% Encoding: UTF-8
@Article{AACI,
Title = {Recycling of strange sets: {I}. {Cycle} expansions},
Author = {R. Artuso and E. Aurell and P. Cvitanovi{\'{c}}},
Journal = {Nonlinearity},
Year = {1990},
Pages = {325--359},
Volume = {3}
}
@Article{AgCheb02,
Title = {On Determining the Eigenprojection and Components of a Matrix},
Author = {R. P. Agaev and P. Yu. Chebotarev},
Journal = {Automation and Remote Control},
Year = {2002},
Pages = {1537--1545},
Volume = {63}
}
@Article{AACII,
Title = {Recycling of strange sets: {II}. {Applications}},
Author = {R. Artuso and E. Aurell and P. Cvitanovi{\'{c}}},
Journal = {Nonlinearity},
Year = {1990},
Pages = {361},
Volume = {3}
}
@Article{AakHoeEhHe07,
Title = {Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes},
Author = {{\AA}kervik, E. and H{\oe}pffner, J. and Ehrenstein, U. and {Henningson}, D. S.},
Journal = {J. Fluid Mech.},
Year = {2007},
Pages = {305--314},
Volume = {579},
DOI = {10.1017/S0022112007005496}
}
@Article{Ab09,
Title = {Effective actions for statistical data assimilation},
Author = {Abarbanel, H. D. I.},
Journal = {Phys. Lett. A},
Year = {2009},
Pages = {4044--4048},
Volume = {373}
}
@Misc{Ab10,
Title = {Self-consistent stochastic model errors in data assimilation},
Author = {Abarbanel, H. D. I.},
Note = {\arXiv{1012.2031}},
Year = {2010}
}
@Article{AbBrKe91,
Title = {{Lyapunov} exponents in chaotic systems: their importance and their evaluation using observed data},
Author = {H. D. I. Abarbanel and R. Brown and M. B. Kennel},
Journal = {Int. J. Mod. Phys. B},
Year = {1991},
Pages = {1347--1375},
Volume = {5}
}
@Article{AbBrKe91a,
Title = {Variation of {Lyapunov} exponents on a strange attractor},
Author = {H. D. I. Abarbanel and R. Brown and M. B. Kennel},
Journal = {J. Nonlinear Sci.},
Year = {1991},
Pages = {175--199},
Volume = {1}
}
@Book{ablowbook,
Title = {Solitions, Nonlinear Evolution Equations and Inverse Scattering},
Author = {M. J. Ablowitz and P. A. Clarkson},
Publisher = {Cambridge Univ. Press},
Year = {1992},
Address = {Cambridge}
}
@Book{Amann90,
Title = {Ordinary Differential Equations: an Introduction to Nonlinear Analysis},
Author = {H. Amann},
Publisher = {De Gruyter},
Year = {1990},
Address = {Berlin}
}
@Book{AbrSte64,
Title = {Handbook of Mathematical Functions},
Editor = {Abramowitz, M. and Stegun, I. A.},
Publisher = {Dover},
Year = {1964},
Address = {New York}
}
@Article{ACFK09,
Title = {Dynamical state and parameter estimation},
Author = {H. D. I. Abarbanel and D. R. Creveling and R. Farsian and M. Kostuk},
Journal = {SIAM J. Appl. Math.},
Year = {2009},
Pages = {1341--1381},
Volume = {8}
}
@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},
Note = {\arXiv{1203.3701}},
Pages = {514--540},
Volume = {721},
DOI = {10.1017/jfm.2013.75}
}
@Article{ACK89,
Title = {Phase transitions on strange irrational sets},
Author = {Artuso, R. and Cvitanovi\'{c}, P. and Kenny, B. G.},
Journal = {Phys. Rev. A},
Year = {1989},
Pages = {268--281},
Volume = {39},
DOI = {10.1103/PhysRevA.39.268}
}
@Article{afind,
Title = {Characterization of unstable periodic orbits in chaotic attractors and repellers},
Author = {O. Biham and W. Wenzel},
Journal = {Phys. Rev. Lett.},
Year = {1989},
Pages = {819},
Volume = {63}
}
@Article{AFT06,
Title = {{H}ermite function expansions versus {H}ermite polynomial expansions},
Author = {Abu-Falahah, I. and Torrea, J. L.},
Journal = {Glasgow Math. J.},
Year = {2006},
Pages = {203--215},
Volume = {48}
}
@Article{AG93,
Title = {Fast dynamos and determinants of singular intergral-opertaors},
Author = {E. Aurell and A. D. Gilbert},
Journal = {Geophys. Astrophys. Fluid Dyn.},
Year = {1993},
Pages = {5--32},
Volume = {73}
}
@Article{AGHks88,
Title = {Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry},
Author = {D. Armbruster and J. Guckenheimer and P. Holmes},
Journal = {Physica D},
Year = {1988},
Pages = {257--282},
Volume = {29},
Abstract = {Consider the normal form on the center manifold for the KSe and
discuss bifurcations with intrinsic O(2) symmetry.}
}
@Article{AGHks89,
Title = {{Kuramoto-Sivashinsky} Dynamics on the Center-Unstable manifold},
Author = {D. Armbuster and J. Guckenheimer and P. Holmes},
Journal = {SIAM J. Appl. Math.},
Year = {1989},
Pages = {676--691},
Volume = {49}
}
@Article{AhRo07,
Title = {Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators},
Author = {S. Ahuja and C. W. Rowley},
Journal = {J. Fluid Mech.},
Year = {2007},
Note = {\arXiv{0902.1207}},
Pages = {447--478},
Volume = {645}
}
@Article{AKcgl02,
Title = {The World of the Complex {G}inzburg-{L}andau Equation},
Author = {I. S. Aranson and L. Kramer},
Journal = {Rev. Mod. Phys.},
Year = {2002},
Pages = {99--143},
Volume = {74}
}
@Misc{akesson98discrete,
Title = {Discrete eigenfunction expansion of multi-dimensional {Brownian} motion and the {Ornstein-Uhlenbeck} process},
Author = {Akesson, F. and Lehoczky, J. P. },
Note = {preprint, Math. Sciences, Carnegie Mellon Univ.},
Year = {1998}
}
@Article{AlBa11,
Title = {Normal forms approach to diffusion near hyperbolic equilibria},
Author = {Almada Monter, S. A. and Bakhtin, Y.},
Journal = {Nonlinearity},
Year = {2011},
Number = {6},
Pages = {1883},
Volume = {24},
DOI = {10.1088/0951-7715/24/6/011}
}
@Article{AlEyRe05,
Title = {Accelerated {Monte Carlo} for optimal estimation of time series},
Author = {Alexander, F. J. and Eyink, G. L. and Restrepo, J. M.},
Journal = {J. Stat. Phys.},
Year = {2005},
Pages = {1331--1345},
Volume = {119}
}
@Article{Alfsen85,
Title = {Systematics of the {Lorenz} model at $\sigma = 10$},
Author = {K. H. Alfsen and J. Fr\o{}yland},
Journal = {Phys. Scr.},
Year = {1985},
Pages = {15},
Volume = {31},
Abstract = {The systematic appearance of limit cycles, homoclinic and
heteroclinic orbits in the Lorenze model has been mapped in the r-b
parameter plane at $\sigma = 10$. New structures in the model are thereby
revealed.}
}
@Article{Alfv50,
Title = {Discussion of the origin of the terrestrial and solar magnetic fields},
Author = {Alfv\'en, H.},
Journal = {Tellus},
Year = {1950},
Pages = {74--82},
Volume = {2}
}
@Misc{AlHa11,
Title = {Quantum chaos and effective thermalization},
Author = {Altland, A. and Haake, F.},
Note = {\arXiv{1110.1270}},
Year = {2011}
}
@Article{AltTel08,
Title = {Poincar\'e recurrences and transient chaos in systems with leaks},
Author = {Altmann, E. G. and T\'el, T.},
Journal = {Phys. Rev. E},
Year = {2009},
Note = {\arXiv{0808.3785}},
Pages = {016204},
Volume = {79},
Abstract = {Simulating observational and experimental
situations, we consider a leak in the phase space of a chaotic
dynamical system. We obtain an expression for the escape rate
of the survival probability applying the theory of transient
chaos. This expression improves previous estimates based on the
properties of the closed system and explains dependencies on
the position and size of the leak and on the initial ensemble.
With a subtle choice of the initial ensemble, we obtain an
equivalence to the classical problem of Poincare recurrences in
closed systems, which is treated in the same framework.
Finally, we show how our results apply to weakly chaotic
systems and justify a split of the invariant saddle in
hyperbolic and non-hyperbolic components, related,
respectively, to the intermediate exponential and asymptotic
power-law decays of the survival probability.},
Numpages = {12}
}
@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}
}
@Misc{angelo-2003,
Title = {Ordered quantization and the {E}hrenfest time scale},
Author = {R. M. Angelo and L. Sanz and K. Furuya},
Note = {\arXiv{quant-ph/0302020}}
}
@Article{angen88,
Title = {The periodic orbits of an area preserving twist-map},
Author = {S. B. Angenent},
Journal = {Commun. Math. Phys.},
Year = {1988},
Pages = {353--374},
Volume = {115}
}
@Article{AnSo01,
Title = {{Lyapunov}, {Lanczos}, and inertia},
Author = {Antoulas, A. C. and Sorensen, D. C. },
Journal = {Linear Algebra Appl.},
Year = {2001},
Pages = {137--150},
Volume = {326}
}
@InProceedings{AnYang,
Author = {K. An and J. Yang},
Booktitle = {Trends in Nano- and Micro-Cavities},
Year = {2011},
Editor = {Kwon, O. D. and Lee, B. and An, K.},
Note = {\arXiv{0912.0164v3}},
Pages = {40--61},
Publisher = {Bentham Science}
}
@Article{ApStVo07,
Title = {Sampling the posterior: {An} approach to non-{Gaussian} data assimilation},
Author = {Apte, A and Hairer, M. and Stuart, A. and Voss, J.},
Journal = {Physica D},
Year = {2007},
Pages = {50--64},
Volume = {230}
}
@Book{arnold,
Title = {Mathematical Methods of Classical Mechanics},
Author = {V. I. Arnol'd},
Publisher = {Springer},
Year = {1978},
Address = {Berlin}
}
@Article{arnold91k,
Title = {Kolmogorov's hydrodynamic attractors},
Author = {V. I. Arnol'd},
Journal = {Proc. R. Soc. Lond. A},
Year = {1991},
Pages = {19--22},
Volume = {434},
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.}
}
@Book{arnold92,
Title = {Ordinary Differential Equations},
Author = {V. I. Arnol'd},
Publisher = {Springer},
Year = {1992},
Address = {Berlin}
}
@Book{ArnoldL74,
Title = {Stochastic Differential Equations: Theory and Applications},
Author = {Arnold, L.},
Publisher = {Wiley},
Year = {1974},
Address = {New York},
ISBN = {9780486482361}
}
@Article{art03int,
Title = {Cycle expansions for intermittent maps},
Author = {R. Artuso and P. Cvitanovi\'{c} and G. Tanner},
Journal = {Proc. Theo. Phys. Supp.},
Year = {2003},
Pages = {1--21},
Volume = {150}
}
@Article{AS87,
Title = {A study of hairpin vortices in a laminar boundary layer},
Author = {Acarlar, M.S. and Smith, C.R.},
Journal = {J. Fluid Mech.},
Year = {1987},
Pages = {1-41 and 45-83},
Volume = {175}
}
@Article{Ascher95,
Title = {Implicit-explicit methods for time-dependent partial differential equations},
Author = {U. Ascher and S. Ruuth and B. Wetton},
Journal = {SIAM J. Numer. Anal.},
Year = {1995},
Pages = {797--823},
Volume = {32}
}
@Article{AtFe75,
Title = {The design of experiments for discriminating between two rival models},
Author = {Atkinson, A. C. and Fedorov, V. V.},
Journal = {Biometrika},
Year = {1975},
Pages = {57--70},
Volume = {62},
Abstract = {Sequential experimental designs are developed for
discriminating between two rival regression models, which
need not be linear in the parameters. Nonsequential
procedures are also derived and numerical examples given of
both classes of design. }
}
@Article{aub95ant,
Title = {Anti-integrability in dynamical and variational problems},
Author = {S. Aubry},
Journal = {Physica D},
Year = {1995},
Pages = {284--296},
Volume = {86}
}
@Article{Aubry88,
Title = {The dynamics of coherent structures in the wall region of turbulent boundary layer},
Author = {N. Aubry and P. Holmes and J.L. Lumley and E. Stone},
Journal = {J. Fluid Mech.},
Year = {1988},
Pages = {115--173},
Volume = {192}
}
@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,
Title = {Average patterns of spatiotemporal chaos: {A} boundary effect},
Author = {V. M. Egu\'{i}luz and P. Alstr{\o}m and E. Hern\'{a}ndez-Garc\'{\i}a and O. Piro},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {2822},
Volume = {59}
}
@Misc{aver_dasbuch,
Author = {P. Cvitanovi\'{c}},
Note = {Chapter {\em ``Averaging''}, in \refref{DasBuch}},
Year = {2012}
}
@Book{AvrFiHow13,
Title = {Analytic Perturbation Theory and Its Applications},
Author = {K. E. Avrachenkov and J. A. Filar and P. G. Howlett},
Publisher = {SIAM},
Year = {2013},
Address = {Philadelphia},
DOI = {10.1137/1.9781611973143}
}
@Book{AzIo89,
Title = {Linear Operators in Spaces with an Indefinite Metric},
Author = {T. Ya. Azizov and I. S. Iohvidov},
Publisher = {Wiley},
Year = {1989},
Address = {New York}
}
@Article{B84,
Title = {The evolution of disturbances in shear flows at high {R}eynolds numbers},
Author = {Benney, D.J.},
Journal = {Stud. Appl. Math.},
Year = {1984},
Pages = {1--19},
Volume = {70}
}
@Article{BaChi87,
Title = {Fast dynamo action in unsteady flows and maps in three dimensions},
Author = {Bayly, B. J. and Childress, S.},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {1573},
Volume = {59}
}
@Article{BaChi88,
Title = {Construction of fast dynamos using unsteady flows and maps in three dimensions},
Author = {Bayly, B. J. and Childress, S.},
Journal = {Geophys. Astrophys. Fluid Dyn.},
Year = {1988},
Pages = {211--240},
Volume = {44}
}
@Article{Backer1,
Title = {Regular-to-chaotic tunneling rates using a fictitious integrable system},
Author = {B\"acker, A. and Ketzmerick, R. and L\"ock, S. and Schilling, L.},
Journal = {Phys. Rev. Lett.},
Year = {2008},
Volume = {100}
}
@Article{BaHuVa14,
Title = {Pseudo-orbits, stationary measures and metastability},
Author = {W. Bahsoun and H. Hu and S. Vaienti},
Journal = {Dyn. Sys.},
Year = {2014},
Pages = {322--336},
Volume = {29},
Abstract = { We characterize absolutely continuous stationary measures (acsms) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of absolutely continuous invariant measures (acims) of the unperturbed system. We focus on those components, called least elements, which attract pseudo-orbits. Under the assumption that the transfer operators of both systems, the random and the unperturbed, satisfy a uniform Lasota--Yorke inequality on a suitable Banach space, we show that each least element is in a one-to-one correspondence with an ergodic acsm of the random system. },
DOI = {10.1080/14689367.2014.890172}
}
@Book{baker:makemson,
Title = {An Introduction to Astrodynamics},
Author = {Baker Jr., R. M. L. and M. W. Makemson},
Publisher = {Academic},
Year = {1960},
Address = {New York}
}
@InProceedings{Baladi_lr,
Title = {Linear response, or else},
Author = {Baladi, V.},
Booktitle = {Proceedings of the International Congress of Mathematicians},
Year = {2014},
Address = {Seoul, South Korea},
Editor = {Jang, S. Y. and Kim, Y. R. and Lee, D.-W. and Yie, I.},
Note = {\arXiv{1408.2937}},
Pages = {525--545},
Publisher = {Kyung Moon Sa Co. Ltd.}
}
@Article{Baladi08,
author = {V. Baladi},
title = {Linear response despite critical points},
journal = {Nonlinearity},
year = {2008},
volume = {21},
pages = {T81--T90},
doi = {10.1088/0951-7715/21/6/t01},
}
@Article{BarChor98,
Title = {New perspectives in turbulence: scaling laws, asymptotics, and intermittency},
Author = { G.I. Barenblatt and A.J. Chorin },
Journal = {SIAM Rev.},
Year = {1998},
Pages = {265--291},
Volume = {40}
}
@Article{BarHuss11,
Title = {The {Moore-Penrose} pseudoinverse. {A} tutorial review of the theory},
Author = {Barata, J. C. A. and Hussein, M. S.},
Journal = {Braz. J. Phys.},
Year = {2012},
Note = {\arXiv{1110.6882}},
Pages = {146--165},
Volume = {42},
Abstract = {In the last decades the Moore-Penrose pseudoinverse
has found a wide range of applications in many areas of Science and
became a useful tool for physicists dealing, for instance, with optimization
problems, with data analysis, with the solution of linear integral equations,
etc. The existence of such applications alone should attract the interest
of students and researchers in the Moore-Penrose pseudoinverse and
in related subjects, like the singular values decomposition theorem for
matrices. In this note we present a tutorial review of the theory of the
Moore-Penrose pseudoinverse. We present the first definitions and
some motivations and, after obtaining some basic results, we center
our discussion on the Spectral Theorem and present an algorithmically
simple expression for the computation of the Moore-Penrose
pseudoinverse of a given matrix.
