem, such as the magnitude of the induced current.},
doi = {10.1063/1.1342079},
}
@Article{Thiffeault11,
Title = {Using multiscale norms to quantify mixing and transport},
Author = {Thiffeault, J.-L.},
Journal = {Nonlinearity},
Year = {2012},
Note = {\arXiv{1105.1101}},
Pages = {1--44},
Volume = {25},
DOI = {10.1088/0951-7715/25/2/R1}
}
@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},
note = {\arXiv{nlin/0101012}},
doi = {10.1016/s0167-2789(02)00588-2},
}
@Article{Thoo98,
author = {Thoo, J. B.},
title = {A picture is worth a thousand words},
journal = {College Math. J.},
year = {1998},
volume = {29},
pages = {408--411},
doi = {10.2307/2687256},
}
@Article{TI03,
author = {S. Toh and T. Itano},
title = {A periodic-like solution in channel flow},
journal = {J. Fluid Mech.},
year = {2003},
volume = {481},
pages = {67--76},
doi = {10.1017/s0022112003003768},
}
@Book{Tinkham,
Title = {Group Theory and Quantum Mechanics},
Author = {Tinkham, M.},
Publisher = {Dover},
Year = {2003},
Address = {New York}
}
@Unpublished{tithof16,
author = {J. Tithof and B. Suri and R. K. Pallantla and R. O. Grigoriev and M. F. Schatz},
title = {Bifurcations in a quasi-two-dimensional {Kolmogorov}-like flow},
note = {Submitted to J. Fluid Mech.},
year = {2016},
url = {https://arXiv.org/abs/1601.00243},
}
@PhdThesis{Tithof2016,
author = {J. Tithof},
title = {Dimensionality reduction of spatiotemporal chaos in a quasi-two-dimensional flow},
school = {Georgia Institute of Technology},
year = {2016}
}
@Article{TKSSG14,
author = {Tuckerman, L. S. and Kreilos, T. and Schrobsdorff, H. and Schneider, T. M. and Gibson, J. F.},
title = {Turbulent-laminar patterns in plane Poiseuille flow},
journal = {Phys. Fluids},
year = {2014},
volume = {26},
pages = {114103},
doi = {10.1063/1.4900874}
}
@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},
abstract = {Pancharatnam's geometric phase is introduced for such nonlinear dissipative
systems as lasers and liquid flows. Two types of geometric; phases
are shown to arise in these systems: the phase induced by the inner
dynamics of the system and the one caused by the cyclic and adiabatic
variation of the system parameters. A possible generalization of
the geometric-effects theory in other dissipative systems is discussed.},
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},
abstract = {We show that such phenomena of laser dynamics as mean-phase-slope
jumps and temporal phase jumps at resonance between the cavity and
spectral line frequencies are intrinsically connected with the topology
of attractors in the space of rays and can be interpreted as the
manifestations of the geometric-phase properties of the evolution
operator.},
doi = {10.1103/physreva.50.878},
keywords = {complex Lorenz, geometric phase, Laser, symmetry},
}
@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},
abstract = {An investigation is made of the geometric phases in a ring laser with
counterpropagating waves. It is shown that the frequency splitting
of the counterpropagating waves that appears in the case of radiation
pulsations or is induced by displacement of an external mirror can
be regarded as a manifestation of a geometric phase.},
doi = {10.1070/qe1997v027n07abeh001007},
}
@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{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--1290},
doi = {10.1364/josab.15.001282},
}
@Article{tompaid96,
author = {S. Tompaidis},
title = {Numerical Study of Invariant Sets of a Quasi-periodic Perturbation of a Symplectic Map},
journal = {Experimental Mathematics},
year = {1996},
volume = {5},
pages = {211--230},
abstract = {{N}ewton method is used to construct periodic orbits of
longer and longer period to approach a invariant torus with specific
rotation vector. Behavior after the break of a torus is described.},
doi = {10.1080/10586458.1996.10504589},
}
@Article{torc96,
author = {A. Torcini},
title = {Order parameter for the transition from phase to amplitude turbulence},
journal = {Phys. Rev. Lett.},
year = {1996},
volume = {77},
pages = {1047},
abstract = {the maximal consersed phase gradient is introduced as an
order parameter to characterize the transition from phase to defect
turbulence in the cgle. it has a finite value in the pt regime and
decreases to zero when the transition to defect turbulence is
approached. a modified kse is able to reproduce the main feature of
the stable waves and to explain their origin.},
doi = {10.1103/physrevlett.77.1047},
}
@Article{toricgl,
author = {P. Tak{\'a}{\v{c}}},
title = {Invariant 2-tori in the time-dependent {Ginzburg-Landau} equation},
journal = {Nonlinearity},
year = {1992},
volume = {5},
pages = {289--321},
doi = {10.1088/0951-7715/5/2/002},
}
@Article{Townsend1961,
author = {A. A. Townsend},
title = {Equilibrium layers and wall turbulence},
journal = {J. Fluid Mech.},
year = {1961},
volume = {11},
pages = {97--120},
doi = {10.1017/S0022112061000883}
}
@Book{Townsend76,
Title = {The Structure of Turbulent Shear Flows, 2\textsuperscript{nd} Edn.},
Author = {A. A. Townsend},
Publisher = {Cambridge Univ. Press},
Year = {1976},
Address = {Cambridge}
}
@Article{transgol,
Title = {Transport by capillary waves, {Part II}: {Scalar} dispersion and the structure of the concentration field},
Author = {R. Ramshankar and J. P. Gollub},
Journal = {Phys. Fluids A},
Year = {1991},
Pages = {1344},
Volume = {3}
}
@Article{Tre97,
author = {L. Trefethen},
title = {Pseudospectra of linear operators},
journal = {SIAM Rev.},
year = {1997},
volume = {39},
pages = {383--406},
doi = {10.1137/s0036144595295284},
}
@Book{Tref00,
Title = {Spectral methods in {M}atlab},
Author = {L. N. Trefethen},
Publisher = {SIAM},
Year = {2000},
Address = {Philadelphia}
}
@Book{Trefethen97,
Title = {Numerical Linear Algebra},
Author = {L. N. Trefethen and D. Bau},
Publisher = {SIAM},
Year = {1997},
Addr = {Philadelphia}
}
@Unpublished{TrThNi14,
Title = {Knotted strange attractors and matrix {Lorenz} systems},
Author = {{Tranchida}, J. and {Thibaudeau}, P. and {Nicolis}, S.},
Note = {\arXiv{1404.7774}},
Year = {2014}
}
@Article{TTRD93,
Title = {Hydrodynamic stability without eigenvalues},
Author = {N. Trefethen and A. E. Trefethen and S. C. Reddy and T. A. Driscoll},
Journal = {Science},
Year = {1993},
Pages = {578--584},
Volume = {261}
}
@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},
note = {\arXiv{physics/0312051}},
abstract = {Perturbed plane Couette flow containing a thin
spanwise-oriented ribbon undergoes a subcritical bifurcation at
Re = 230 to a steady 3D state containing streamwise vortices.