We present a complete and self-contained
tutorial review, useful for those more devoted to applications, for
those more theoretically oriented and for those who already have
some working knowledge of the subject.}
}
@Article{Barkley94,
Title = {{Euclid}ean symmetry and the dynamics of rotating spiral waves},
Author = {Barkley, D.},
Journal = {Phys. Rev. Lett.},
Year = {1994},
Pages = {164--167},
Volume = {72}
}
@Article{Barraud77,
Title = {A numerical algorithm to solve {$A^T XA - X = Q$}},
Author = {Barraud, A. Y.},
Journal = {IEEE Trans. Auto. Contr.},
Year = {1977},
Pages = {883--885},
Volume = {22}
}
@Article{BasLee08,
Title = {Asymptotic properties of an estimator of the drift coefficients of multidimensional {Ornstein-Uhlenbeck} processes that are not necessarily stable},
Author = {G. K. Basak and P. Lee},
Journal = {Electronic J. Statistics},
Year = {2008},
Note = {\arXiv{0805.4535}},
Pages = {1309--1344},
Volume = {2}
}
@Article{BaSt72,
Title = {Algorithm 432: {Solution} of the matrix equation {AX + XB = C}},
Author = {R. H. Bartels and G. W. Stewart},
Journal = {Comm. ACM},
Year = {1972},
Pages = {820--826},
Volume = {15}
}
@Article{BaVa13,
Title = {Escape rates formulae and metastablilty for randomly perturbed maps},
Author = {W. Bahsoun and S. Vaienti},
Journal = {Nonlinearity},
Year = {2013},
Pages = {1415},
Volume = {26},
Abstract = {We provide escape rates formulae for piecewise expanding interval maps with {\textquoteleft}random holes{\textquoteright}. Then we obtain rigorous approximations of invariant densities of randomly perturbed metastable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.},
DOI = {10.1088/0951-7715/26/5/1415}
}
@Article{BaVo86,
Title = {Chaos on the pseudosphere},
Author = {N. Balasz and A. Voros},
Journal = {Phys. Rep.},
Year = {1986},
Pages = {109--240},
Volume = {143}
}
@Article{BBB,
Title = {Orbital motion of spiral waves in excitable media},
Author = {Biktashev, V. N. and Barkley, D. and Biktasheva, I. V.},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {58302},
Volume = {104}
}
@Article{BBW09,
Title = {Noise management by molecular networks},
Author = {F. J. Bruggeman and N. Bl\"{u}thgen and H. V. Westerhoff},
Journal = {PloS Computational Biology},
Year = {2009},
Pages = {e1000506},
Volume = {5}
}
@Article{BC89,
Title = {A mean flow first harmonic theory for hydrodynamic instabilities},
Author = {Benney, D.J. and Chow, K.A.},
Journal = {Stud. Appl. Math.},
Year = {1989},
Pages = {37--73},
Volume = {80}
}
@Article{BCOR11,
Title = {Bifurcations in the {Lozi} map},
Author = {Botella-Soler, V. and Castelo, J. M. and Oteo, J. A. and Ros, J.},
Journal = {J. Phys. A},
Year = {2011},
Note = {\arXiv{1102.0034}},
Pages = {D5101},
Volume = {44}
}
@Book{BeGe06,
Title = {Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach},
Author = {Berglund, N. and Gentz, B.},
Publisher = {Springer},
Year = {2005},
Address = {Berlin},
ISBN = {9781846281860}
}
@Article{BeHa87,
Title = {Optimal projection equations for discrete-time fixed-order dynamic compensation of linear systems with multiplicative white noise},
Author = {D. S. Bernstein and W. M. Haddad},
Journal = {Int. J. Control},
Year = {1987},
Pages = {65--73},
Volume = {46}
}
@Article{BeiramiZigzag,
Title = {Zigzag map: a variability-aware discrete-time chaotic-map truly random number generator},
Author = {Beirami, A. and Nejati, H. and Ali, W. H.},
Journal = {Electron. Lett.},
Year = {2012},
Pages = {1537--1538},
Volume = {48},
DOI = {10.1049/el.2012.2762}
}
@Book{Bell57,
Title = {{Dynamic Programming}},
Author = {Bellman, R.},
Publisher = {Princeton Univ. Press},
Year = {1957},
Address = {Princeton},
ISBN = {9780486317199}
}
@Book{Bell60,
Title = {{Introduction to Matrix Analysis}},
Author = {Bellman, R.},
Publisher = {SIAM},
Year = {1997},
Address = {Philadelphia},
Edition = {2},
ISBN = {9781611971170}
}
@Article{Belonosov83,
Title = {On the indices of instability of unbounded operators},
Author = {V. S. Belonosov},
Journal = {Dokl. Akad. Nauk SSSR},
Year = {1983},
Pages = {11--14},
Volume = {273}
}
@Article{Belonosov84,
Title = {On instability indices of unbounded operators. {I}},
Author = {V. S. Belonosov},
Journal = {Some Applications of Functional Analysis to Problems in Mathematical Physics [in Russian], Novosibirsk},
Year = {1984},
Pages = {25--51},
Volume = {2}
}
@Article{Belonosov85,
Title = {On instability indices of unbounded operators. {I}},
Author = {V. S. Belonosov},
Journal = {Some Applications of Functional Analysis to Problems in Mathematical Physics [in Russian], Novosibirsk},
Year = {1985},
Pages = {5--33},
Volume = {2}
}
@Article{Bender87,
Title = {{Lyapunov}-like equations and reachability / observabiliy {Gramians} for descriptor systems},
Author = {Bender, D. J.},
Journal = {IEEE Trans. Auto. Contr.},
Year = {1987},
Pages = { 343--348},
Volume = {32}
}
@Article{benks66,
Title = {Long waves in liquid films},
Author = {D. J. Benney},
Journal = {J. Math. Phys},
Year = {1966},
Pages = {150--155},
Volume = {45}
}
@Article{Berkooz94,
Title = {Observations regarding ``{C}oherence and chaos in a model of turbulent boundary layer'' by {X}. {Z}hou and {L}. {S}irovich},
Author = {G. Berkooz and P. Holmes and J. L. Lumley and N. Aubry and E. Stone},
Journal = {Phys. Fluids},
Year = {1994},
Pages = {1574--1578},
Volume = {6}
}
@Article{berry85,
Title = {Semiclassical theory of spectral rigidity},
Author = {M. V. Berry},
Journal = {Proc. R. Soc. Lond. A},
Year = {1985},
Pages = {229--251},
Volume = {400}
}
@Article{Ber-Up,
author = {M.V. Berry and C. Upstill},
title = {Catastrophe optics: {Morphologies} of caustics and their diffraction patterns},
journal = {Progr. Optics},
year = {1980},
volume = {18},
pages = {257--346},
doi = {10.1016/s0079-6638(08)70215-4},
}
@Misc{BeSa10,
Title = {A {Galerkin-{Newton}-ADI} method for solving large-scale algebraic {Riccati} equations},
Author = {P. Benner and J. Saak},
Year = {2010}
}
@Book{Bevington,
Title = {Data Reduction and Error Analysis for the Physical Sciences},
Author = {P. R. Bevington and D. K. Robinson},
Publisher = {McGraw-Hill},
Year = {1992},
Address = {New York}
}
@Article{BFF,
Title = {Intermittent distribution of inetrial particles in turbulent flows},
Author = {Balkovsky, E. and Falkovich, G. and Fouxon, A.},
Journal = {Phys. Rev. Lett.},
Year = {2001},
Pages = {2790},
Volume = {86}
}
@Article{BG81,
Title = {A new mechanism for linear and nonlinear hydrodynamic instability},
Author = {{Benney}, D. J. and {Gustavsson}, L. H.},
Journal = {Studies in Applied Mathematics},
Year = {1981},
Pages = {185--209},
Volume = {64}
}
@Book{BH86,
Title = {Asymptotic Expansions of Integrals},
Author = {N. Bleistein and R. A. Handelsman},
Publisher = {Dover},
Year = {1986},
Address = {New York}
}
@Article{biham90c,
Title = {Unstable periodic orbits and the symbolic dynamics of the complex {H\'{e}non} map},
Author = {O. Biham and W. Wenzel},
Journal = {Phys. Rev. E},
Year = {1990},
Pages = {4639},
Volume = {42},
Abstract = {Previous work is extended to the complex plane so that 2^n
complex orbits are found for symbol sequences of length n.}
}
@Article{Bik_Hol,
Title = {Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities},
Author = {Biktashev,V. N. and Holden, A. V.},
Journal = {Chaos Solitons Fractals},
Year = {1995},
Pages = {575},
Volume = {5}
}
@Article{BillBoll05,
Title = {Invariant densities for skew tent maps},
Author = {Billings, L. and Bollt, E. M.},
Journal = {Chaos Solitons Fractals},
Year = {2001},
Addendum = {See also \weblink{www.mathstat.concordia.ca/pg/bilbollt.html}.},
Pages = {365},
Volume = {12},
URL = {http://people.clarkson.edu/~bolltem/Papers/csf_2001.pdf}
}
@Article{BK90,
Title = {A rule for quantizing chaos},
Author = {M. V. Berry and J. P. Keating},
Journal = {J. Phys. A},
Year = {1990},
Number = {21},
Pages = {4839--4849},
Volume = {23}
}
@Article{bknk,
Title = {Formations of spatial patterns and holes in the generalized {Ginzburg-Landau} equation},
Author = {N. Bekki and K. Nozaki},
Journal = {Phys. Lett. A},
Year = {1985},
Pages = {133--135},
Volume = {110},
Abstract = {A new exact propagating-hole solutionis obtained in the generalized Ginzburg-Landau equation and a phase-jump in the hole is shown to generate definite spatial patterns in a stable homogeneous state. },
DOI = {10.1016/0375-9601(85)90759-5}
}
@Article{bknk83,
Title = {Pattern selection and spatiotemporal transition to chaos in the {G}inzburg-{L}andau 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 {G}inzburg-{L}andau equation},
Author = {K. Nozaki and N. Bekki},
Journal = {J. Phys. Soc. Japan},
Year = {1984},
Pages = {1581--1582},
Volume = {53}
}
@Book{bl,
Title = {Introduction to Numerical Analysis},
Author = {J. Stoer and R. Bulirsch},
Publisher = {Springer},
Year = {1983},
Address = {New York}
}
@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 = {391-422},
doi = {10.1093/qjmam/24.4.391}
}
@Article{bog_keat,
Title = {Gutzwiller's trace formula and spectral statistics: beyond the diagonal approximation},
Author = {E. B. Bogomolny and J. P. Keating},
Journal = {Phys. Rev. Lett.},
Year = {1996},
Pages = {1472},
Volume = {77}
}
@Article{bog92,
Title = {Semiclassical quantization of multidimensional systems},
Author = {E. B. Bogomolny},
Journal = {Nonlinearity},
Year = {1992},
Pages = {805--866},
Volume = {5}
}
@Misc{BoGaMcK09,
Title = {Limit cycles, complex {Floquet} multipliers and intrinsic noise},
Author = {Boland, R. P. and Galla, T. and {McKane}, A. J.},
Note = {\arXiv{0903.5248}},
Year = {2009},
Abstract = {We study the effects of intrinsic noise on
chemical reaction systems, which in the deterministic limit
approach a limit cycle in an oscillatory manner. Previous
studies of systems with an oscillatory approach to a fixed
point have shown that the noise can transform the oscillatory
decay into sustained coherent oscillations with a large
amplitude. We show that a similar effect occurs when the
stable attractors are limit cycles. We compute the
correlation functions and spectral properties of the
fluctuations in suitably co-moving Frenet frames for several
model systems including driven and coupled Brusselators, and
the {Willamowski-Roessler} system. The effect occurs whenever
the Floquet multipliers of the limit cycle are complex, with
the amplitude of the oscillations increasing as the
instability boundary is approached.}
}
@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{bollt06,
Title = {Basis {Markov} partitions and transition matrices for stochastic systems},
Author = {E. Bollt and P. G\'{o}ra and A. Ostruszka and K. \.{Z}yczkowski},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2008},
Note = {\arXiv{nlin/0605017}},
Pages = {341--360},
Volume = {7}
}
@Misc{Bonanca10,
author = {{Bonanca}, M. V. S.},
title = {{Lyapunov} decoherence rate in classically chaotic systems},
year = {2010},
note = {\arXiv{1010.2115}},
}
@Book{BenGre74,
Title = {Generalized Inverses: Theory and Applications},
Author = {A. Ben-Israel and T. N. E. Greville},
Publisher = {Wiley},
Year = {1974},
Address = {New York}
}
@Article{Sieber96,
author = {M. Sieber},
title = {Uniform approximations for bifurcations of periodic orbits with high repetition numbers},
journal = {J. Phys. A},
year = {1996},
volume = {29},
pages = {4715},
doi = {10.1088/0305-4470/29/15/034},
}
@Article{BoringGuy2,
Title = {Bifurcations of periodic orbits and uniform approximations},
Author = {H. Schomerus and M. Sieber},
Journal = {J. Phys. A},
Year = {1997},
Pages = {4537},
Volume = {30}
}
@Book{Botti89,
Title = {The Kinematics of Mixing: Stretching, Chaos and Transport},
Author = {Ottino, J. M.},
Publisher = {Cambridge Univ. Press},
Year = {1989},
Address = {Cambridge}
}
@Article{BouTou12,
Title = {Non-classical large deviations for a noisy system with non-isolated attractors},
Author = {Bouchet, F. and Touchette, H.},
Journal = {J. Stat. Mech.},
Year = {2012},
Note = {\arXiv{1204.6269}},
Pages = {P05028},
Volume = {2012}
}
@Book{bowen,
Title = {Equilibrium States and the Ergodic Theory of {A}nosov Diffeomorphisms},
Author = {R. Bowen},
Publisher = {Springer},
Year = {1975},
Address = {Berlin}
}
@Article{Bowen70,
Title = {{Markov} partitions for {Axiom A} diffeomorphisms},
Author = {Bowen, R.},
Journal = {Amer. J. Math.},
Year = {1970},
Pages = {725--747},
Volume = {92}
}
@Article{Boy84,
Title = {On the significance of absolutely continuous invariant measures},
Author = {A. Boyarsky},
Journal = {Physica D},
Year = {1984},
Pages = {130--146},
Volume = {11},
DOI = {10.1016/0167-2789(84)90439-1}
}
@Book{BoyGor97,
Title = {Laws of Chaos: Invariant Measures and Dynamical Systems in One Dimension},
Author = {A. Boyarsky and P. G\'ora},
Publisher = {Birkh\"{a}user},
Year = {1997},
Address = {Boston},
ISBN = {9781461220244}
}
@Book{Brack,
Title = {Semiclassical Physics},
Author = {M. Brack and R. K. Bhaduri},
Publisher = {Addison-Wesley},
Year = {1997},
Address = {Reading, MA}
}
@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}\~{n}ez}},
Note = {\arXiv{astro-ph/0109497}},
Pages = {269--344}
}
@Misc{Braun11,
Title = {Beyond the {Heisenberg} time: {Semiclassica} treatment of spectral correlations in chaotic systems with spin 1/2},
Author = {Braun, P.},
Note = {\arXiv{1110.4567}},
Year = {2011}
}
@Article{BrCoTh04,
Title = {Gramian matrices and balanced model of generalized systems},
Author = {R. Bru and C. Coll and N. Thome},
Journal = {Appl. Math. Comp.},
Year = {2004},
Pages = {341--350},
Volume = {148}
}
@Book{BrHo75,
Title = {Applied Optimal Control},
Author = {Bryson, A. E. and Y. C. Ho},
Publisher = {Hemisphere Publ.},
Year = {1975},
Pages = {328--338}
}
@Article{bro94sur,
Title = {Nonlinear surface waves in a plasma with a diffuse boundary},
Author = {G. Brodin and J. Lundberg},
Journal = {Phys. Plasmas},
Year = {1994},
Pages = {96},
Volume = {1}
}
@Article{broer97,
Title = {Algorithms for computing {N}ormally {H}yperbolic {I}nvariant {M}anifolds},
Author = {H. W. Broer and H. M. Osinga and G. Vegter},
Journal = {Z. Angew. Math. Phys.},
Year = {1997},
Pages = {480},
Volume = {48}
}
@Misc{Brouwer07,
Title = {Semiclassical theory of the {E}hrenfest-time dependence of quantum transport},
Author = {{Brouwer}, P.~W.},
Note = {\arXiv{0706.1487}},
Year = {2007}
}
@Book{BrPetr,
Title = {The Theory of Open Quantum Systems},
Author = {H. P. Breuer and F. Petruccione},
Publisher = {Oxford Univ. Press},
Year = {2002},
Address = {Oxford}
}
@Article{BTBmaw03,
Title = {Nonlinear analysis of the {E}ckhaus instability: modulated amplitude waves and phase chaos with nonzero average phase gradient},
Author = {L. Brusch and A. Torcini and M. B\"{a}r},
Journal = {Physica D},
Year = {2003},
Pages = {152--167},
Volume = {174}
}
@Article{BTHmaw01,
Title = {Modulated amplitude waves and defect formation in the one-dimensional complex {{G}inzburg-{L}andau} equation},
Author = {L. Brusch and A. Torcini and M. van Hecke and M. G. Zimmermann and M. B\"{a}r},
Journal = {Physica D},
Year = {2001},
Pages = {127--148},
Volume = {160}
}
@Article{BTU,
Title = {Manifestations of classical phase space structures in quantum mechanics},
Author = {Bohigas, O. and Tomsovic, S. and Ullmo, D.},
Journal = {Phys. Rep.},
Year = {1993},
Pages = {43},
Volume = {223},
DOI = {10.1016/0370-1573(93)90109-Q}
}
@Article{BuChu11,
Title = {On computing the instability index of a non-self-adjoint differential operator associated with coating and rimming flows},
Author = {A. Burchard and M. Chugunova},
Journal = {SIAM J. Math. Anal.},
Year = {2011},
Note = {\arXiv{0905.1834}},
Pages = {367--388},
Volume = {43},
DOI = {10.1137/090759495}
}
@Article{BuFengDong12,
Title = {A note on computational formulas for the {Drazin} inverse of certain block matrices},
Author = {C. Bu and C. Feng and P. Dong},
Journal = {J. Appl. Math. Comput.},
Year = {2012},
Pages = {631--640},
Volume = {38},
DOI = {10.1007/s12190-011-0501-4}
}
@Article{BuKe03,
Title = {Estimating good discrete partitions from observed data: {Symbolic} false nearest neighbors},
Author = {Kennel, M. B. and Buhl, M.},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Note = {\arXiv{nlin/0304054}},
Pages = {084102},
Volume = {91}
}
@InProceedings{BuKe03a,
Title = {Estimating good discrete partitions from observed data: symbolic false nearest neighbors},
Author = {Kennel, M. B. and Buhl, M.},
Booktitle = {Experimental Chaos: Seventh Experimental Chaos Conference},
Year = {2003},
Address = {Melville, NY},
Editor = {Ko\v{c}arev, L. and Carroll, T. L. and Gluckman, B. J. and Boccaletti, S. and Kurths, J.},
Pages = {380--380},
Publisher = {American Institute of Physics}
}
@Article{BuKe05,
Title = {Statistically relaxing to generating partitions for observed time-series data},
Author = {{Buhl}, M. and {Kennel}, M.~B.},
Journal = {Phys. Rev. E},
Year = {2005},
Pages = {046213},
Volume = {71},
DOI = {10.1103/PhysRevE.71.046213}
}
@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{Busse04,
Title = {Visualizing the dynamics of the onset of turbulence},
Author = {Busse, F.H.},
Journal = {Science},
Year = {2004},
Pages = {1574--1575},
Volume = {305}
}
@Article{C02,
Title = {Subcritical transition in channel flows},
Author = {Chapman, S.J.},
Journal = {J. Fluid Mech.},
Year = {2002},
Pages = {35--97},
Volume = {451}
}
@Misc{CaLiZh16,
Title = {Explore Stochastic Instabilities of Periodic Points by Transition Path Theory},
Author = {Y. Cao and L. Lin and X. Zhou},
Note = {\arXiv{1601.01424}}
}
@Article{CaMi89,
Title = {Role of shear in the isotropic-to-lamellar transition},
Author = {Cates, M. E. and Milner, S. T.},
Journal = {Phys. Rev. Lett.},
Year = {1989},
Pages = {1856--1859},
Volume = {62},
DOI = {10.1103/PhysRevLett.62.1856}
}
@Book{CamMey79,
Title = {Generalized Inverses of Linear Transformations},
Author = {S. L. Campbell and C. D. Meyer},
Publisher = {Pitman},
Year = {1979},
Address = {London}
}
@Article{CamPre02,
Title = {Quantum breaking time near classical equilibrium points},
Author = {F. Cametti and C. Presilla},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Note = {\arXiv{quant-ph/0201147}},
Pages = {040403},
Volume = {89},
Abstract = {By using numerical and semiclassical methods, we
evaluate the quantumbreaking, or Ehrenfest time for a
wave packet localized around classicalequilibrium
points of autonomous one-dimensional systems with
polynomialpotentials. We find that the Ehrenfest time
diverges logarithmically with theinverse of the Planck
constant whenever the equilibrium point is
exponentiallyunstable. For stable equilibrium points,
we have a power law divergence withexponent determined
by the degree of the potential near the equilibrium
point.}
}
@Book{Canuto88,
Title = {Spectral Methods in Fluid Dynamics},
Author = {C. Canuto and M.Y. Hussaini and A. Quateroni and T.A. Zhang},
Publisher = {Springer},
Year = {1988},
Addr = {Berlin}
}
@Article{Cao_Mot,
Title = {Marginally unstable periodic orbits in semiclassical mushroom billiards},
Author = {Andreasen, J. and Cao, H. and Wiersig, J. and Motter, A.},
Journal = {Phys. Rev. Lett.},
Year = {2009},
Volume = {103},
DOI = {10.1103/PhysRevLett.103.154101}
}
@Article{car88,
Title = {{P}ainlev\'{e} expansions for nonintegrable evolution equations},
Author = {F. Cariello and M. Tabor},
Journal = {Physica D},
Year = {1989},
Pages = {77},
Volume = {39}
}
@Article{CardBifc,
Title = {Predicting the onset of period-doubling bifurcations in noisy cardiac systems},
Author = {T. Quail and A. Shrier and L. Glass},
Journal = {Proc. Natl. Acad. Sci. USA},
Year = {2015},
Pages = {9358--9363},
Volume = {112}
}
@Article{CarLit45,
author = {M. L. Cartwright and J. E. Littlewood},
title = {On non-linear differential equations of the second order},
journal = {J. London Math. Soc.},
year = {1945},
volume = {20},
pages = {180--189},
doi = {10.1112/jlms/s1-20.3.180},
}
@Article{CarlSchn62,
Title = {Inertia theorems for matrices: the semi-definite case},
Author = {D. Carlson and H. Schneider},
Journal = {Bull. Amer. Math. Soc.},
Year = {1962},
Pages = {479--484},
Volume = {68}
}
@InProceedings{carsim,
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},
Editor = {D. Benest and C. Froeschl\'{e}},
Pages = {285--329}
}
@Article{Case08,
Title = {Wigner functions and {Weyl} transforms for pedestrians},
Author = {W. B. Case},
Journal = {Amer. J. Phys.},
Year = {2008},
Pages = {937},
Volume = {76}
}
@Misc{CatCaf07,
Title = {From Information Geometry to {N}ewtonian Dynamics},
Author = {A. Caticha and C. Cafaro},
Note = {\arXiv{0710.1071}},
Year = {2007}
}
@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{CC92,
Title = {Periodic orbit quantization of the anisotropic {Kepler} problem},
Author = {F. Christiansen and P. Cvitanovi\'c},
Journal = {Chaos},
Year = {1992},
Pages = {61},
Volume = {2}
}
@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},
Number = {7405},
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{CDKK10,
Title = {A fast explicit operator splitting method for passive scalar advection},
Author = {Chertock, A. and Doering, C. R. and Kashdan, E. and Kurganov, A.},
Journal = {J. Sci. Comp.},
Year = {2010},
Pages = {200--214},
Volume = {45},
DOI = {10.1007/s10915-010-9381-2}
}
@Article{CEEks93,
Title = {Analyticity for the {Kuramoto-Sivashinsky} equation},
Author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe},
Journal = {Physica D},
Year = {1993},
Pages = {321--326},
Volume = {67},
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.}
}
@Article{CEEksgl93,
Title = {A global attracting set for the {Kuramoto-Sivashinsky} equation},
Author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe},
Journal = {Commun. Math. Phys.},
Year = {1993},
Pages = {203--214},
Volume = {152},
Abstract = {New bounds are given for the L^2 norm of solutions of the KSe (not
necessarily antisymmetric).}
}
@Article{CEGR14,
Title = {Ermakov systems with multiplicative noise},
Author = {E. Cervantes-L\'opez and P.B. Espinoza and A. Gallegos and H.C. Rosu},
Journal = {Physica A},
Year = {2014},
Pages = {141--147},
Volume = {401},
DOI = {10.1016/j.physa.2014.01.027}
}
@Book{cellwolf,
Title = {Cellular Automata and Complexity},
Author = {S. Wolfram},
Publisher = {Addison-Wesley},
Year = {1994},
Address = {Red-wood City}
}
@Book{CG96,
Title = {Stretch, twist, fold: the fast dynamo},
Author = {S. Childress and A. D. Gilbert},
Publisher = {Springer},
Year = {1995},
Address = {Berlin}
}
@Article{cgole92,
Title = {A new proof of the {A}ubry-{M}ather's theorem},
Author = {C. Gol\'{e}},
Journal = {Math. Z.},
Year = {1992},
Pages = {441--448},
Volume = {210},
Abstract = {A auxiliary infinite gradient-like flow is constructed for
the area-preserving map such that orbits of the original system are rest points
of the new system. In this way, existence of orbits of any rotation number is
proved.}
}
@Article{ChaKer12,
Title = {Invariant recurrent solutions embedded in a turbulent two-dimensional {Kolmogorov} flow},
Author = {Chandler, G. J. and Kerswell, R. R.},
Journal = {J. Fluid Mech.},
Year = {2013},
Note = {\arXiv{1207.4682}},
Pages = {554--595},
Volume = {722},
DOI = {10.1017/jfm.2013.122}
}
@Article{chand03tf,
Title = {Time-frequency analysis of chaotic systems},
Author = {C. Chandre and S. Wiggins and T. Uzer},
Journal = {Physica D},
Year = {2003},
Pages = {171},
Volume = {181},
Abstract = {Use wavelets to extract local frequencies and use the major
frequencies to identify the characteristics of phase space motion.}
}
@Article{Chandr43,
Title = {Stochastic problems in physics and astronomy},
Author = {S. Chandrasekhar},
Journal = {Rev. Mod. Phys.},
Year = {1943},
Pages = {1--89},
Volume = {15},
DOI = {10.1103/RevModPhys.15.1}
}
@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}
}
@Article{chate94,
Title = {Spatiotemporal intermittency regimes of the one-dimensional complex {Ginzburg-Landau} equation},
Author = {H. Chat\'e},
Journal = {Nonlinearity},
Year = {1994},
Pages = {185--204},
Volume = {7},
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 "laminar" state.}
}
@Article{chfield,
Title = {Chaotic Field Theory: a Sketch},
Author = {Predrag Cvitanovi\'{c}},
Journal = {Physica A},
Year = {2000},
Note = {\arXiv{nlin/0001034}},
Pages = {61},
Volume = {288}
}
@Article{Chiu96,
Title = {Model reduction by the low-frequency approximation balancing method for unstable systems},
Author = {Chiu, T.},
Journal = {IEEE Trans. Automatic Control},
Year = {1996},
Pages = {995},
Volume = {AC-41}
}
@Article{Chorin02,
Title = {Optimal prediction with memory},
Author = {A.J. Chorin and O.H. Hald and R. Kupferman},
Journal = {Physica D},
Year = {2002},
Pages = {239--257},
Volume = {166}
}
@Book{Chossat94,
Title = {The {T}aylor-{C}ouette Problem},
Author = {P. Chossat and G. Iooss},
Publisher = {Springer},
Year = {1994}
}
@Article{Christiansen97,
Title = {Spatiotemporal chaos in terms of unstable recurrent patterns},
Author = {F. Christiansen and P. Cvitanovi\'{c} and V. Putkaradze},
Journal = {Nonlinearity},
Year = {1997},
Note = {\arXiv{chao-dyn/9606016}},
Pages = {55--70},
Volume = {10}
}
@Article{ChrLueOtt11,
Title = {Stretching and folding versus cutting and shuffling: {An} illustrated perspective on mixing and deformations of continua},
Author = {Christov, I. C. and {Lueptow}, R. M. and {Ottino}, J. M.},
Journal = {Amer. J. Phys.},
Year = {2011},
Note = {\arXiv{1010.2256}},
Pages = {359--367},
Volume = {79},
DOI = {10.1119/1.3533213}
}
@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{CK97,
Title = {Canonically invariant formulation of {Langevin} and {Fokker-Planck} equations},
Author = {O. Cepas and J. Kurchan},
Journal = {Eur. Phys. J. B},
Year = {1998},
Pages = {221--223},
Volume = {2},
DOI = {10.1007/s100510050243},
URL = {http://arxiv.org/abs/cond-mat/9706296}
}
@Article{CM87tran,
Title = {Transition to turbulence via spatiotemporal intermittency},
Author = {H. Chat\'{e} and P. Manneville},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {112},
Volume = {58}
}
@Article{CoHeDa96,
Title = {Quantum suppression of cold atom collisions},
Author = {R. Cot\'e and Heller, E. J. and A. Dalgarno},
Journal = {Phys. Rev. A},
Year = {1996},
Pages = {234},
Volume = {53}
}
@Article{cohen72,
Title = {Non-linear saturation of the dissipative trapped-ion mode by mode coupling},
Author = {B. I. Cohen and J. A. Krommes and W. M. Tang and M. N. Rosenbluth},
Journal = {Nucl. Fusion},
Year = {1972},
Pages = {971--991},
Volume = {16}
}
@Article{CoIv04,
Title = {Empirical balanced truncation of nonlinear systems},
Author = {Condon, M. and Ivanov, R.},
Journal = {J. Nonlinear Sci.},
Year = {2004},
Pages = {405--414},
Volume = {14},
DOI = {10.1007/s00332-004-0617-5}
}
@Article{collet80,
Title = {Universal Properties of Maps on an interval},