This bifurcation is followed by several others giving rise to a
fascinating series of stable and unstable steady states of
different symmetries and wavelengths. First, the
backwards-bifurcating branch reverses direction and becomes
stable near Re = 200. Then, the spanwise reflection symmetry is
broken, leading to two asymmetric branches which are themselves
destabilized at Re = 420. Above this Reynolds number, time
evolution leads first to a metastable state whose spanwise
wavelength is halved and then to complicated time-dependent
behavior. These features are in agreement with experiments.},
doi = {10.1007/s00162-002-0064-y},
}
@Article{TuckBar07,
author = {L. S. Tuckerman and D. Barkley},
title = {Mean flow and modeling of turbulent-laminar patterns in plane {Couette} flow},
journal = {Springer Proc. Physics},
year = {2007},
volume = {117},
pages = {224--226},
doi = {10.1007/978-3-540-72604-3_71},
}
@Article{tucker2002ros,
author = {Tucker, W.},
title = {A rigorous {ODE} solver and {Smale's 14th} problem},
journal = {Found. Comp. Math},
year = {2002},
volume = {2},
pages = {53--117},
address = {New York},
doi = {10.1007/s002080010018},
publisher = {Springer},
}
@Book{Tung85,
Title = {Group Theory in Physics},
Author = {Tung, W.-K.},
Publisher = {World Scientific},
Year = {1985},
Address = {Singapore}
}
@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{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}
}
@Phdthesis{vanDoorne04,
Title = {Stereoscopic {PIV} on transition in pipe flow},
Author = {C. W. H. van Doorne},
School = {Delft},
Year = {2004},
URL = {www.ahd.tudelft.nl}
}
@Article{VC08,
Title = {Stable manifolds and the transition to turbulence in pipe flow},
Author = {Viswanath, D. and Cvitanovi{\'c}, P.},
Journal = {J. Fluid Mech.},
Year = {2009},
Pages = {215--233},
Volume = {627},
DOI = {10.1017/S0022112009006041}
}
@Article{ViSa09,
Title = {Complex singularities and the {Lorenz} attractor},
Author = {Viswanath, D. and \c{S}ahuto\u{g}lu, S.},
Journal = {SIAM Rev.},
Year = {2010},
Pages = {294--314},
Volume = {52},
DOI = {10.1137/090753474}
}
@Article{VK11,
author = {L. van Veen and G. Kawahara},
title = {Homoclinic tangle on the edge of shear turbulence},
journal = {Phys. Rev. Lett.},
year = {2011},
volume = {107},
pages = {114501},
doi = {10.1103/physrevlett.107.114501},
}
@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{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 = {Technical Physics},
year = {1998},
volume = {43},
pages = {877--884},
doi = {10.1134/1.1259094},
}
@Article{vN32,
author = {J. von Neumann},
title = {{Zur Operatorenmethode In Der Klassischen Mechanik}},
journal = {Ann. Math.},
year = {1932},
volume = {33},
pages = {587--642},
note = {See additions \cite{vonNeum32}. Reprinted in \cite{Taub61}.},
doi = {10.2307/1968537},
}
@Article{vonNeum32,
Title = {{Zus{\"a}tze zur Arbeit ``Zur Operatorenmethode in der klassischen Mechanik''}. ({German}) [{Additions} to the work ``{On} operator methods in classical mechanics'']},
Author = {J. von Neumann},
Journal = {Ann. Math.},
Year = {1932},
Pages = {789--791},
Volume = {33}
}
@Article{Voros87,
Title = {Spectral functions, special functions and the {Selberg} zeta function},
Author = {Voros, A.},
Journal = {Commun. Math. Phys.},
Year = {1987},
Pages = {439--465},
Volume = {110},
DOI = {10.1007/BF01212422}
}
@Article{Voros92,
Title = {Spectral zeta functions},
Author = {Voros, A.},
Journal = {Adv. Stud. Pure Math},
Year = {1992},
Pages = {327--358},
Volume = {21}
}
@Book{Vorst03,
Title = {Iterative Krylov Methods for Large Linear Systems},
Author = {H. A. Vorst},
Publisher = {Cambridge Univ. Press},
Year = {2003},
Address = {Cambridge}
}
@Article{voth02,
Title = {Experimental measurements of streching fields in fluid mixing},
Author = {G. A. Voth and G. Haller and J. P. Gollub},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Pages = {254501},
Volume = {88},
}
@Article{voth07,
author = {K.-Y. Chan and D. Stich and G. A. Voth},
title = {Real-time image compression for high-speed particle tracking},
journal = {Rev. Sci. Inst.},
year = {2007},
volume = {78},
pages = {02374},
doi = {10.1063/1.2536719},
}
@Article{vp98,
author = {A. Varga and S. Pieters},
title = {Gradient-Based Approach to Solve Optimal Periodic Output Feedback Control Problems},
journal = {Automatica},
year = {1998},
volume = {34},
pages = {477--481},
abstract = {A numerical method based on the gradient minimization
and Periodic Schur Decomposition (PSD) is devised to solve the
linear-quadratic (LQ) optimization problem the linear periodic
discrete-time control systems. It can be used as a discretized
version of the similar problem in the continuous regime.},
doi = {10.1016/s0005-1098(97)00214-8},
}
@Article{VSE98,
author = {J. Vollmer and T. M. Schneider and B. Eckhardt},
title = {Basin boundary, edge of chaos, and edge state in a two-dimensional model},
journal = {New J. Phys.},
year = {2009},
volume = {11},
pages = {013040},
doi = {10.1088/1367-2630/11/1/013040},
}
@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 = {Shigeo Kida},
Pages = {115--128},
Publisher = {National Center of Sciences, Tokyo, Japan}
}
@Article{W03,
author = {F. Waleffe},
title = {Homotopy of exact coherent structures in plane shear flows},
journal = {Phys. Fluids},
year = {2003},
volume = {15},
pages = {1517--1543},
doi = {10.1063/1.1566753},
}
@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}
}
@Article{W95a,
author = {F. Waleffe},
title = {Hydrodynamic stability and turbulence: {Beyond} transients to a {Self-Sustaining Process}},
journal = {Stud. Applied Math.},
year = {1995},
volume = {95},
pages = {319--343},
doi = {10.1002/sapm1995953319},
}
@Article{W95b,
author = {F. Waleffe},
title = {Transition in shear flows: {Nonlinear} normality versus non-normal linearity},
journal = {Phys. Fluids},
year = {1995},
volume = {7},
pages = {3060--3066},
doi = {10.1063/1.868682},
}
@Article{W97,
Title = {On a {Self-Sustaining Process} in shear flows},
Author = {F. Waleffe},
Journal = {Phys. Fluids},
Year = {1997},
Pages = {883--900},
Volume = {9},
DOI = {10.1063/1.869185}
}
@Article{W98,
author = {F. Waleffe},
title = {Three-dimensional coherent states in plane shear flows},
journal = {Phys. Rev. Lett.},
year = {1998},
volume = {81},
pages = {4140--4143},
doi = {10.1103/physrevlett.81.4140},
}
@Misc{Waleffe2005,
author = {F. Waleffe},
title = {On transition scenarios in channel flows},
year = {1990},
note = {preprint},
url = {http://www.math.wisc.edu/~waleffe/M812/obtran.pdf}
}
@Unpublished{Waleffe90,
Title = {Proposal for a self-sustaining mechanism in shear flows},
Author = {F. Waleffe},
Note = {Center for Turbulence Research, Stanford University/NASA Ames, unpublished preprint (1990)},
Year = {1990},
URL = {http://www.math.wisc.edu/~waleffe/ECS/sspctr90.pdf}
}
@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 = {www.math.wisc.edu/~waleffe/ECS/WK97.pdf}
}
@Phdthesis{Way08,
Title = {Dynamics in the {Hopf} bundle, the geometric phase and implications for dynamical systems},
Author = {Way, R.},
School = {Dept. of Mathematics, U. Surrey},
Year = {2008}
}
@Article{WBHZ14,
Title = {Unstable flow structures in the {Blasius} boundary layer},
Author = {H. Wedin and A. Bottaro and A. Hanifi and G. Zampogna},
Journal = {Eur. Phys. J. E},
Year = {2014},
Pages = {34},
Volume = {37},
DOI = {10.1140/epje/i2014-14034-1}
}
@InProceedings{WeBoHaZa13,
Title = {Three-dimensional nonlinear states in the {Blasius} boundary layer},
Author = {Wedin, H. and Bottaro, A. and Hanifi, A. and Zampogna, G.},
Booktitle = {AIMETA Conference, 17-20 September 2013},
Year = {2013},
Address = {Torino, Italy},
Volume = {XXI},
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{WegSol02,
Title = {On some mathematics for visualizing high dimensional data},
Author = {Wegman, E. J. and Solka, J. L.},
Journal = {Sankhy{\=a}: Indian J. Statistics, Ser. A},
Year = {2002},
Pages = {429--452}
}
@Article{Weil49,
author = {Weil, A.},
title = {Numbers of solutions of equations in finite fields},
journal = {Bull. Amer. Math. Soc},
year = {1949},
volume = {55},
pages = {497--508},
doi = {10.1007/978-1-4757-1705-1_50},
}
@Article{weiss82,
author = {J. Weiss and M. Tabor and G. Carnevale},
title = {The {P}ainlev{\'e} property for partial differential equations},
journal = {J. Math. Phys.},
year = {1983},
volume = {24},
pages = {522},
doi = {10.1063/1.525721},
}
@Article{weiss83,
Title = {The {P}ainlev{\'e} for partial differential equations. {II}: {B\"a}cklund transformation, {Lax} pairs, and the {Schwarzian} derivative},
Author = {J. Weiss},
Journal = {J. Math. Phys.},
Year = {1983},
Pages = {1405},
Volume = {24}
}
@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},
doi = {10.1063/1.527134},
}
@Misc{WeissFeig,
Title = {Feigenbaum constant},
Author = {Weisstein, E. W.},
Note = {mathworld.wolfram.com/FeigenbaumConstant.html},
Year = {2012}
}
@Book{Weyl39,
Title = {The Classical Groups: Their Invariants and Representations},
Author = {Weyl, H.},
Publisher = {Princeton Univ. Press},
Year = {1939},
Address = {Princeton, NJ},
ISBN = {9780691057569}
}
@Article{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},
journal = {J. Fluid Mech.},
year = {2017},
volume = {833},
pages = {274--301},
doi = {10.1017/jfm.2017.699},
}
@Article{WGW07,
author = {J. Wang and J. F. Gibson and F. Waleffe},
title = {Lower branch coherent states in shear flows: {Transition} and control},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {98},
pages = {204501},
note = {\arXiv{physics/0703072}},
doi = {10.1103/physrevlett.98.204501},
}
@Article{WHC10,
author = {A. P. Willis and Y. Hwang and C. Cossu},
title = {Optimally amplified large-scale streaks and drag reduction in turbulent pipe flow},
journal = {Phys. Rev. E},
year = {2010},
volume = {82},
pages = {036321},
doi = {10.1103/physreve.82.036321},
}
@Unpublished{WiAvCv12,
Title = {Symmetries of turbulent flows: {How} to slice them},
Author = {Willis, A. P. and Avila, M. and Cvitanovi{\'c}, P.},
Note = {In preparation},
Year = {2012}
}
@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},
Author = {S. Wiggins},
Publisher = {Springer},
Year = {1988},
Address = {New York}
}
@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{WillKer07,
author = {A. P. Willis and R. R. Kerswell},
title = {Critical behavior in the relaminarization of localized turbulence in pipe flow},
journal = {Phys. Rev. Lett.},
year = {2007},
volume = {98},
pages = {014501},
doi = {10.1103/physrevlett.98.014501},
}
@Article{WillKer08,
author = {A. P. Willis and R. R. Kerswell},
title = {Coherent structures in localised and global pipe turbulence},
journal = {Phys. Rev. Lett.},
year = {2008},
volume = {100},
pages = {124501},
doi = {10.1103/physrevlett.100.124501},
}
@Article{WillKer09,
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{Wimmer73,
author = {H. K. Wimmer},
title = {{On the Ostrowski-Schneider Inertia Theorem}},
journal = {J. Math. Anal. Appl.},
year = {1973},
volume = {41},
pages = {164--169},
doi = {10.1016/0022-247x(73)90190-x},
}
@Article{Win92,
author = {D. Wintgen and K. Richter and G. Tanner},
title = {Quantization of chaotic systems},
journal = {Chaos},
year = {1992},
volume = {2},
pages = {53},
doi = {10.1063/1.165897},
}
@Article{WiShCv15,
author = {Willis, A. P. and Short, K. Y. and Cvitanovi{\'c}, P.},
title = {Symmetry reduction in high dimensions, illustrated in a turbulent pipe},
journal = {Phys. Rev. E},
year = {2016},
volume = {93},
pages = {022204},
doi = {10.1103/PhysRevE.93.022204},
}
@Article{witt99hol,
author = {R. W. Wittenberg and P. Holmes},
title = {Scale and space localization in the {Kuramoto-Sivashinsky} equation},
journal = {Chaos},
year = {1999},
volume = {9},
pages = {452},
abstract = {Using a wavelet basis, the spatiotemporally chaotic regime of
the KSe is explored where a good seperation of scales is observed.
In large scales, the dynamics is Gaussian.