Author = {P. Collet and J.-P. Eckmann and O. E. Lanford},
Journal = {Commun. Math. Phys.},
Year = {1980},
Pages = {211},
Volume = {76}
}
@Article{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,
Title = {Trace formulae for stochastic evolution operators: {Smooth} conjugation method},
Author = {P. Cvitanovi\'{c} and C. P. Dettmann and R. Mainieri and G. Vattay},
Journal = {Nonlinearity},
Year = {1999},
Note = {\arXiv{chao-dyn/9811003}},
Pages = {939},
Volume = {12}
}
@Article{CoNoBa07,
Title = {A strict {Lyapunov} function for boundary control of hyperbolic systems of conservation laws},
Author = {M. Coron and B. d'Andr\'ea Novel and G. Bastin},
Journal = {IEEE Trans. Auto. Contr.},
Year = {2007},
Pages = {2--11},
Volume = {52}
}
@Book{contebook,
Title = {The {P}ainlev\'{e} Property: One Century Later},
Author = {R. Conte},
Publisher = {Springer},
Year = {1999},
Address = {New York}
}
@Book{CoVanLo88,
Title = {Handbook for Matrix Computations},
Author = {Coleman, T. F. and Van Loan, C.},
Publisher = {SIAM},
Year = {1988},
Address = {Philadelphia}
}
@Article{Cox64,
Title = {On the estimation of state variables and parameters for noisy dynamic systems},
Author = {Cox, H.},
Journal = {IEEE Trans. Auto. Contr.},
Year = {1964},
Pages = {5--12},
Volume = {9}
}
@Article{cpmani,
Title = {On the computation of invariant manifolds of fixed points},
Author = {A.J. Homburg and H.M. Osinga and G. Vegter},
Journal = {Z. Angew. Math. Phys.},
Year = {1995},
Pages = {171},
Volume = {46}
}
@Article{Crkov,
Title = {Resonance processes in magnetic traps},
Author = {Chirikov, B.V. },
Journal = {At. Energ.},
Year = {1959},
Pages = {630},
Volume = {6}
}
@Article{Crooks,
Title = {Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences},
Author = {G. E. Crooks},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {2721},
Volume = {60}
}
@Article{cross93,
Title = {Pattern formation outside of equilibrium},
Author = {M. C. Cross and P. C. Hohenberg},
Journal = {Rev. Mod. Phys},
Year = {1993},
Pages = {851},
Volume = {65}
}
@Article{cross94sp,
Title = {Spatiotemporal Chaos},
Author = {M. C. Cross and P. C. Hohenberg},
Journal = {Science},
Year = {1994},
Pages = {1569--1570},
Volume = {263},
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{CruFarHub82,
Title = {Fluctuations and simple chaotic dynamics},
Author = {J. P. Crutchfield and J. D. Farmer and B. A. Huberman},
Journal = {Phys. Rep.},
Year = {1982},
Pages = {45--82},
Volume = {92},
DOI = {10.1016/0370-1573(82)90089-8}
}
@Article{CruPack83,
Title = {Symbolic dynamics of noisy chaos},
Author = {J. P. Crutchfield and N. H. Packard},
Journal = {Physica D},
Year = {1983},
Pages = {201--223},
Volume = {7},
DOI = {10.1016/0167-2789(83)90127-6}
}
@Article{Crutchfield80,
Title = {Fluctuations and the onset of chaos},
Author = {J.P. Crutchfield and B.A. Huberman},
Journal = {Phys. Lett. A},
Year = {1980},
Pages = {407--410},
Volume = {77},
DOI = {10.1016/0375-9601(80)90524-1}
}
@Article{Crutchfield81,
Title = {Scaling for external noise at the onset of chaos},
Author = {J. R. Crutchfield and M. Nauenberg and J. Rudnick},
Journal = {Phys. Rev. Lett.},
Year = {1981},
Pages = {933--935},
Volume = {46},
DOI = {10.1103/PhysRevLett.46.933}
}
@Article{CV93,
Title = {Entire {Fredholm} determinants for evaluation of semiclassical and thermodynamical spectra},
Author = {P. Cvitanovi\'c and G. Vattay },
Journal = {Phys. Rev. Lett.},
Year = {1993},
Pages = {4138--4141},
Volume = {71}
}
@Unpublished{CviGib10,
Title = {Geometry of turbulence in wall-bounded shear flows: {Periodic} orbits},
Author = {Cvitanovi{\'c}, P. and Gibson, J. F.},
Note = {in S. I. Abarzhi and K. R. Sreenivasan, eds., {\em Turbulent Mixing and Beyond, Proc. 2\textsuperscript{nd} Int. Conf. ICTP, Trieste}, % 75-?? {\em Phys. Scr.}, to appear},
Year = {2010}
}
@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, NY},
Editor = {M. Robnik and V. G. Romanovski},
Note = {\arXiv{1206.5506}},
Pages = {82--126},
Publisher = {American Institute of Physics},
DOI = {10.1063/1.4745574}
}
@Article{CvitaEckardt,
Title = {Symmetry decomposition of chaotic dynamics},
Author = {P. Cvitanovi\'{c} and B. Eckhardt},
Journal = {Nonlinearity},
Year = {1993},
Note = {\arXiv{chao-dyn/9303016}},
Pages = {277},
Volume = {6}
}
@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},
Edition = {2},
ISBN = {9780852742600}
}
@Book{DaKr70,
Title = {Stability of solutions to differential equations in Banach space [in {Russia}n]},
Author = {Yu. L. Daletskii, M. G. Krein},
Publisher = {Nauka},
Year = {1970},
Address = {Moscow}
}
@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}
}
@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 Institute},
Year = {2016},
Address = {Copenhagen},
URL = {http://ChaosBook.org/}
}
@Article{Datta03,
Title = {A new block algorithm for full-rank solution of the {Sylvester}-observer equation},
Author = {K. Datta and Y. Hong},
Journal = {IEEE Trans. Auto. Contr.},
Year = {2003},
Pages = {2223--2228},
Volume = {48}
}
@Article{Davidchack00,
Title = {Estimating generating partitions of chaotic systems by unstable periodic orbits},
Author = {Davidchack, R.L. and Lai, Y.C. and Bollt, E.M. and Dhamala, M. },
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {1353},
Volume = {61}
}
@Article{Davies92,
Title = {Noise reduction schemes for chaotic time series},
Author = {Davies, M.},
Journal = {Physica D},
Year = {1992},
Pages = {174--192},
Volume = {79}
}
@InProceedings{DDS90,
Title = {Automated pattern eduction from turbulent flow diagnostics},
Author = {Stretch, D.D.},
Booktitle = {Annual Research Briefs},
Year = {1990},
Pages = {145--157},
Publisher = {Center for Turbulence Research, Stanford Univ.}
}
@Article{decar,
Title = {Symbolic dynamics and periodic orbits of the {Lorenz} attractor},
Author = {D. Viswanath},
Journal = {Nonlinearity},
Year = {2003},
Pages = {1035--1056},
Volume = {16}
}
@Article{decar3,
Title = {The {L}indstedt-{P}oincar\'e technique as an algorithm for finding periodic orbits},
Author = {D. Viswanath},
Journal = {SIAM Rev.},
Year = {2002},
Pages = {478--496},
Volume = {43}
}
@Article{Decell65,
Title = {An application of the {Cayley-Hamilton} theorem to generalized matrix inversion},
Author = {H. P. Decell},
Journal = {SIAM Rev.},
Year = {1965},
Pages = {526--528},
Volume = {7},
DOI = {10.1137/1007108}
}
@Book{Delch88,
Title = {State Space and Input-Output Linear Systems},
Author = {D. Delchamps},
Publisher = {Springer},
Year = {1988},
Address = {Berlin}
}
@Article{DelJun98,
Title = {An adaptive subdivision technique for the approximation of attractors and invariant measure},
Author = {M. Dellnitz and O. Junge},
Journal = {Computing and Visualization in Science},
Year = {1998},
Pages = {63--68},
Volume = {1}
}
@Article{DellFroSer00,
Title = {On the isolated spectrum of the {Perron-Frobenius} operator},
Author = {{Dellnitz}, M. and {Froyland}, G. and {Sertl}, S.},
Journal = {Nonlinearity},
Year = {2000},
Pages = {1171--1188},
Volume = {13}
}
@Article{DemaGasp09,
Title = {Noise-induced escape from bifurcating attractors: {Symplectic} approach in the weak-noise limit},
Author = {Demaeyer, J. and Gaspard, P.},
Journal = {Phys. Rev. E},
Year = {2009},
Pages = {031147},
Volume = {80},
DOI = {10.1103/PhysRevE.80.031147}
}
@Article{DemaGasp13,
Title = {A trace formula for activated escape in noisy maps},
Author = {J. Demaeyer and P. Gaspard},
Journal = {J. Stat. Mech.},
Year = {2013},
Pages = {P10026},
Volume = {2013},
Abstract = {Using path-integral methods, a formula is deduced for the
noise-induced escape rate from an attracting fixed point across an unstable
fixed point in one-dimensional maps. The calculation starts from the trace
formula for the eigenvalues of the Frobenius�Perron operator ruling the
time evolution of the probability density in noisy maps. The escape rate is
determined from the loop formed by two heteroclinic orbits connecting back
and forth the two fixed points of the one-dimensional map extended to a
two-dimensional symplectic map. The escape rate is obtained with the
expression of the prefactor to the Arrhenius�van�t�Hoff exponential
factor.},
DOI = {10.1088/1742-5468/2013/10/P10026}
}
@Article{DeRonc95,
Title = {Semiclassical approximation as a small-noise expansion},
Author = {A. Defendi and M. Roncadelli},
Journal = {J. Phys. A},
Year = {1995},
Pages = {515--520},
Volume = {28},
DOI = {10.1088/0305-4470/28/21/001}
}
@InProceedings{DeTeran10,
Title = {Canonical forms for congruence of matrices: a tribute to {H.W. Turnbull and A.C. Aitken}},
Author = {De Ter{\'a}n, F.},
Booktitle = {Proceedings of ALAMA 2010, Valencia},
Year = {2010},
Pages = {2010--1},
URL = {gauss.uc3m.es/web/personal_web/fteran}
}
@Article{Dettmann04,
Title = {Fractal asymptotics},
Author = {C. P. Dettmann},
Journal = {Physica D},
Year = {2004},
Pages = {214--222},
Volume = {187},
DOI = {10.1016/j.physd.2003.09.011}
}
@Article{Dettmann99,
Title = {Traces and determinants of strongly stochastic operators},
Author = {Dettmann, C. P.},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {5231--5234},
Volume = {59},
DOI = {10.1103/PhysRevE.59.5231}
}
@Book{devnmap,
Title = {An Introduction to Chaotic Dynamical Systems},
Author = {R. L. Devaney},
Publisher = {Addison-Wesley},
Year = {1989},
Address = {Redwood City}
}
@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{DFT03,
Title = {A review of symbolic analysis of experimental data},
Author = {{Daw}, C.~S. and {Finney}, C.~E.~A. and {Tracy}, E.~R.},
Journal = {Rev. Sci. Instrum.},
Year = {2003},
Pages = {915--930},
Volume = {74},
DOI = {10.1063/1.1531823}
}
@Article{DHBEks96,
Title = {Local models of spatio-temporally complex fields},
Author = {H. Dankowicz and P. Holmes and G. Berkooz and J. Elezgaray},
Journal = {Physica D},
Year = {1996},
Pages = {387--407},
Volume = {90}
}
@Article{diag_Fred,
Title = {Spectrum of stochastic evolution operators: {Local} matrix representation approach},
Author = {P. Cvitanovi\'{c} and N. S{\o}ndergaard and G. Palla and G. Vattay and C. P. Dettmann},
Journal = {Phys. Rev. E},
Year = {1999},
Note = {\arXiv{chao-dyn/9904027}},
Pages = {3936},
Volume = {60}
}
@Article{DiBaCo11,
Title = {{Lyapunov} exponential stability of linear hyperbolic systems of balance laws},
Author = {A. Diagne and G. Bastin and J-M Coron},
Journal = {Automatica},
Year = {2011},
Note = {accepted for publication}
}
@Article{Dirac33,
Title = {The {Lagrangian} in quantum mechanics},
Author = {Dirac, P. A. M.},
Journal = {Phys. Z. Sowjetunion},
Year = {1933},
Pages = {64--72},
Volume = {3}
}
@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{DLBconv92,
Title = {Spatio-temporal intermittency in a {1D} convective pattern: theoretical model and experiments},
Author = {F. Daviaud and J. Lega and P. Berg\'{e} and P. Coullet and M. Dubois},
Journal = {Physica D},
Year = {1992},
Pages = {287--308},
Volume = {55},
Abstract = {Describe the occurrence of the spatio-temporal intermittency in a 1-d
convective system that shows time-independent patterns based on the amplitude equation
approach}
}
@Article{DM97,
Title = {Stability ordering of cycle expansions},
Author = {Dettmann, C. P. and Morriss, G. P.},
Journal = {Phys. Rev. Lett.},
Year = {1997},
Pages = {4201--4204},
Volume = {78},
DOI = {10.1103/PhysRevLett.78.4201}
}
@Article{doeb94nls,
Title = {Properties of nonlinear Schr\"{o}dinger equations associated with diffeomorphism group representations},
Author = {H. -D. Doebner and G. A. Goldin},
Journal = {J. Phys. A},
Year = {1994},
Pages = {1771--1780},
Volume = {27}
}
@Article{doelman91n,
Title = {Finite-dimensional models of the {G}inzburg-{L}andau equation},
Author = {A. Doelman},
Journal = {Nonlinearity},
Year = {1991},
Pages = {231--250},
Volume = {4}
}
@Article{doercgl87,
Title = {Exact {Lyapunov} Dimension of the Universal Attractor for the Complex {G}inzburg-{L}andau Equation},
Author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {2911--2914},
Volume = {59}
}
@Article{doercgl88,
Title = {Low-dimensional behaviour in the complex {G}inzburg-{L}andau equation},
Author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko},
Journal = {Nonlinearity},
Year = {1988},
Pages = {279--309},
Volume = {1},
Abstract = {The stability of plane waves of the CGLe is analyzed in a
periodic domain. The mass and energy integrals are estimated to give an
upper bound of the magnitude of the field variable. After that, cone
condition is established for the CGLe which indicates the existence of
the inertial manifold and proves the existence of finite dimensionality of
the attractor in this infinite-dimensional system. The Lyapunov dimension
is estimated. Note the defition of Lyapunov exponents which is a little
different from usual.}
}
@Article{Dolgo04,
Title = {On differentiability of {SRB} states for partially hyperbolic systems},
Author = {D. Dolgopyat},
Journal = {Invent. Math.},
Year = {2004},
Pages = {389},
Volume = {155}
}
@Article{Doob42,
Title = {The {Brownian} movement and stochastic equations},
Author = {J. L. Doob},
Journal = {Ann. Math.},
Year = {1942},
Pages = {351--369},
Volume = {43},
DOI = {10.2307/1968873}
}
@Article{Doob57,
Title = {Conditional Brownian motion and the boundary limits of harmonic functions},
Author = {J. L. Doob},
Journal = {Bull. Soc. Math. France},
Year = {1957},
Pages = {431--458},
Volume = {85},
URL = {http://www.numdam.org/item?id=BSMF_1957__85__431_0}