In the intermediate scales, the dynamics is reminiscent of travelling waves
and heteroclinic cyces which is the typical behavior for small system size.
In the small scales, the dynamics is intermittent. Through investigation of
the interaction between different scales, we see the intermediate structures
give the defining shape of the cell and the large scales trigger
the spatiotemporal chaos. The small scales dissipate energy
and modify the background in a average sense.},
doi = {10.1063/1.166419},
}
@Article{WK04,
author = {H. Wedin and R. R. Kerswell},
title = {Exact coherent structures in pipe flow: {Traveling} wave solutions},
journal = {J. Fluid Mech.},
year = {2004},
volume = {508},
pages = {333--371},
doi = {10.1017/s0022112004009346},
}
@InProceedings{WKH93,
Title = {On the origin of streaks in turbulent shear flows},
Author = {F. Waleffe and J. Kim and J. Hamilton},
Booktitle = {Turbulent Shear Flows 8: Selected papers from the Eighth International Symposium on Turbulent Shear Flows, Munich, Germany, Sept.\ 9-11, 1991},
Year = {1993},
Address = {Berlin},
Editor = {F. Durst and R. Friedrich and B. E. Launder and F. W. Schmidt and U. Schumann and J. H. Whitelaw},
Pages = {37--49},
Publisher = {Springer}
}
@Article{WoSa07,
author = {Wolfe, C. L. and Samelson, R. M.},
title = {An efficient method for recovering {Lyapunov} vectors from singular vectors},
journal = {Tellus A},
year = {2007},
volume = {59},
pages = {355--366},
abstract = {
Standard techniques for computing Lyapunov vectors produce
results which are norm-dependent and lack invariance under
the linearized flow. An efficient, norm-independent method
for constructing the n most rapidly growing Lyapunov
vectors from n-1 leading forward and n leading backward
asymptotic singular vectors is proposed. The Lyapunov
vectors so constructed are invariant under the linearized
flow in the sense that, once computed at one time, they are
defined, in principle, for all time through the tangent
linear propagator. An analogous method allows the
construction of the n most rapidly decaying Lyapunov
vectors from n decaying forward and n-1 decaying backward
singular vectors.},
doi = {10.3402/tellusa.v59i3.15003},
}
@Article{WPKM08,
author = {A. P. Willis and J. Peixinho and R. R. Kerswell and T. Mullin},
title = {Experimental and theoretical progress in pipe flow transition},
journal = {Phil. Trans. R. Soc. A},
year = {2008},
volume = {366},
pages = {2671--2684},
doi = {10.1098/rsta.2008.0063},
}
@Techreport{Wri06,
Title = {Eigtool, a graphical tool for nonsymmetric eigenproblems},
Author = {T. Write},
Institution = {Oxford Univ.},
Year = {2006},
Note = {{\tt web.comlab.ox.ac.uk/projects/pseudospectra/eigtool}}
}
@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}
}
@Book{Wu85,
Title = {Group theory in physics},
Author = {Wu, K.-T.},
Publisher = {World Scientific},
Year = {1985},
Address = {Singapore}
}
@Article{Wulff00,
Title = {Transitions from relative equilibria to relative periodic orbits},
Author = {C. Wulff},
Journal = {Doc. Math.},
Year = {2000},
Pages = {227--274},
Volume = {5}
}
@Article{Wulff01,
author = {Wulff, C. and Lamb, J. S. W. and Melbourne, I.},
title = {Bifurcation from relative periodic solutions},
journal = {Ergod. Theor. Dynam. Syst.},
year = {2001},
volume = {21},
pages = {605--635},
doi = {10.1017/s0143385701001298},
}
@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,
author = {C. Wulff},
title = {Persistence of {Hamiltonian} relative periodic orbits},
journal = {J. Geometry and Physics},
year = {2003},
volume = {48},
pages = {309--338},
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}
}
@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}
}
@Article{WygCha73,
author = {I. J. Wygnanski and F. H. Champagne},
title = {On transition in a pipe. {Part 1. The} origin of puffs and slugs and the flow in a turbulent slug},
journal = {J. Fluid Mech.},
year = {1973},
volume = {59},
pages = {281--335},
month = jun,
address = {Cambridge, UK},
day = {01},
doi = {10.1017/S0022112073001576}
}
@Article{wygnanski2006tpp,
author = {Wygnanski, I. and Sokolov, M. and Friedman, D.},
title = {On transition in a pipe. {Part 2. The} equilibrium puff},
journal = {J. Fluid Mech.},
year = {1975},
volume = {69},
pages = {283--304},
doi = {10.1017/s0022112075001449},
}
@Article{Xia92,
author = {Xia, Z.},
title = {Existence of invariant tori in volume-preserving diffeomorphisms},
journal = {Ergod. Theor. Dynam. Syst.},
year = {1992},
volume = {12},
pages = {621--31},
doi = {10.1017/s0143385700006969},
}
@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},
}
@phdthesis{yoffe2012,
title={Investigation of the transfer and dissipation of energy in isotropic turbulence},
author={Yoffe, S. R.},
year={2012},
url={https://arxiv.org/abs/1306.3408},
school={The University of Edinburgh}
}
@Article{YTGCR08,
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{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,
Title = {Coupled Electron Surface Plasma Wave Solitons in Slabs},
Author = {S. V. Vladimirov and M. Y. Yu},
Journal = {Phys. Lett. A},
Year = {1994},
Pages = {459},
Volume = {184}
}
@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},
abstract = {By using the natural measure to construct the canonical
conjugate of the observed signal, the authors can identify the
dynamical equivalence of two signals from one process.},
doi = {10.1103/physrevlett.85.4265},
}
@Article{Zagarola98,
author = {M. V. Zagarola and A. J. Smits},
title = {Mean flow scaling of turbulent pipe flow},
journal = {J. Fluid Mech.},
year = {1998},
volume = {373},
pages = {33--79},
doi = {10.1017/s0022112098002419},
}
@Article{ZamEck14,
Title = {Streamwise and doubly-localised periodic orbits in plane {Poiseuille} flow},
Author = {Zammert, S. and Eckhardt, B.},
Journal = {J. Fluid Mech.},
Year = {2014},
Pages = {348--359},
Volume = {761},
DOI = {10.1017/jfm.2014.633}
}
@Article{ZamEck14a,
Title = {A spotlike edge state in plane {Poiseuille} flow},
Author = {Zammert, S. and Eckhardt, B.},
Journal = {PAMM},
Year = {2014},
Pages = {591--592},
Volume = {14},
DOI = {10.1002/pamm.201410283}
}
@Article{ZamEck14b,
Title = {Periodically bursting edge states in plane {Poiseuille} flow},
Author = {Zammert, S. and Eckhardt, B.},
Journal = {Fluid Dyn. Research},
Year = {2014},
Pages = {041419},
Volume = {46},
DOI = {10.1088/0169-5983/46/4/041419}
}
@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}
}
@Misc{ZamEck16a,
Title = {Streamwise decay of localized states in channel flow},
Author = {Zammert, S. and Eckhardt, B.},
Year = {2016},
URL = {https://arxiv.org/abs/1609.06514}
}
@Article{Zang91,
author = {T. A. Zang},
title = {On the rotation and skew-symmetric forms for incompressible flow simulations},
journal = {Appl. Num. Math.},
year = {1991},
volume = {7},
pages = {27--40},
doi = {10.1016/0168-9274(91)90102-6},
}
@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--22},
doi = {10.1364/josab.2.000018},
}
@Article{ZG96,
Title = {Spatially localized unstable periodic orbits of a high-dimensional chaotic system},
Author = {S. M. Zoldi and H. S. Greenside},
Journal = {Phys. Rev. E},
Year = {1998},
Addendum = {\arXiv{chao-dyn/9704005}},
Pages = {R2511--R2514},
Volume = {57},
DOI = {10.1103/PhysRevE.57.R2511}
}
@Article{Zhou92,
author = {X. Zhou and L. Sirovich},
title = {Coherence and Chaos in a model of turbulent boundary layer},
journal = {Phys. Fluids A},
year = {1992},
volume = {4},
pages = {2855--2874},
doi = {10.1063/1.858340},
}
@Article{zielinska95,
author = {B. J. A. Zielinska and J. E. Wesfreid},
title = {On the spatial structure of global modes in wake flow},
journal = {Phys. Fluids},
year = {1995},
volume = {7},
pages = {1418--1424},
doi = {10.1063/1.868529},
}
@Article{Schlichting33,
author = {Schlichting, H.},
title = {{Zur Enstehung der Turbulenz bei der Plattenstr{\"o}mung}},
journal = {Nachr. Ges. Wiss. Gottingen, Math.-Phys.},
year = {1933},
volume = {1933},
pages = {181-208},
url = {http://eudml.org/doc/59420},
}
@Article{OT80,
author = {Y. Oono and Y. Takahashi},
title = {Chaos, external noise and {Fredholm} theory},
journal = {Progr. Theor. Phys.},
year = {1980},
volume = {63},
pages = {1804--1807},
doi = {10.1143/PTP.63.1804},
}
@Book{Mezic17,
title = {{Spectral Koopman Operator Methods in Dynamical Systems}},
publisher = {Springer},
year = {2017},
author = {Mezi\'c, I.},
address = {New York},
note = {In preparation},
}
@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},
}
@Article{Donzis_2014,
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},
}
@PhdThesis{Neelavara17,
author = {Acharya Neelavara, S.},
title = {Numerical study of transition to turbulence in plane {Poiseuille} flow in physical space and state space},
school = {{Universit{\'e} Paris-Saclay}},
year = {2017},
url = {https://tel.archives-ouvertes.fr/tel-01476343},
}
@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{Kim87,
author = {J. Kim and P. Moin and R. Moser},
title = {Turbulence statistics in fully developed channel flow at low {R}eynolds number},
journal = {J. Fluid Mech.},
year = {1987},
volume = {177},
pages = {133--166},
doi = {10.1017/s0022112087000892},
}
@Book{Wat07,
title = {The Matrix Eigenvalue Problem: {GR} and {Krylov} Subspace Methods},
publisher = {SIAM},
year = {2007},
author = {Watkins, D. S.},
address = {Philadelphia},
}
@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{dCH02,
author = {de Carvalho, A. and Hall, T.},
title = {How to prune a horseshoe},
journal = {Nonlinearity},
year = {2002},
volume = {15},
pages = {R19–R68},
doi = {10.1088/0951-7715/15/3/201},
}
@Article{BenCar91,
author = {M. Benedicks and L. Carleson},
title = {The dynamics of the {H{\'e}non} map},
journal = {Ann. Math.},
year = {1991},
volume = {133},
pages = {73},
doi = {10.2307/2944326},
}
@InCollection{statespDummies,
author = {P. Cvitanovi{\'c}},
title = {Life in extreme dimensions},
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#flows},
}
@Article{Wil12,
author = {Willis, A. P.},
title = {Optimization of the magnetic dynamo},
journal = {Phys. Rev. Lett.},
year = {2012},
volume = {109},
pages = {251101},
doi = {10.1103/physrevlett.109.251101},
}
@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{BjoGol73,
author = {Bj{\"o}rck, \AA. and Golub, G. H.},
title = {Numerical methods for computing angles between linear subspaces},
journal = {Math. Comput.},
year = {1973},
volume = {27},
pages = {579--594},
doi = {10.1090/S0025-5718-1973-0348991-3},
}
@Article{DWCDDEGHLSPSST13,
author = {Dijkstra, H. A. and Wubs, F. W. and Cliffe, A. K. and Doedel, E. and Dragomirescu, I. F. and Eckhardt, B. and Gelfgat, A. Y. and Hazel, A. L. and Lucarini, V. and Salinger, A. G. and Phipps, E. T. and Sanchez-Umbria, J. and Schuttelaars, H. and Tuckerman, L. S. and Thiele, U.},
title = {Numerical bifurcation methods and their application to fluid dynamics: {Analysis} beyond simulation},
journal = {Commun. Comput. Phys.},
year = {2014},
volume = {15},
pages = {1–-45},
doi = {10.4208/cicp.240912.180613a},
}
@Article{Willis17,
author = {Willis, A.P.},
title = {The {Openpipeflow Navier–Stokes} solver},
journal = {SoftwareX},
year = {2017},
volume = {6},
pages = {124-127},
doi = {10.1016/j.softx.2017.05.003},
}
@Misc{AhmSha17,
author = {M. A. Ahmed and A. Sharma},
title = {New equilibrium solution branches of plane {Couette} flow discovered using a project-then-search method},
year = {2017},
url = {https://arxiv.org/abs/1706.05312},
}
@Article{ZaFiEc16,
author = {Zammert, S. and Fischer, N. and Eckhardt, B.},
title = {Transition in the asymptotic suction boundary layer over a heated plate},
journal = {J. Fluid Mech.},
year = {2016},
volume = {803},
pages = {175–199},
doi = {10.1017/jfm.2016.514},
}
@Article{SaLeAl16,
author = {M. Sala and J. C. Leitão and E. G. Altmann},
title = {Searching chaotic saddles in high dimensions},
journal = {Chaos},
year = {2016},
volume = {26},
pages = {123124},
doi = {10.1063/1.4973235},
}
@Article{NeDuLu17,
author = {Acharya Neelavara, S. and Y. Duguet and F. Lusseyran},