}
@Book{DR81,
Title = {Hydrodynamic Stability},
Author = {P. Drazin and W.H. Reid},
Publisher = {Cambridge Univ. Press},
Year = {1981},
Address = {Cambridge, UK}
}
@Article{Drazin58,
Title = {Pseudo-inverses in associative rings and semigroups},
Author = {M. P. Drazin},
Journal = {Am. Math. Monthly},
Year = {1958},
Pages = {506--514},
Volume = {65},
DOI = {10.2307/2308576}
}
@Article{Driebe96,
Title = {Using symmetries of the {Frobenius-Perron} operator to determine spectral decompositions},
Author = {D. J. Driebe and G. E. Ordnez},
Journal = {Phys. Lett. A},
Year = {1996},
Pages = {204--210},
Volume = {211},
Keywords = {Frobenius-Perron, piecewise-linear, map}
}
@Article{DrTe11,
Title = {Chaotic saddles in a gravitational field: {The} case of inertial particles in finite domains},
Author = {Dr\'otos, G. and T\'el, T.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {056203},
Volume = {83}
}
@Article{du87,
Title = {Effect of closed classical orbits on quantum spectra: {Ionization} of atoms in a magnetic field},
Author = {M. L. Du and J. B. Delos},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {1731},
Volume = {58},
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.}
}
@Book{Durb_Koop,
Title = {Time series analysis by state space methods},
Author = {J. Durbin and S. J. Koopman},
Publisher = {Oxford Univ. Press},
Year = {2012},
Address = {Oxford}
}
@Article{DV2000,
Title = {Phase space analysis of a dynamical model for the subcritical transition to turbulence in plane {C}ouette flow},
Author = {O. Dauchot and N. Vioujard},
Journal = {Eur. Phys. J. B},
Year = {2000},
Pages = {377--381},
Volume = {14}
}
@Article{DyChuRo93,
Title = {Stationary probability distribution near stable limit cycles far from {Hopf} bifurcation points},
Author = {Dykman, M. and Chu, X. and Ross, J.},
Journal = {Phys. Rev. E},
Year = {1993},
Pages = {1646},
Volume = {48}
}
@Article{DyMiSm94,
Title = {Observable and hidden singular features of large fluctuations in nonequilibrium systems},
Author = {Dykman, M. I. and Millonas, M. M. and Smelyanskiy, V. N.},
Journal = {Phys. Lett. A},
Year = {1994},
Pages = {53--58},
Volume = {195}
}
@Article{EAS87,
Title = {Chaos: a mixed metaphor for turbulence},
Author = {E. A. Spiegel},
Journal = {Proc. Roy. Soc.},
Year = {1987},
Pages = {87},
Volume = {A413}
}
@Article{Eben02,
Title = {Growth and structure of stochastic sequences},
Author = {E. Ben-Naim and P. L. Krapivsky},
Journal = {J. Phys. A},
Year = {2002},
Pages = {557--563},
Volume = {35},
Abstract = {A class of stochastic integer sequences are introduced with
every element being a sum of two previous elements. The interplay between
randomness and memory leads to a wide variety of behaviors rangin from
stretched exponential to log-normal to algebraic growth. The set of all
possible sequence values has an intricate structure.}
}
@Article{eck81,
Title = {Roads to turbulence in dissipative dynamical systems},
Author = {J.-P. Eckmann},
Journal = {Rev. Mod. Phys.},
Year = {1981},
Pages = {643},
Volume = {53}
}
@Article{eckcgl,
Title = {The {E}ckhaus instability for traveling waves},
Author = {B. Janiaud and A. Pumir and D. Bensimon and V. Croquette and H. Richter and L. Kramer},
Journal = {Physica D},
Year = {1992},
Pages = {269--286},
Volume = {55}
}
@Article{eckerg,
Title = {Ergodic theory of chaos and strange attractors},
Author = {J.-P. Eckmann and D. Ruelle},
Journal = {Rev. Mod. Phys.},
Year = {1985},
Pages = {617},
Volume = {57}
}
@Article{ecklp88,
Title = {Liapunov spectra for infinite chains of nonlinear oscillators},
Author = {J. -P. Eckmann and C. E. Wayne },
Journal = {J. Stat. Phys.},
Year = {1988},
Pages = {853--878},
Volume = {50}
}
@Book{eckman80map,
Title = {Iterated Maps on the Interval as Dynamical Systems},
Author = {J.-P. Eckman and P. Collet},
Publisher = {Birkh\"{a}user},
Year = {1980},
Address = {Boston}
}
@Article{EFKKLM08,
Title = {Vacuum stress-energy density and its gravitational implications},
Author = {R. Estrada and S. A. Fulling and L. Kaplan and K. Kirsten and Z. Liu and and K. A. Milton},
Journal = {J. Phys. A},
Year = {2008},
Pages = {164055},
Volume = {41}
}
@Article{egolf00,
Title = {Mechanisms of extensive spatiotemporal chaos in {Rayleigh-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},
Abstract = {Numerical study on Boussinesq equation(pseudospectral method
with time splitting scheme). Demonstrate the extensivity of Lyapunov
dimension of the extended system and showed that the generating mechanism
is breaking or connecting rolls mediated by defects at the domain boundary
and exsisting for only a short time.}
}
@Article{egolf94,
Title = {Relation between fractal dimension and spatial correlation length for extensive chaos},
Author = {D. A. Egolf and H. S. Greenside},
Journal = {Nature},
Year = {1994},
Pages = {129},
Volume = {369},
Abstract = {Numerical study on CGLe. Show that even though the fractal
dimension increases with system size the simple scaling relation is not
correct, i.e. the correlation length can not be used to directly calculate
the fractal dimension.}
}
@Article{egolf98,
Title = {Importance of local pattern properties in spiral defect chaos},
Author = {D. A. Egolf and I. V. Melnikov and E. Bodenschatz},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {3228},
Volume = {80}
}
@Article{EGtran95,
Title = {Characterization of the transition from defect to phase turbulence},
Author = {D. A. Egolf and H. S. Greenside},
Journal = {Phys. Rev. Lett.},
Year = {1995},
Pages = {1751},
Volume = {74},
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.}
}
@Article{EhTr97,
Title = {Optimal prediction of forecast error covariances through singular vectors},
Author = {Ehrendorfer, M. and Tribbia, J. J.},
Journal = {J. Atmos. Sci.},
Year = {1997},
Pages = {286--313},
Volume = {54}
}
@Misc{eigendensity,
Author = {R. Artuso and H. H. Rugh and P. Cvitanovi\'{c}},
Note = {Chapter {\em ``Why does it work?''}, in \refref{DasBuch}},
Year = {2012}
}
@Article{Einstein05,
Title = {{\"Uber die von der molekularkinetischen Theorie der W\"arme geforderte Bewegung von in ruhenden Fl\"ussigkeiten suspendierten Teilchen}},
Author = {A. Einstein},
Journal = {Ann. Physik},
Year = {1905},
Pages = {549--560},
Volume = {17},
DOI = {10.1002/andp.19053220806}
}
@Book{ellip,
Title = {Elliptic Functions and Applications},
Author = {D. F. Lawden},
Publisher = {Springer},
Year = {1989},
Address = {New York}
}
@Article{EM99,
Title = {Transition to turbulence in a shear flow},
Author = {Eckhardt, B. and Mersmann, A.},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {509--517},
Volume = {60}
}
@Article{Erm_spike,
Title = {Relating neural dynamics to neural coding},
Author = {Ermentrout, B. G. and Galan, R. F. and Urban, N. K.},
Journal = {Phys. Rev. Lett.},
Year = {2007},
Pages = {248103},
Volume = {99}
}
@Article{ErmShep12,
Title = {Ulam method and fractal {Weyl law} for {Perron-Frobenius} operators},
Author = {L. Ermann and D.L. Shepelyansky},
Journal = {Eur. Phys. J. B},
Year = {2012},
Pages = {299},
Volume = {75},
DOI = {10.1140/epjb/e2010-00144-0}
}
@Article{ErSar08,
Title = {A periodic orbit basis for the quantum baker's map},
Author = {Saraceno, M. and Ermann, L.},
Journal = {Phys. Rev. E},
Year = {2008},
Note = {\arXiv{0806.4590}},
Pages = {036221 },
Volume = {78}
}
@Article{Ershov_contract,
Title = {Even the first iterate of a {Markov} operator is contracting in an {$L_2$} norm},
Author = {Ershov, S. V.},
Journal = {J. Stat. Phys.},
Year = {1994},
Pages = {783--813},
Volume = {74}
}
@Article{Ershov_dilemma,
Title = {Is a perturbation theory for dynamical chaos possible?},
Author = {Ershov, S. V.},
Journal = {Phys. Lett. A},
Year = {1993},
Pages = {180--185},
Volume = {177}
}
@Unpublished{Eva07,
Title = {STAT206{B}, Stochastic Processes course},
Author = {Steven N. Evans},
Note = {\\ www.stat.berkeley.edu/users/evans/206notes\_Spring06.pdf},
Year = {2007}
}
@Article{expholm88,
Title = {Exponentially small splittings of separatrices with applications to {KAM} theory and degenerate bifurcations},
Author = {P. Holmes and J. Marsden and J. Scheurle},
Journal = {Cont. Math., AMS},
Year = {1988},
Pages = {213--244},
Volume = {81}
}
@Article{FaIo01,
Title = {Accurate low-dimensional approximation of the linear dynamics of fluid flow},
Author = {B. F. Farrell and P. J. Ioannou},
Journal = {J. Atmos. Sci.},
Year = {2001},
Pages = {2771},
Volume = {58},
DOI = {10.1175/1520-0469(2001)058¡2771:ALDAOT¿2.0.CO;2}
}
@Incollection{FaIo06,
Title = {Approximating optimal state estimation},
Author = {B. F. Farrell and P. J. Ioannou},
Booktitle = {Predictability of Weather and Climate},
Publisher = {Cambridge Univ. Press},
Year = {2006},
Address = {Cambridge},
Editor = {Palmer, T. and Hagedorn, R.},
Pages = {181--216}
}
@Misc{FaIo14,
Title = {{Statistical State Dynamics}: a new perspective on turbulence in shear flow},
Author = {B. F. Farrell and P. J. Ioannou},
Note = {\arXiv{1412.8290}},
Year = {2014}
}
@Article{Fano,
Title = {Effects of configuration interaction on intensities and phase shifts},
Author = {Fano, U.},
Journal = {Phys. Rev.},
Year = {1961},
Pages = {1866--1878},
Volume = {124},
DOI = {10.1103/PhysRev.124.1866}
}
@Article{farmer87,
Title = {Predicting chaotic time series},
Author = {J. D. Farmer and J. J. Sidorowich},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Pages = {845},
Volume = {59}
}
@Article{faure06,
Title = {Semi-classical formula beyond the {Ehrenfest} time in quantum chaos. {(I) Trace} formula},
Author = {F. Faure},
Journal = {Ann. Inst. Fourier},
Year = {2007},
Note = {\arXiv{nlin/0610004}},
Pages = {2525--2599},
Volume = {57}
}
@Article{FE03,
Title = {Traveling waves in Pipe Flow},
Author = {Faisst, H. and Eckhardt, B.},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Pages = {224502},
Volume = {91}
}
@Article{FE03a,
Title = {Lifetimes of noisy repellors},
Author = {Faisst, H. and Eckhardt, B.},
Journal = {Phys. Rev. E},
Year = {2003},
Pages = {026215},
Volume = {68},
Abstract = {effects of additive noise on the lifetimes of
chaotic repellors. Using first-order perturbation theory, we argue
that noise will increase the lifetime if the escape holes lie in
regions where the unperturbed density ishigher than that in the
immediate vicinity and that it decreases if the densityis lower}
}
@Article{FedKha86,
Title = {Duality of optimal designs for model discrimination and parameter estimation},
Author = {V. Fedorov and V. Khabarov},
Journal = {Biometrika},
Year = {1986},
Pages = {183--190},
Volume = {73},
Abstract = {In the present paper, ideas of Atkinson \&
Fedorov (1975) are generalized and clarified. The results
illuminate the deep connection between estimation and model
testing problems.}
}
@Book{Fedorov72,
Title = {Theory of Optimal Experiments},
Author = {V. Fedorov},
Publisher = {Academic},
Year = {1972},
Address = {New York}
}
@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}
}
@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,
Title = {The universal metric properties of nonlinear transformations},
Author = {M. J. Feigenbaum},
Journal = {J. Stat. Phys.},
Year = {1979},
Note = {Reprinted in \refref{cvt89b}.},
Pages = {669--706},
Volume = {21}
}
@Article{feigen79scal,
Title = {The onset spectrum of turbulence},
Author = {M. J. Feigenbaum},
Journal = {Phys. Lett. A},
Year = {1979},
Pages = {375--378},
Volume = {74}
}
@Book{Feynman65,
Title = {Quantum Mechanics and Path Integrals},
Author = {R.P. Feynman and A.R. Hibbs},
Publisher = {McGraw-Hill Book Co.},
Year = {1965},
Address = {New York}
}
@Article{FeyVer63,
Title = {The theory of a general quantum system interacting with a linear dissipative system},
Author = {Feynman, R. P. and Vernon, F. L.},
Journal = {Ann. Physics},
Year = {1963},
Pages = {547--607},
Volume = {24}
}
@Article{FiOtt88,
Title = {Chaotic flows and magnetic dynamos},
Author = {Finn,J. M. and Ott, E.},
Journal = {Phys. Rev. Lett.},
Year = {1988},
Pages = {760--763},
Volume = {60}
}
@Incollection{FiRa02,
Title = {Relaxation and noise in chaotic systems},
Author = {Fishman, S. and Rahav, S.},
Booktitle = {Dynamics of Dissipation},
Publisher = {Springer},
Year = {2002},
Address = {Berlin},
Editor = {Garbaczewski, P. and Olkiewicz, R.},
Pages = {165--192}
}
@Article{FJolly95,
Title = {On the numerical algebraic approximation of global attractors},
Author = {C. Foias and M. S. Jolly},
Journal = {Nonlinearity},
Year = {1995},
Pages = {295--319},
Volume = {8},
Abstract = {An algebraic approximation of the global attractors is developed for
the {L}orenz and KS system.}
}
@Article{fl92,
Title = {Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors},
Author = {C. Falcolini and R. de la Llave},
Journal = {J. Stat. Phys.},
Year = {1992},
Pages = {645--666},
Volume = {67},
Abstract = {Study the complex domains of validity in generalized
standard mappings and compare Pad\'{e} methods and periodic orbit methods.}
}
@Article{FNSTks85,
Title = {Inertial manifold for the {Kuramoto-Sivashinsky} equation},
Author = {C. Foias and B. Nicolaenko and G.R. Sell and R. Temam},
Journal = {C. R. Acad. Sci. I-Math},
Year = {1985},
Pages = {285--288},
Volume = {301}
}
@Article{FNSTks88,
Title = {Inertial manifold for the {Kuramoto-Sivashinsky} equation and an estimate of their lowest dimension},
Author = {C. Foias and B. Nicolaenko and G.R. Sell and R. Temam},
Journal = {J. Math. Pure Appl.},
Year = {1988},
Pages = {197--226},
Volume = {67}
}
@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{Fogedby05a,
author = {H. C. Fogedby},
title = {Localized growth modes, dynamic textures, and upper critical dimension for the {Kardar-Parisi-Zhang} equation in the weak noise limit},
journal = {Phys. Rev. Lett.},
year = {2005},
volume = {94},
pages = {195702},
doi = {10.1103/physrevlett.94.195702},
}
@Article{Fogedby06a,
author = {H. C. Fogedby},
title = {{Kardar-Parisi-Zhang} equation in the weak noise limit: {Pattern} formation and upper critical dimension},
journal = {Phys. Rev. E},
year = {2006},
volume = {73},
pages = {031104},
doi = {10.1103/physreve.73.031104},
}
@Article{FogRen09,
Title = {Minimum action method for the {Kardar-Parisi-Zhang} equation},
Author = {Fogedby, H. C. and Ren, W.},
Journal = {Phys. Rev. E},
Year = {2009},
Pages = {041116},
Volume = {80},
DOI = {10.1103/PhysRevE.80.041116}
}
@Article{foias88,
Title = {On the computation of inertial manifolds},
Author = {C. Foias and M.S. Jolly and I.G. Kevrekidis and G.R. Sell and E.S. Titi},
Journal = {Phys. Lett. A},
Year = {1988},
Pages = {433},
Volume = {131}
}
@Article{Foiasks88,
Title = {{Kuramoto-Sivashinsky} equation},
Author = {C. Foias and B. Nicolaenko and G.R. Sell and R. T\'{e}mam},
Journal = {J. Math. Pure Appl.},
Year = {1988},
Pages = {197},
Volume = {67}
}
@Misc{FoMe11,
Title = {Distribution of {Brownian} particles in turbulence},
Author = {Fouxon, I and Mednikov, E.},
Note = {\arXiv{1110.5073}},
Year = {2011}
}
@Article{foulkes:043136,
Title = {Alternative stable scroll waves and conversion of autowave turbulence},
Author = {A. J. Foulkes and D. Barkley and V. N. Biktashev and I. V. Biktasheva},
Journal = {Chaos},
Year = {2010},
Pages = {043136},
Volume = {20},
DOI = {10.1063/1.3517079},
Keywords = {bioelectric phenomena; cardiology; diseases; flow simulation; haemodynamics; muscle; turbulence; vortices},
Numpages = {13}
}
@Article{Fox78,
author = {Fox, R. F.},
title = {{Gaussian} stochastic processes in physics},
journal = {Phys. Rep.},
year = {1978},
volume = {48},
pages = {179--283},
doi = {10.1016/0370-1573(78)90145-X},
}
@Misc{FraDah11,
Title = {Lectures on Dynamic Systems and Control},
Author = {E. Frazzoli and M. Dahleh},
Note = {MIT course 6.241J / 16.338J},
URL = {http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-241j-dynamic-systems-and-control-spring-2011}
}
@Misc{Frasca12,
Title = {Quantum mechanics is the square root of a stochastic process},
Author = {Frasca, M.},
Note = {\arXiv{1201.5091}},
Year = {2012}
}
@Article{FrBe66,
Title = {Estimation of the state of a nonlinear process in the presence of non-{Gaussian} noise and disturbances},
Author = {Friedland, B. and Bernstein, I.},
Journal = {J. Franklin. Inst.},
Year = {1966},
Pages = {455--480},
Volume = {281}
}
@Article{Fred86,
Title = {Nonequilibrium structure of the homogeneous phase of block copolymers under steady flow},
Author = {Fredrickson, G. H.},
Journal = {J. Chem. Phys.},
Year = {1986},
Pages = {5306--5313},
Volume = {85},
DOI = {10.1063/1.451673}
}
@Book{Freidlin98,
Title = {Random Perturbations of Dynamical Systems},
Author = {M. I. Freidlin and A. D. Wentzel},
Publisher = {Springer},
Year = {1998},
Address = {Berlin},
ISBN = {9781461206118}
}
@Article{FrHe87,
Title = {Fluctuation effects in the theory of microphase separation in block copolymers},
Author = {Fredrickson, G. H. and E. Helfand},
Journal = {J. Chem. Phys.},
Year = {1987},
Pages = {697--705},
Volume = {87},
DOI = {10.1063/1.453566}
}
@Article{FrHe88,
Title = {Rheology of homogeneous block copolymers near the microphase separation transition},
Author = {Fredrickson, G. H. and E. Helfand},
Journal = {J. Chem. Phys.},
Year = {1988},
Pages = {5890--5897},
Volume = {89},
DOI = {10.1063/1.455540}
}
@Article{Frigo05,
Title = {The design and implementation of {FFTW3}},
Author = {Frigo, Matteo and Johnson, Steven~G.},
Journal = {Proceedings of the IEEE},
Year = {2005},
Pages = {216--231},
Volume = {93}
}
@Book{frisch,
Title = {Turbulence},
Author = {U. Frisch},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Address = {Cambridge, England}
}
@Article{frisch86,
Title = {Lattice-gas automata for the {Navier-Stokes} equation},
Author = {U. Frisch and B. Hasslacher and Y. Pomeau},
Journal = {Phys. Rev. Lett.},
Year = {1986},
Pages = {1505--1508},
Volume = {56}
}
@Article{frisch87,
Title = {Large-scale flow driven by the anisotropic kinetic alpha effect},
Author = {U. Frisch and Z. S. She and P.-L. Sulem},
Journal = {Physica D},
Year = {1987},
Pages = {382--392},
Volume = {28}
}
@Article{FrLa87,
Title = {Viscoelasticity of homogeneous polymer melts near a critical point},
Author = {Fredrickson, G. H. and R. G. Larson},
Journal = {J. Chem. Phys.},
Year = {1987},
Pages = {1553--1560},
Volume = {86},
DOI = {10.1063/1.452194}
}
@Article{FroSta13,
Title = {Metastability, {Lyapunov} exponents, escape rates, and topological entropy in random dynamical systems},
Author = {G. Froyland and O. Stancevic},
Journal = {Stochastics and Dynamics},
Year = {2013},
Number = {04},
Pages = {1350004},
Volume = {13},
DOI = {10.1142/S0219493713500044},
Eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0219493713500044}
}
@Article{Froy07a,
author = {G. Froyland},
title = {On {Ulam} approximation of the isolated spectrum and eigenfunctions of hyperbolic maps},
journal = {Discrete and continuous dynamical systems},
year = {2007},
volume = {17},
pages = {671--689},
doi = {10.3934/dcds.2007.17.671},
}
@Article{Froy-1,
author = {G. Froyland},
title = {Computer-assisted bounds for the rate of decay of correlation},
journal = {Commun. Math. Phys.},
year = {1997},
volume = {189},
pages = {237--257},
doi = {10.1007/s002200050198},
}
@Inproceedings{Froy-2,
author = {G. Froyland},
title = {Extracting dynamical behaviour via {Markov} models},
booktitle = {{Nonlinear Dynamics and Statistics: Proc. Newton Institute, Cambridge 1998}},
year = {2001},
editor = {A. Mees},
isbn = {978-1-4612-6648-8},
pages = {281--321},
address = {Boston},
publisher = {Birkh\"{a}user},
doi = {10.1007/978-1-4612-0177-9_12},
}
@Article{Froy99,
author = {Froyland, G.},
title = {Using {Ulam}'s method to calculate entropy and other dynamical invariants},
journal = {Nonlinearity},
year = {1999},
volume = {12},
pages = {79--101},
doi = {10.1088/0951-7715/12/1/006},
}
@Article{FroyHD98,
Title = {Approximating physical invariant measures of mixing dynamical systems in higher dimensions},
Author = {{Froyland}, G.},
Journal = {Nonlinear Analysis, Theory, Methods and Applications},
Year = {1998},
Pages = {831--860},
Volume = {32}
}
@Article{Froyland83,
Title = {{Lyapunov} exponents for multidimensional orbits},
Author = {J. Fr\o{}yland},
Journal = {Phys. Lett. A},
Year = {1983},
Pages = {8--10},
Volume = {97},
DOI = {10.1016/0375-9601(83)90087-7}
}
@Article{Froyland83a,
Title = {Some symmetric, two-dimensional, dissipative maps},
Author = {J. Fr\o{}yland},
Journal = {Physica D},
Year = {1983},
Pages = {423--434},
Volume = {8}
}
@Article{Froyland84,
Title = {{Lyapunov} exponent spectra for the {Lorenz} model},
Author = {J. Fr\o{}yland and K. H. Alfsen},
Journal = {Phys. Rev. A},
Year = {1984},
Pages = {2928--2931},
Volume = {29},
DOI = {10.1103/PhysRevA.29.2928}
}
@Article{FSTks86,
Title = {Viscoelastic behavior of cellular solutions to the {Kuramoto-Sivashinsky} model},
Author = {U. Frisch and Z. S. She and O. Thual},
Journal = {J. Fluid Mech.},
Year = {1986},
Pages = {221--240},
Volume = {168},
Abstract = {The KSe on the periodic interval has stable steady states of period
2*pi/N. These "cellular" states exhibit elastic behavior under perturbations of
wavelength much longer than that of itself.}
}
@InProceedings{FuOn08,
Title = {On balanced realization and finite-dimensional approximation for infinite-dimensional nonlinear systems},
Author = {Fujimoto, K. and Ono, S.},
Booktitle = {47\textsuperscript{th} IEEE Conference on Decision and Control. CDC 2008},
Year = {2008},
Organization = {IEEE},
Pages = {4215--4220}
}
@Article{G00,
Title = {The onset of shear turbulence},
Author = {Grossmann, S.},
Journal = {Rev. Mod. Phys.},
Year = {2000},
Pages = { 603--618},
Volume = {72}
}
@Article{GalCoh95,
Title = {Dynamical ensembles in nonequilibrium statistical mechanics},
Author = {G. Gallavotti and E.G.D. Cohen},
Journal = {Phys. Rev. Lett.},
Year = {1995},
Pages = {2694--2697},
Volume = {74},
DOI = {10.1103/PhysRevLett.74.2694}
}
@Book{GaQu95,
Title = {{Lyapunov} Matrix Equation in System Stability and Control},
Author = {Z. Gaji\'c and M. Qureshi},
Publisher = {Academic},
Year = {1995},
Address = {New York}
}
@Article{garnier,
Title = {Nonlinear dynamics of waves and modulated waves in {1D} 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{Gaspard15,
Title = {Cycles, randomness, and transport from chaotic dynamics to stochastic processes},
Author = {Gaspard, P.},
Journal = {Chaos},
Year = {2015},
Volume = {25},
DOI = {10.1063/1.4916922}
}
@Article{GasPro95,
Title = {Spectral signature of the pitchfork bifurcation: {Liouville} equation approach},
Author = {{Gaspard}, P. and {Nicolis}, G. and Provata, A. and Tasaki, S.},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {74--94},
Volume = {51}
}
@Book{gauge,
Title = {Chaos and Gauge Field Theory},
Author = {T. S. Bir\'{o} and S. G. Matinyan and B. M\"{u}ller},
Publisher = {World Scientific},
Year = {1994},
Address = {Singapore}
}
@Article{GeQi12,
Title = {Landscapes of non-gradient dynamics without detailed balance: {Stable} limit cycles and multiple attractors},
Author = {Ge, H. and Qian, H.},
Journal = {Chaos},
Year = {2012},
Pages = {023140},
Volume = {22},
DOI = {10.1063/1.4729137}
}
@Unpublished{GHC08a,
Title = {Periodic orbits of plane {C}ouette flow},
Author = {Gibson, J. F. and Cvitanovi{\'c}, P.},
Note = {In preparation},
Year = {2010}
}
@Article{GHCW07,
Title = {Visualizing the geometry of state-space in plane {C}ouette flow},
Author = {J. F. Gibson and J. Halcrow and P. Cvitanovi{\'c}},
Journal = {J. Fluid Mech.},
Year = {2008},
Note = {\arXiv{0705.3957}},
Pages = {107--130},
Volume = {611},
DOI = {10.1017/S002211200800267X}
}
@Article{GibMcCLE82,
Title = {The real and complex {Lorenz} equations in rotating fluids and lasers},
Author = {Gibbon, J. D. and McGuinness, M. J.},
Journal = {Physica D},
Year = {1982},
Pages = {108--122},
Volume = {5}
}
@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}
}
@Phdthesis{GibsonPhD,
Title = {Dynamical-systems models of wall-bounded, shear-flow turbulence},
Author = {J. F. Gibson},
School = {Cornell Univ.},
Year = {2002}
}
@Book{gil_lf,
Title = {The topology of chaos},
Author = {Gilmore, R. and Lefranc, M.},
Publisher = {Wiley},
Year = {2002},
Address = {New York}
}
@Misc{GiPaPe11,
Title = {Global attractor and asymptotic dynamics in the {Kuramoto} model for coupled noisy phase oscillators},
Author = {{Giacomin}, G. and {Pakdaman}, K. and {Pellegrin}, X.},
Note = {\arXiv{1107.4501}},
Year = {2011}
}
@Book{Gitterman05,
Title = {The noisy oscillator: the first hundred years, from {Einstein} until now},
Author = {Gitterman, M.},
Publisher = {World Scientific},
Year = {2005},
Address = {Singapore}
}
@Article{glaub_haake,
Title = {Superradiant pulses and directed angular momentum states},
Author = {Glauber, R.J. and Haake, F.},
Journal = {Phys. Rev. A},
Year = {1976},
Pages = {357},
Volume = {13}
}
@Article{GM00aut,
Title = {Computing periodic orbits and their bifurcations with automatic differentiation},
Author = {J. Guckenheimer and B. Meloon},
Journal = {SIAM J. Sci. Comp.},
Year = {2000},
Pages = {951--985},
Volume = {22}
}
@Misc{Goldobin12,
Title = {Limit distribution of averages over unstable periodic orbits forming chaotic attractor},
Author = {Goldobin, D. S.},
Note = {\arXiv{1208.1691}},
Year = {2012}
}
@Article{Goldobin14,
Title = {Uncertainty principle for control of ensembles of oscillators driven by common noise},
Author = {Goldobin, D.S.},
Journal = {Eur. Phys. J. Special Topics},
Year = {2014},
Pages = {677--685},
Volume = {223},
DOI = {10.1140/epjst/e2014-02133-y}
}
@Article{Goldobin14a,
Title = {Noise can reduce disorder in chaotic dynamics},
Author = {Goldobin, D. S.},
Journal = {Eur. Phys. J. Special Topics},
Year = {2014},
Pages = {1699--1709},
Volume = {223},
DOI = {10.1140/epjst/e2014-02179-9}
}
@Book{golubII,
Title = {Singularities and Groups in Bifurcation Theory, vol. II},
Author = {M. Golubitsky and I. Stewart and D. G. Schaeffer},
Publisher = {Springer},
Year = {1988},
Address = {New York}
}
@Article{golubord,
Title = {Order and disorder in fluid motion},
Author = {J. P. Gollub},
Journal = {Proc. Natl. Acad. Sci.},
Year = {1995},
Pages = {6705},
Volume = {92},
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,
Title = {Symmetries and pattern selection in {R}ayleigh-{B}ernard convection},
Author = {M. Golubitsky and J. W. Swift and E. Knobloch},
Journal = {Physica D},
Year = {1984},
Pages = {249},
Volume = {10}
}
@Article{GoMiRe11,
Title = {Controlling overestimation of error covariance in ensemble {Kalman} filters with sparse observations: {A} variance limiting {Kalman} filter},
Author = {Gottwald, G. A. and {Mitchell}, L. and {Reich}, S.},
Journal = {Mon. Wea. Rev.},
Year = {2011},
Addendum = {\arXiv{1108.5801}},
Pages = {2650--2667},
Volume = {139},
DOI = {10.1175/2011MWR3557.1}