title = {State space analysis of minimal channel flow},
journal = {Fluid Dyn. Research},
year = {2017},
volume = {49},
pages = {035511},
doi = {10.1088/1873-7005/aa6790},
}
@Article{AHMNPTB03,
author = {M. Abid and C. Huepe and S. Metens and C. Nore and C. T. Pham and L. S. Tuckerman and M. E. Brachet},
title = {{Gross–Pitaevskii} dynamics of {Bose–Einstein} condensates and superfluid turbulence},
journal = {Fluid Dyn. Research},
year = {2003},
volume = {33},
pages = {509--544},
doi = {10.1016/j.fluiddyn.2003.09.001},
}
@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{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},
}
@Incollection{kornyak-2007,
author = {Kornyak, V. V.},
title = {Symmetries and dynamics of discrete systems},
booktitle = {{Computer Algebra in Scientific Computing: 10th International Workshop, CASC 2007, Bonn}},
publisher = {Springer},
year = {2007},
editor = {Ganzha, V. G. and Mayr, E. W. and Vorozhtsov, E. V.},
pages = {236--251},
address = {Berlin},
doi = {10.1007/978-3-540-75187-8_19},
}
@Incollection{KREROSLIDE13,
author = {Krauss, J. and Ertun\c{c}, \"{O}. and Ostwald, C. and Lienhart, H. and Delgado, A.},
title = {Probability of occurrence of the turbulent flow structures in transitional pipe flows},
booktitle = {{New Results in Numerical and Experimental Fluid Mechanics VIII}},
publisher = {Springer},
year = {2013},
editor = {Dillmann, A. and Heller, G. and Kreplin, H.-P. and Nitsche, W. and Peltzer, I.},
pages = {271--278},
address = {New York},
doi = {10.1007/978-3-642-35680-3_33},
isbn = {978-3-642-35680-3},
}
@Misc{SmiWis17,
author = {Smith, W. R. and Wissink, J. G.},
title = {Asymptotic analysis of the attractors in two-dimensional {Kolmogorov} flow},
year = {2017},
note = {Eur. J. Appl. Math., to appear},
url = {http://bura.brunel.ac.uk/handle/2438/14877},
}
@Article{OleMog07,
author = {Olesen, P. and Jensen, M. H.},
title = {Exact periodic solutions of shell models of turbulence},
journal = {Nonlinearity},
year = {2007},
volume = {20},
pages = {2333},
doi = {10.1088/0951-7715/20/10/004},
}
@Article{JensenBakBohr1983,
author = {Jensen, M. H. and Bak, P. and Bohr, T.},
title = {Complete devil's staircase fractal dimension and universality of mode-locking structure in the circle map},
journal = {Phys. Rev. Lett.},
year = {1983},
volume = {50},
pages = {1637--1639},
doi = {10.1103/PhysRevLett.50.1637},
}
@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},
}
@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://ChaosBook.org/projects/theses.html},
}
@Article{rowley_reduction_2003,
author = {Rowley, C. W. and Kevrekidis, I. G. and Marsden, J. E. and Lust, K.},
title = {Reduction and reconstruction for self-similar dynamical systems},
journal = {Nonlinearity},
year = {2003},
volume = {16},
pages = {1257--1275},
doi = {10.1088/0951-7715/16/4/304}
}
@Article{rowley_reconstruction_2000,
author = {Rowley, C. W. and Marsden, J. E.},
title = {Reconstruction equations and the {Karhunen-Lo{\'e}ve} expansion for systems with symmetry},
journal = {Physica D},
year = {2000},
volume = {142},
pages = {1--19},
doi = {10.1016/S0167-2789(00)00042-7},
}
@Article{rowley04,
author = {Rowley, C. W.},
title = {Model reduction for fluids, using balanced proper orthogonal decomposition},
journal = {Int. J. Bifur. Chaos},
year = {2005},
volume = {15},
pages = {997--1013},
doi = {10.1142/S0218127405012429},
eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218127405012429},
}
@Article{RoMeBaSchHe09,
author = {Rowley, C. W. and Mezi\'c, I. and Bagheri, S. and Schlatter, P. and Henningson, D. S.},
title = {Spectral analysis of nonlinear flows},
journal = {J. Fluid Mech.},
year = {2009},
volume = {641},
pages = {115},
doi = {10.1017/s0022112009992059},
}
@Article{Knyazev02,
author = {A. V. Knyazev and M. E. Argentati},
title = {Principal angles between subspaces in an {A-based} scalar product: {Algorithms} and perturbation estimates},
journal = {SIAM J. Sci. Comput.},
year = {2002},
volume = {23},
pages = {2008--2040},
doi = {10.1137/S1064827500377332},
}
@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{Gribov77,
author = {Gribov, V. N.},
title = {Quantization of nonabelian gauge theories},
journal = {Nucl. Phys.},
year = {1978},
volume = {B139},
pages = {1--19},
doi = {10.1016/0550-3213(78)90175-X},
}
@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{cresson-2006,
author = {J. Cresson and C. Guillet},
title = {Hyperboliity versus partial-hyperbolicity and the transversality-torsion phenomenon},
journal = {J. Diff. Eqn.},
year = {2008},
volume = {244},
pages = {2123--2132},
doi = {10.1016/j.jde.2008.02.009},
}
@Article{EDUR15,
author = {Engl, T. and Urbina, J. D. and Richter, K.},
title = {The semiclassical propagator in {Fock} space: dynamical echo and many-body interference},
journal = {Phil. Trans. R. Soc. A},
year = {2016},
volume = {374},
pages = {20150159},
doi = {10.1098/rsta.2015.0159},
}
@Article{foias88,
author = {C. Foias and M. S. Jolly and I. G. Kevrekidis and G. R. Sell and E. S. Titi},
title = {On the computation of inertial manifolds},
journal = {Phys. Lett. A},
year = {1988},
volume = {131},
pages = {433--436},
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 Temam, R.},
address = {Cambridge},
isbn = {9781139428996},
doi = {10.1017/cbo9780511546754},
}
@Article{FNSTks85,
author = {C. Foias and B. Nicolaenko and G. R. Sell and R. Temam},
title = {Inertial manifold for the {Kuramoto-Sivashinsky} equation},
journal = {C. R. Acad. Sci., Paris},
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. Temam},
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 Temam, R.},
title = {Inertial manifolds for nonlinear evolutionary equations},
journal = {J. Diff. Eqn.},
year = {1988},
volume = {73},
pages = {309--353},
doi = {10.1016/0022-0396(88)90110-6},
}
@Article{LevnMezi08,
author = {Levnaji{\'c}, Z. and Mezi{\'c}, I.},
title = {Ergodic theory and visualization. {I. Mesochronic} plots for visualization of ergodic partition and invariant sets},
journal = {Chaos},
year = {2010},
pages = {033114},
doi = {10.1063/1.3458896},
}
@Article{Li08,
author = {Y. C. Li and D. Viswanath},
title = {Exact and asymptotic conditions on traveling wave solutions of the {Navier–Stokes} equations},
journal = {Phys. Fluids},
year = {2009},
volume = {21},
pages = {101703},
doi = {10.1063/1.3244660},
}
@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{Postl08,
author = {C. M. Postlethwaite},
title = {Stabilisation of long-period periodic orbits using time-delayed feedback control},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2009},
volume = {8},
pages = {21--39},
doi = {10.1137/080721510},
}
@Article{HBWF11,
author = {Heng-Bin, A. and Wen, J. and Feng, T.},
title = {On finite difference approximation of a matrix-vector product in the Jacobian-free Newton-Krylov method},
journal = {J. Comput. Appl. Math.},
year = {2011},
volume = {236},
pages = {1399--1409},
doi = {10.1016/j.cam.2011.09.003},
}
@Article{DV02,
author = {D. Viswanath},
title = {The {Lindstedt-Poincar{\'e}} technique as an algorithm for finding periodic orbits},
journal = {SIAM Rev.},
year = {2001},
volume = {43},
pages = {478--495},
doi = {10.1137/S0036144500375292},
}
@Article{DV03,
author = {D. Viswanath},
title = {Symbolic dynamics and periodic orbits of the {Lorenz} attractor},
journal = {Nonlinearity},
year = {2003},
volume = {16},
pages = {1035--1056},
doi = {10.1088/0951-7715/16/3/314},
}
@Article{DV04,
author = {D. Viswanath},
title = {The fractal property of the {Lorenz} attractor},
journal = {Physica D},
year = {2004},
volume = {190},
pages = {115--128},
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 = {Phil. Trans. Royal Soc. A},
year = {2009},
volume = {367},
pages = {561--576},
doi = {10.1098/rsta.2008.0225},
}
@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{DVLindstedt,
author = {D. Viswanath},
title = {The {Lindstedt-Poincar{\'e}} technique as an algorithm for finding periodic orbits},
journal = {{SIAM} Review},
year = {2001},
volume = {43},
pages = {478--495},
doi = {10.1137/s0036144500375292},
}
@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{Barkley16,
author = {Barkley, D.},
title = {Theoretical perspective on the route to turbulence in a pipe},
journal = {J. Fluid Mech.},
year = {2016},
volume = {803},
pages = {1--80},
doi = {10.1017/jfm.2016.465},
}
@Article{GibSch16,
author = {Gibson, J. F. and Schneider, T. M.},
title = {Homoclinic snaking in plane {Couette} flow: bending, skewing and finite-size effects},
journal = {J. Fluid Mech.},
year = {2016},
volume = {794},
pages = {530–551},
doi = {10.1017/jfm.2016.177},
}
@Misc{CaVeJi17,
author = {Cardesa, J.~I. and Vela-Mart{\'{\i}}n, A. and Jim{\'e}nez, J.},
title = {The turbulent cascade in five dimensions},
year = {2017},
note = {Science 357 (2017), to appear},
url = {https://arxiv.org/abs/1708.00706},
}
@Book{Goldenfeld92,
title = {{Lectures on Phase Transitions and the Renormalization Group}},
publisher = {Westview Press},
year = {1992},
author = {Goldenfeld, N.},
isbn = {9780201554090},
}
@Book{Kardar07,
title = {{Statistical Physics of Fields}},
publisher = {Cambridge Univ. Press},
year = {2007},
author = {Kardar, M.},
isbn = {9780521873413},
doi = {10.1017/cbo9780511815881},
}
@Book{Kadanoff00,
title = {{Statistical Physics: Statics, Dynamics and Renormalization}},
publisher = {World Scientific},
year = {2000},
author = {Kadanoff, L.P.},
isbn = {9789810237646},
address = {Singapore},
}
@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},
}
@Misc{RZEA17,
author = {Ritter, P. and Zammert, S. and Eckhardt, B. and Avila, M.},
title = {Sensitivity analysis of systems using unstable periodic orbits},
year = {2017},
url = {https://arxiv.org/abs/1703.08730},
}
@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{ZamEck16,
author = {Zammert, S. and Eckhardt, B.},
title = {Harbingers and latecomers - {The} order of appearance of exact coherent structures in plane {Poiseuille} flow},
journal = {J. Turbul.},
year = {2017},
volume = {18},
pages = {103-114},
doi = {10.1080/14685248.2016.1245420},
}
@Article{MaLiLa13,
author = {Ma, H. and Lin, W. and Lai, Y.-.},
title = {Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: {Reconstruction} meeting with adaptation},
journal = {Phys. Rev. E},
year = {2013},
volume = {87},
pages = {050901},
doi = {10.1103/PhysRevE.87.050901},
}
@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},
}
@TechReport{Inubushi13,
author = {Inubushi, M.},
title = {Covariant {Lyapunov} analysis of {Navier-Stokes} turbulence},
institution = {Kyoto Univ.},
year = {2013},
number = {RIMS Preprint 1770},
address = {Kyoto},
url = {http://www.kurims.kyoto-u.ac.jp/preprint/file/RIMS1770.pdf},
}
@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},
}
@Article{InKoTaYa12,
author = {Inubushi, M. and Kobayashi, M. U. and Takehiro, S.-i. and Yamada, M.},
title = {Covariant {Lyapunov} analysis of chaotic {Kolmogorov} flows},
journal = {Phys. Rev. E},
year = {2012},
volume = {85},
pages = {016331},
doi = {10.1103/PhysRevE.85.016331},
}
@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},
}
@Article{RaCoRi17,
author = {S. Rawat and C. Cossu and F. Rincon},
title = {Exact invariant solutions for coherent turbulent motions in {Couette} and {Poiseuille} flows},
journal = {Procedia IUTAM},
year = {2017},
volume = {20},
pages = {94--98},
doi = {https://doi.org/10.1016/j.piutam.2017.03.013},
}
@Misc{YaWiHw17,
author = {Yang, Q. and Willis, A. P. and Hwang, Y.},
title = {Energy production and self-sustained turbulence at the {Kolmogorov} scale in {Couette} flow},
year = {2017},
note = {J. Fluid Mech., to appear},
url = {http://eprints.whiterose.ac.uk/121604/},
}
@Misc{ZamEck17,
author = {Zammert, S. and Eckhardt, B.},
title = {Small scale exact coherent structures at large {Reynolds} numbers in plane {Couette} flow},
year = {2017},
url = {https://arxiv.org/abs/1710.00741},
}
@Article{LucBot14,
author = {P. Luchini and A. Bottaro},
title = {Adjoint equations in stability analysis},