}
@Article{GoNaVanLo79,
Title = {A {Hessenberg-Schur} method for the problem {AX + XB = C}},
Author = {Golub, G.H. and Nash, S. and Van Loan, C.F.},
Journal = {IEEE Trans. Auto. Contr.},
Year = {1979},
Pages = {909--913},
Volume = {24}
}
@Misc{gora05,
Title = {Stationary distributions of a noisy logistic process},
Author = {P. F. Gora},
Note = {\arXiv{cond-mat/0502389}},
Year = {2005}
}
@Article{GoSuOr87,
Title = {Stability and {Lyapunov} stability of dynamical systems: A differential approach and a numerical method},
Author = {Goldhirsch, I. and Sulem, P. L. and Orszag, S. A.},
Journal = {Physica D},
Year = {1987},
Pages = {311--337},
Volume = {27}
}
@Article{GoTeNaEr10,
Title = {Dynamics of limit-cycle oscillators subject to general noise},
Author = {Goldobin, D. S. and Teramae, J.-n. and Nakao, H. and Ermentrout, B. G.},
Journal = {Phys. Rev. Let.},
Year = {2010},
Pages = {154101},
Volume = {105}
}
@Inbook{GottYan,
Title = {Quantum Mechanics: Fundamentals},
Author = {K. Gottfried and T. Yan},
Chapter = {Low-Dimensional Systems},
Pages = {181--184},
Publisher = {Springer},
Year = {2003},
Address = {New York},
Edition = {2},
ISBN = {9780387216232}
}
@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{GoZa10,
Title = {Noise reduces disorder in chaotic dynamics},
Author = {Goldobin, D. S. and Zaks, M. A. },
Note = {\arXiv{1008.0073}},
Year = {2010}
}
@Book{Gradshteyn65,
Title = {Table of Integrals. Series, and Products},
Author = {I. S. Gradshteyn and I. M. Ryzhik},
Publisher = {Academic},
Year = {1965},
Address = {New York}
}
@Article{Graham84,
Title = {On the weak-noise limit of the {Fokker-Planck} models},
Author = {R. Graham and T. T\'{e}l},
Journal = {J. Stat. Phys.},
Year = {1984},
Pages = {729},
Volume = {35}
}
@Article{Graham84a,
Title = {Existence of a potential for dissipative dynamical systems},
Author = {R. Graham and T. T\'{e}l},
Journal = {Phys. Rev. Lett.},
Year = {1984},
Pages = {9--12},
Volume = {52}
}
@Article{Graham85,
Title = {Integrability of {Hamiltonians} associated with {Fokker-Planck} equations},
Author = {R. Graham and D. Roekaerts and T. T\'{e}l},
Journal = {Phys. Rev. A},
Year = {1985},
Pages = {3364},
Volume = {31}
}
@Article{Graham86,
Title = {Nonequilibrium potential for coexisting attractors},
Author = {R. Graham and T. T\'{e}l},
Journal = {Phys. Rev. A},
Year = {1986},
Pages = {1322--1337},
Volume = {33}
}
@Article{Graham90,
Title = {Steady-state ensemble for the complex {Ginzburg-Landau} equation with weak noise},
Author = {R. Graham and T. T\'{e}l},
Journal = {Phys. Rev. A},
Year = {1990},
Pages = {4661--4677},
Volume = {42}
}
@Article{Graham91,
Title = {Nonequilibrium potentials for dynamical systems with fractal attractors or repellers},
Author = {R. Graham and A. Hamm and T. T\'{e}l},
Journal = {Phys. Rev. Lett.},
Year = {1991},
Pages = {3089--3092},
Volume = {66}
}
@Article{grass89,
Title = {On the symbolic dynamics of {H\'{e}non} map},
Author = {P. Grassberger and H. Kantz and U. Moenig},
Journal = {J. Phys. A},
Year = {1989},
Pages = {5217--5230},
Volume = {22},
Abstract = {Discuss Biham-Wenzel method in {H\'{e}non} map and point out its
defficiency: 1. It converges to a limit cycle sometimes. 2. Two symbol
sequence converges to the same cycle.}
}
@Article{greb90shad,
Title = {Shadowing of physical trajectories in chaotic dynamics: Containment and refinement},
Author = {C. Grebogi and S. M. Hammel and J. A. Yorke and T. Sauer},
Journal = {Phys. Rev. Lett.},
Year = {1990},
Pages = {1527--1530},
Volume = {65}
}
@Book{Greco_Val,
Title = {Lezioni di Algebra Lineare e Geometria},
Author = {S. Greco and P. Valabrega},
Publisher = {Levrotto e Bella},
Year = {1992},
Address = {Torino}
}
@Book{greshosani,
Title = {Incompressible Flow and the Finite Element Method},
Author = {P. M. Gresho and R. L. Sani},
Publisher = {Wiley},
Year = {2000},
Address = {New York}
}
@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{GugAnt04,
Title = {A survey of model reduction by balanced truncation and some new results},
Author = {Gugercin, S. and Antoulas, A. C.},
Journal = {Int. J. Control},
Year = {2004},
Pages = {748--766},
Volume = {77},
DOI = {10.1080/00207170410001713448}
}
@Article{GuKr99,
Title = {Control of adaptive refinement technique technique of generalized cell mapping by system dynamics},
Author = {Guder, R. and Kreuzer, E.},
Journal = {Nonlinear Dynamics},
Year = {1999},
Pages = {21--32},
Volume = {20}
}
@Book{Gurtin81,
Title = {An Introduction to Continuum Mechanics},
Author = {Gurtin, M. E.},
Publisher = {Academic},
Year = {1981},
Address = {New York}
}
@Book{gutbook,
Title = {Chaos in Classical and Quantum Mechanics},
Author = {M.C. Gutzwiller},
Publisher = {Springer},
Year = {1990},
Address = {Berlin}
}
@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}
}
@Book{haake01,
title = {{Quantum Signatures of Chaos}},
publisher = {Springer},
year = {2010},
author = {Haake, F.},
address = {Berlin},
edition = {3},
doi = {10.1007/978-3-662-04506-0},
}
@Book{HaCh08,
Title = {Nonlinear Dynamical Systems and Control: A {Lyapunov}-Based Approach},
Author = {Haddad, W. M. and Chellaboina, V.},
Publisher = {Princeton U. Press},
Year = {2008}
}
@Misc{HagJoy99,
Title = {Exponentially accurate semiclassical dynamics: propagation, localization, {E}hrenfest times, scattering and more general states},
Author = {Hagedorn, G. A. and Joye, A.},
Note = {\arXiv{math-ph/9911036}},
Year = {1999},
Abstract = {We prove six theorems concerning exponentially
accurate semiclassical quantum mechanics. Two of these
theorems are known results, but have new proofs. Under
appropriate hypotheses, they conclude that the exact
and approximate dynamics of an initially localized wave
packet agree up to exponentially small errors in
$\hbar$ for finite times and for Ehrenfest times. Two
other theorems state that for such times the wave
packets are localized near a classical orbit up to
exponentially small errors. The fifth theorem deals
with infinite times and states an exponentially
accurate scattering result. The sixth theorem provides
extensions of the other five by allowing more general
initial conditions.}
}
@Article{Haken81,
Title = {{Chapman-Kolmogorov} equation and path integrals for discrete chaos in presence of noise},
Author = {H. Haken and G. Mayer-Kress},
Journal = {Z. Phys. B},
Year = {1981},
Pages = {185--187},
Volume = {43}
}
@Article{Haken82,
Title = {Some exact results on discrete noisy maps},
Author = {H. Haken and A. Wunderlin},
Journal = {Z. Phys. B},
Year = {1982},
Pages = {181--184},
Volume = {46}
}
@Article{HaKiWa95,
Title = {Regeneration mechanisms of near-wall turbulence structures},
Author = {Hamilton, J. and Kim, J. and Waleffe, F.},
Journal = {J. Fluid Mech.},
Year = {1995},
Pages = {317--348},
Volume = {287}
}
@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},
Author = {J. Hale},
Publisher = {Wiley},
Year = {1969},
Address = {New York}
}
@Article{hamm_graham,
Title = {Quasipotentials for simple noisy maps with complicated dynamics},
Author = {A. Hamm and R. Graham},
Journal = {J. Stat. Phys.},
Year = {1992},
Pages = {689--725},
Volume = {66}
}
@Article{Hammar82,
Title = {Numerical solution of the stable, non-negative definite {Lyapunov} equation},
Author = {Hammarling, S. J.},
Journal = {IMA J. Num. Anal.},
Year = {1982},
Pages = {303--325},
Volume = {2}
}
@Phdthesis{hansen,
Title = {Symbolic Dynamics in Chaotic systems},
Author = {K. T. Hansen},
School = {Univ. of Oslo},
Year = {1993},
Address = {Box 1048, Blindern, N-0316, Oslo, Norway}
}
@Article{hansen92,
Title = {Remarks on the symbolic dynamics for the {H\'{e}non} map},
Author = {K. T. Hansen},
Journal = {Phys. Lett. A},
Year = {1992},
Pages = {100--104},
Volume = {165},
Abstract = {Discuss the change of the symbol sequence of one particular
periodic orbit in the {H\'{e}non} map.}
}
@Book{hao90b,
Title = {Chaos II},
Author = {B.-L. Hao},
Publisher = {World Scientific},
Year = {1990},
Address = {Singapore}
}
@Book{hao98,
title = {{Applied Symbolic Dynamics and Chaos}},
publisher = {World Scientific},
year = {2018},
author = {B.-L. Hao and W.-M. Zheng},
isbn = {9789813236448},
address = {Singapore},
edition = {2},
doi = {10.1142/10887},
}
@Book{hartmanb,
Title = {Ordinary Differential Equations},
Author = {P. Hartman},
Publisher = {Wiley},
Year = {1964},
Address = {New York}
}
@Article{hell78,
Title = {Periodic Solutions of Arbitrary Period, Variational Methods},
Author = {R. Helleman and T. Bountis},
Journal = {LNP},
Year = {1978},
Pages = {353},
Volume = {93}
}
@Article{Heller01,
Title = {Quantum physics: {A}ir juggling and other tricks},
Author = {Heller, E. J.},
Journal = {Nature},
Year = {2001},
Pages = {33--34},
Volume = {412}
}
@Article{Heller75,
Title = {Time-dependent approach to semiclassical dynamics},
Author = {E. J. Heller},
Journal = {J. Chem. Phys.},
Year = {1975},
Pages = {1544},
Volume = {62}
}
@Article{Heller76,
Title = {Classical {S}-matrix limit of wave-packet dynamics},
Author = {E. J. Heller},
Journal = {J. Chem. Phys.},
Year = {1976},
Pages = {4979},
Volume = {65}
}
@Article{Heller76W,
Title = {Wigner phase space method: {Analysis} for semiclassical applications},
Author = {E. J. Heller},
Journal = {J. Chem. Phys.},
Year = {1976},
Pages = {1289},
Volume = {65}
}
@Article{Heller80,
Title = {Quantum dynamical tunneling in bound states},
Author = {M. J. Davis and Heller, E. J.},
Journal = {J. Chem. Phys.},
Year = {1980},
Pages = {2461},
Volume = {75}
}
@Article{Heller84,
Title = {Bound-state eigenfunctions of classically chaotic {Hamiltonian} systems: {Scars} of periodic orbits},
Author = {E. J. Heller},
Journal = {Phys. Rev. Lett.},
Year = {1984},
Pages = {1515--1518},
Volume = {53}
}
@InProceedings{Heller89,
Title = {Wavepacket dynamics and quantum chaology},
Author = {Heller, E. J.},
Booktitle = {Les Houches Lecture Notes, Chaos and Quantum Physics},
Year = {1989},
Address = {Amsterdam },
Editor = {M.-J. Giannoni and A. Voros and J. Zinn-Justin},
Pages = {547},
Publisher = {North Holland}
}
@Article{Heller91,
Title = {Semiclassical time evolution without root searches - {Comments and Perspective - Reply}},
Author = {Heller, E. J. },
Journal = {J. Chem. Phys.},
Year = {1991},
Pages = {9431--9432},
Volume = {95}
}
@Article{Heller99,
Title = {The many faces of tunneling},
Author = {Heller, E. J.},
Journal = {J. Phys. Chem. A},
Year = {1999},
Pages = {10433--10444},
Volume = {103}
}
@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},
}
@Book{henonrtb2,
Title = {Generating Families in the Restricted Three-Body Problem II. Quantitative Study of Bifurcations},
Author = {M. H\'{e}non},
Publisher = {Springer},
Year = {2001},
Address = {New York}
}
@Unpublished{HerGot10,
Title = {The large core limit of spiral waves in excitable media},
Author = {S. Hermann and G. A. Gottwald},
Note = {\arXiv{1003.5830}, SIAM J. Appl. Dyn. Syst., to appear},
Year = {2010}
}
@Article{heron87,
Title = {Dimension of the attractors associated to the {G}inzburg-{L}andau partial differential equation},
Author = {J. M. Ghidaglia and B. H\'{e}ron},
Journal = {Physica D},
Year = {1987},
Pages = {282--304},
Volume = {28}
}
@Article{HeusMull,
Title = {Periodic orbit theory of level correlations},
Author = {S. Heusler and S. Mueller and A. Altland and P. Braun and F. Haake },
Journal = {Phys. Rev. Lett.},
Year = {2007},
Pages = {44103},
Volume = {98}
}
@Article{HGC08,
Title = {Equilibrium and traveling-wave solutions of plane {Couette} flow},
Author = {Gibson, J. F. and Halcrow, J. and Cvitanovi{\'c}, P.},
Journal = {J. Fluid Mech.},
Year = {2009},
Note = {\arXiv{0808.3375}},
Pages = {243--266},
Volume = {638}
}
@Article{hhrugh92,
Title = {The correlation spectrum for hyperbolic analytic maps},
Author = {Rugh, H. H.},
Journal = {Nonlinearity},
Year = {1992},
Pages = {1237},
Volume = {5}
}
@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--79},
doi = {10.1086/109234}
}
@Article{Higham88,
Title = {{FORTRAN} codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation},
Author = {Higham, N. J.},
Journal = {A.C.M. Trans. Math. Soft.},
Year = {1988},
Pages = {381--396},
Volume = {14}
}
@Book{hille,
Title = {Ordinary Differential Equations in the Complex Domain},
Author = {E. Hille},
Publisher = {Dover},
Year = {1997},
Address = {New York}
}
@Article{HJM03,
Title = {Scaling of the Turbulence Transition Threshold in a Pipe},
Author = {Hof, B. and Juel, A. and Mullin, T.},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Pages = {244502},
Volume = {91}
}
@Article{HNks86,
Title = {The {Kuramoto-Sivashinsky} equation: a bridge between PDE's and dynamical systems},
Author = {J. M. Hyman and B. Nicolaenko},
Journal = {Physica D},
Year = {1986},
Pages = {113--126},
Volume = {18},
Abstract = {Numerical work on the transition to chaos of the KSe. The attracting
solution manifold undergoes a complex bifurcation sequence including fixed points, limit
cycles, travelling waves, homoclinic orbits, invariant tori.}
}
@Article{HNZks86,
Title = {Order and complexity in the {Kuramoto-Sivashinsky} model of weakly turbulent interfaces},
Author = {J. M. Hyman and B. Nicolaenko and S. Zaleski},
Journal = {Physica D},
Year = {1986},
Pages = {265--292},
Volume = {23},
Abstract = {The properties of the KSe is discussed in even larger domains. Still
the dynamical behavior is dominated by the skeleton of low dimensional vector fields.