journal = {Ann. Rev. Fluid Mech.},
year = {2014},
volume = {46},
pages = {493-517},
doi = {10.1146/annurev-fluid-010313-141253},
}
@Misc{OtShSa17,
author = {J. J. Otero and A. Sharma and R. D. Sandberg},
title = {Compressible invariant solutions in open cavity flows},
year = {2017},
url = {https://arxiv.org/abs/1710.03060},
}
@Book{OrtRhe70,
title = {{Iterative Solution of Nonlinear Equations in Several Variables}},
publisher = {SIAM},
year = {1970},
author = {Ortega, J. M. and Rheinboldt, W. C.},
isbn = {9780898719468},
address = {Philadelphia, PA},
}
@Book{Kuzn04,
title = {{Elements of Applied Bifurcation Theory}},
publisher = {Springer},
year = {2004},
author = {Y. A. Kuznetsov},
isbn = {978-1-4419-1951-9},
address = {New York},
edition = {3},
doi = {10.1007/978-1-4757-3978-7},
}
@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},
}
@Book{AllGeo03,
title = {{Introduction to Numerical Continuation Methods}},
publisher = {SIAM},
year = {2003},
author = {Allgower, E. L. and Georg, K.},
isbn = {9780898715446},
doi = {10.1137/1.9780898719154},
}
@Book{BenGre03,
title = {{Generalized Inverses: Theory and Applications}},
publisher = {Springer},
year = {2003},
author = {Ben-Israel, A. and Greville, T. N. E.},
isbn = {9780387216348},
address = {New York},
}
@Book{KrOsGa07,
title = {{Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems}},
publisher = {Springer},
year = {2007},
author = {Krauskopf, B. and Osinga, H. M. and Galan-Vioque, J.},
isbn = {9781402063565},
}
@TechReport{LOCA,
author = {A. G. Salinger and M. Bou-Rabee and R. P. Pawlowski and E. D. Wilkes and E. A. Burroughs and R. B. Lehouc and L. A. Romero},
title = {{{LOCA}: A library of continuation algorithms - theory and implementation manual}},
institution = {Sandia Nat. Lab.},
year = {2001},
url = {http://www.cs.sandia.gov/projects/loca/},
}
@Article{WuSche06,
author = {Wulff, C. and Schebesch, A.},
title = {Numerical continuation of symmetric periodic orbits},
journal = {SIAM J. Appl. Dyn. Syst.},
year = {2006},
volume = {5},
pages = {435--475},
doi = {10.1137/050637170},
}
@Book{Miller73,
title = {{Symmetry Groups and Their Applications}},
publisher = {Elsevier},
year = {1973},
author = {Miller, W.},
isbn = {9780080873657},
}
@Book{Olver95,
title = {{Equivalence, Invariants and Symmetry}},
publisher = {Cambridge Univ. Press},
year = {1995},
author = {Olver, P. J.},
isbn = {9780521478113},
doi = {10.1017/cbo9780511609565},
}
@Article{WDOW17,
author = {Willis, A. P. and Duguet, Y. and Omel’chenko, O. and Wolfrum, M.},
title = {Surfing the edge: using feedback control to find nonlinear solutions},
journal = {J. Fluid Mech.},
year = {2017},
volume = {831},
pages = {579–591},
doi = {10.1017/jfm.2017.656},
}
@Article{OZSVL17,
author = {Ostilla-M\'onico, R. and Zhu, X. and Spandan, V. and Verzicco, R. and Lohse, D.},
title = {Life stages of wall-bounded decay of {Taylor-Couette} turbulence},
journal = {Phys. Rev. Fluids},
year = {2017},
volume = {2},
pages = {114601},
doi = {10.1103/PhysRevFluids.2.114601},
}
@Article{ChTuBa17,
author = {Chantry, M. and Tuckerman, L. S. and Barkley, D.},
title = {Universal continuous transition to turbulence in a planar shear flow},
journal = {J. Fluid Mech.},
year = {2017},
volume = {824},
pages = {R1},
doi = {10.1017/jfm.2017.405},
}
@Misc{Lasagna17a,
author = {D. Lasagna},
title = {Sensitivity analysis of systems using unstable periodic orbits},
year = {2017},
url = {https://arxiv.org/abs/1708.04121},
}
@Misc{SheGra17,
author = {A. Shekar and M. D. Graham},
title = {Sensitivity analysis of systems using unstable periodic orbits},
year = {2017},
url = {https://arxiv.org/abs/1709.02484},
}
@Misc{TuGiWi17,
author = {L. S. Tuckerman and J. F. Gibson and A. Willis,},
title = {Stokes preconditioning for rapid calculation of steady states and traveling waves},
year = {2017},
note = {In preparation},
}
@Misc{BudHof17a,
author = {N. B. Budanur and B. Hof},
title = {State-space geometry of the laminar-turbulent boundary in pipe flow},
year = {2017},
note = {In preparation},
}
@Article{HaMeZaGa17,
author = {I. Hameduddin and C. Meneveau and T. Zaki and D. F. Gayme},
title = {Geometric decomposition of the conformation tensor in viscoelastic turbulence},
journal = {J. Fluid Mech.},
year = {2017},
note = {To appear},
}
@Article{HamGay17,
author = {I. Hameduddin and D. F. Gayme},
title = {A model-based scale by scale analysis of convective velocities in turbulent channels},
journal = {J. Fluid Mech.},
year = {2017},
note = {To appear},
}
@Article{GuWiHoiAv17,
author = {Guseva, A. and Willis, A. P. and Hollerbach, R. and Avila, M.},
title = {Transport Properties of the Azimuthal Magnetorotational Instability},
journal = {Astrophys. J.},
year = {2017},
volume = {849},
pages = {92},
doi = {10.3847/1538-4357/aa917d},
}
@Article{GuHoWiAv17,
author = {Guseva, A. and Hollerbach, R. and Willis, A. P. and Avila, M.},
title = {Dynamo action in a quasi-{Keplerian Taylor-Couette} flow},
journal = {Phys. Rev. Lett.},
year = {2017},
volume = {119},
pages = {164501},
doi = {10.1103/physrevlett.119.164501},
}
@Article{ZhScScXi17,
author = {L. Zhu and H. Schrobsdorff and T. Schneider and L. Xi},
title = {Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids},
journal = {J. Non-Newt. Fluid Mech.},
year = {2017},
note = {Submitted},
}
@Article{Shankar_2017,
author = {S. Shankar and M. J. Bowick and M. Cristina Marchetti},
title = {Topological Sound and Flocking on Curved Surfaces},
journal = {Physical Review X},
year = {2017},
volume = {7},
doi = {10.1103/physrevx.7.031039},
}
@Article{DelMarVen17,
author = {P. Delplace and J. B. Marston and A. Venaille},
title = {Topological origin of equatorial waves},
journal = {Science},
year = {2017},
pages = {eaan8819},
doi = {10.1126/science.aan8819},
}
@Article{LecKer17,
author = {D. Lecoanet and and Kerswell, R. R.},
title = {Connection between nonlinear energy optimization and instantons},
journal = {Phys. Rev. Lett.},
year = {2017},
note = {To appear},
}
@Comment{jabref-meta: databaseType:bibtex;}