More complex dynamics happens in large domain where intermittency is accurately
identified only by high-precision numerical method. The presence of strange fixed points
overrun the cellular fixed points in large scales which generates complex spatial
structure to the solutions. The Large scale statistical behavior
of the system is computed.}
}
@Misc{ho07,
Title = {Deformed multi-variable {Fokker-Planck} equations},
Author = {C.-L. Ho and R. Sasaki},
Year = {2007},
Eprint = {cond-mat/0703291}
}
@Book{HoJo90,
Title = {Matrix Analysis},
Author = {Horn, R. A. and Johnson, C. R.},
Publisher = {Cambridge Univ. Press},
Year = {1990},
Address = {Cambridge}
}
@Book{Holmes96,
Title = {Turbulence, Coherent Structures, Dynamical Systems and Symmetry},
Author = {P. Holmes and J.L. Lumley and G. Berkooz},
Publisher = {Cambridge Univ. Press},
Year = {1996},
Address = {Cambridge}
}
@Article{HolstKa08,
Title = {Optimal {Markov} approximations and generalized embeddings},
Author = {Holstein, D. and Kantz, H.},
Journal = {Phys. Rev. E},
Year = {2009},
Note = {\arXiv{0808.1513}},
Pages = {056202},
Volume = {79},
Abstract = {Based on information theory, we present a
method to determine an optimal Markov approximation for
modelling and prediction from time series data. The method
finds a balance between minimal modelling errors by taking
as much as possible memory into account and minimal
statistical errors by working in embedding spaces of rather
small dimension. A key ingredient is an estimate of the
statistical error of entropy estimates.}
}
@Article{hoopks85,
Title = {Nonlinear instability at the interface between two viscous fluids},
Author = {A. P. Hooper and R. Grimshaw},
Journal = {Phys. Fluids},
Year = {1985},
Pages = {37--45},
Volume = {28}
}
@Book{Hopf37,
Title = {Ergodentheorie},
Author = {E. Hopf},
Publisher = {Springer},
Year = {1937},
Address = {Berlin}
}
@Article{hopf48,
Title = {A mathematical example displaying features of turbulence},
Author = {E. Hopf},
Journal = {Comm. Appl. Math.},
Year = {1948},
Pages = {303--322},
Volume = {1}
}
@Article{hopf50,
Title = {The partial differential equation $u_t + uu_x = u_{xx}$},
Author = {E. Hopf},
Journal = {Comm. Pure Appl. Math.},
Year = {1950},
Pages = {201--230},
Volume = {3}
}
@Article{Hornung08,
Title = {Noise propagation and signaling sensitivity in biological networks},
Author = {G. Hornung and N. Barkai},
Journal = {PloS Computational Biology},
Year = {2008},
Pages = {e80055},
Volume = {4}
}
@Article{HSGsize98,
Title = {Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable media},
Author = {M. C. Strain and H. S. Greenside},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {2306--2309},
Volume = {80}
}
@Misc{GoPaDu16,
author = {A. Gouasmi and E. Parish and K. Duraisamy},
title = {Characterizing memory effects in coarse-grained nonlinear systems using the {Mori-Zwanzig} formalism},
year = {2016},
url = {https://arxiv.org/abs/1611.06277},
}
@Article{HW90,
Title = {Spectral properties of strongly perturbed {Coulomb} systems: {Fluctuation} properties},
Author = {H\"onig, A. and Wintgen, D.},
Journal = {Phys. Rev. A},
Year = {1989},
Pages = {5642--5657},
Volume = {39},
DOI = {10.1103/PhysRevA.39.5642}
}
@Book{ince,
Title = {Ordinary Differential Equations},
Author = {E. L. Ince},
Publisher = {Dover},
Year = {1956},
Address = {New York}
}
@Book{infdymnon,
title = {{Infinite-Dimensional Dynamical Systems in Mechanics and Physics}},
publisher = {Springer},
year = {1988},
author = {R. Temam},
address = {New York},
}
@Article{inv,
Title = {Invariant measurement of strange sets in terms of cycles},
Author = {P. Cvitanovi\'{c}},
Journal = {Phys. Rev. Lett.},
Year = {1988},
Pages = {2729},
Volume = {61}
}
@Article{IoFa69,
author = {P. J. Ioannou and B. F. Farrell},
title = {Generalized stability theory. {Part I: Autonomous} operators},
journal = {J. Atmos. Sci.},
year = {1996},
volume = {53},
pages = {2025--2040},
doi = {10.1175/1520-0469(1996)053<2025:gstpia>2.0.co;2},
}
@Article{IShudoSchom,
Title = {Weyl law for open systems with sharply divided mixed phase space},
Author = {A. Ishii and A. Akaishi and A. Shudo and H. Schomerus},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {046203},
Volume = {85},
DOI = {10.1103/PhysRevE.85.046203}
}
@Article{IT01,
Title = {The dynamics of bursting process in wall turbulence},
Author = {Itano, T. and Toh, S.},
Journal = {J. Phys. Soc. Japan},
Year = {2001},
Pages = {703--716},
Volume = {70}
}
@Article{Ito,
Title = {Stochastic integral},
Author = {K. It\^{o}},
Journal = {Proc. Imp. Acad. Tokyo},
Year = {1944},
Pages = {519--524},
Volume = {20}
}
@Article{Jac97,
Title = {{Laplace} and the origin of the {Ornstein-Uhlenbeck} process},
Author = {Jacobsen, M.},
Journal = {Bernoulli},
Year = {1997},
Pages = {271--286},
Volume = {2},
Annote = {a second-order partial differential equation, found by Laplace in 1810, is the Fokker-Planck equation for a one-dimensional Ornstein-Uhlenbeck process. It is argued that Laplace's reasoning, although not rigorous, can be entirely justified by using the modern theory of weak convergence of stochastic processes. The solutions to the differential equation found by Laplace and others, using expansions in terms of Hermite polynomials, are discussed. },
DOI = {10.2307/3318524}
}
@Book{Jack,
Title = {Classical Electrodynamics},
Author = {J. D. Jackson},
Publisher = {Wiley},
Year = {1962},
Address = {New York}
}
@Article{jaeger_kantz,
Title = {Homoclinic tangencies and non-normal Jacobians - {Effects} of noise in nonhyperbolic chaotic systems},
Author = {L. Jaeger and H. Kantz},
Journal = {Physica D},
Year = {1997},
Pages = {79--96},
Volume = {105}
}
@Book{JBG97,
Title = {Poincar\'e and the Three Body Problem},
Author = {J. Barrow-Green},
Publisher = {Amer. Math. Soc.},
Year = {1997},
Address = {Providence R.I.}
}
@Book{jeffb,
Title = {Methods of Mathematical Physics},
Author = {H. Jeffreys and B. Jeffreys},
Publisher = {Cambridge Univ. Press},
Year = {1999},
Address = {Cambridge}
}
@Article{jensen84,
Title = {Transition to chaos by interaction of resonances in dissipative systems},
Author = {M. H. Jensen and P. Bak and T. Bohr},
Journal = {Phys. Rev. A},
Year = {1984},
Pages = {1960},
Volume = {30}
}
@Article{JGB86,
Title = {On the origin of streamwise vortices in a turbulent boundary layer},
Author = {Jang, P. S. and {Gran}, R. L. and {Benney}, D. .},
Journal = {J. Fluid Mech.},
Year = {1986},
Pages = {109--123},
Volume = {169}
}
@Book{jhos,
Title = {Oscillations in Nonlinear Systems},
Author = {J. K. Hale},
Publisher = {McGraw-Hill},
Year = {1963},
Address = {New York}
}
@Article{Ji02,
Title = {A finite algorithm for the {Drazin} inverse of a polynomial matrix},
Author = {J. Ji},
Journal = {Appl. Math. Comput.},
Year = {2002},
Pages = {243--251},
Volume = {130},
DOI = {10.1016/S0096-3003(01)00092-3}
}
@Article{JKSN05,
Title = {Characterization of near-wall turbulence in terms of equilibrium and `bursting' solutions},
Author = {Jimenez, J. and Kawahara, G. and Simens, M.P. and Nagata, M.},
Journal = {Phys. Fluids},
Year = {2005},
Pages = {015105 (16pp.)},
Volume = {17}
}
@Article{johnston04,
Title = {Accurate, stable and efficient {N}avier-{S}tokes solvers based on explicit treatment of the pressure term},
Author = {H. Johnston and J.-G. Liu},
Journal = {J. Comput. Physics},
Year = {2004},
Pages = {221--259},
Volume = {199}
}
@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,
Title = {Transverse velocity components in fully developed unsteady flows},
Author = {Joseph, D.D. and Tao, L.N.},
Journal = {J. Appl. Mech.},
Year = {1963},
Pages = {147--148},
Volume = {30}
}
@Article{K31,
Title = {Hamiltonian systems and transformations in {Hilbert} space},
Author = {B. O. Koopman},
Journal = {Proc. Natl. Acad. Sci.},
Year = {1931},
Pages = {315--318},
Volume = {17}
}
@Article{KaHe98,
Title = {Linear and nonlinear theory of eigenfunction scars},
Author = {Kaplan, L. and Heller, E. J.},
Journal = {Ann. Phys.},
Year = {1998},
Pages = {171--206},
Volume = {264}
}
@Article{KaHe99,
Title = {Measuring scars of periodic orbits},
Author = {Kaplan, L. and Heller, E. J.},
Journal = {Phys. Rev. E },
Year = {1999},
Pages = {6609},
Volume = {59}
}
@Article{KaKiZh15,
Title = {Path optimization with limited sensing ability},
Author = {S. H. Kang and S. J. Kim and H. Zhou},
Journal = {J. Comput. Phys.},
Year = {2015},
Pages = {887--901},
Volume = {299},
DOI = {10.1016/j.jcp.2015.07.037}
}
@Book{Kal97,
Title = {Foundations of Modern Probability},
Author = {Olav Kallenberg},
Publisher = {Springer},
Year = {1997}
}
@Article{Kalman60,
Title = {A new approach to linear filtering and prediction problems},
Author = {Kalman, R. E.},
Journal = {J. Basic Eng.},
Year = {1960},
Pages = {35--45},
Volume = {82},
DOI = {10.1115/1.3662552}
}
@Article{KampenKubo,
Title = {Case against linear response theory},
Author = {van Kampen, N. G.},
Journal = {Phys. Norv.},
Year = {1971},
Pages = {279},
Volume = {5}
}
@Article{kaplan-2004-70,
Title = {Semiclassical accuracy in phase space for regular and chaotic dynamics},
Author = {L. Kaplan},
Journal = {Phys. Rev. E},
Year = {2004},
Note = {\arXiv{nlin/0406054}},
Pages = {026223},
Volume = {70}
}
@Article{kaplan-2005-72,
Title = {Brownian motion model of quantization ambiguity and universality in chaotic systems},
Author = {L. Kaplan},
Journal = {Phys. Rev. E},
Year = {2005},
Note = {\arXiv{nlin/0507046}},
Pages = {036214},
Volume = {72}
}
@Article{kaplan98,
Title = {Multiplicative semiclassical dynamics and the quantization time},
Author = {L. Kaplan},
Journal = {Phys. Rev. E},
Year = {1998},
Pages = {2983},
Volume = {58}
}
@Article{Kato03,
Title = {Unstable periodic solutions embedded in a shell model turbulence},
Author = {S. Kato and M. Yamada},
Journal = {Phys. Rev. E},
Year = {2003},
Pages = {025302},
Volume = {68},
Abstract = {A UPO is fo und 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.}
}
@Book{Kato80,
Title = {{Perturbation Theory for Linear Operators}},
Author = {Kato, T.},
Publisher = {Springer},
Year = {1980},
Address = {Berlin},
ISBN = {9783662126783}
}
@Book{Katok95,
Title = {Introduction to the Modern Theory of Dynamical Systems},
Author = {A. Katok and B. Hasselblatt},
Publisher = {Cambridge Univ. Press},
Year = {1995},
Address = {Cambridge}
}
@Article{KawKida01,
Title = {Periodic motion embedded in plane {C}ouette turbulence: regeneration cycle and burst},
Author = {G. Kawahara and S. Kida},
Journal = {J. Fluid Mech.},
Year = {2001},
Pages = {291--300},
Volume = {449},
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.}
}
@Article{Keane98,
Title = {Computing invariant measures for expanding circle maps},
Author = {M. Keane and R. Murray and L.-S. Young},
Journal = {Nonlinearity},
Year = {1998},
Pages = {27--46},
Volume = {11}
}
@Book{Keizer87,
Title = {Statistical Thermodynamics of Nonequilibrium Processes},
Author = {J. Keizer},
Publisher = {Springer},
Year = {1987},
Address = {Berlin}
}
@Book{kellbv,
Title = {Numerical Methods for Two-Point Boundary-Value Problems},
Author = {H. B. Keller},
Publisher = {Dover},
Year = {1992},
Address = {New York}
}
@Article{KellerEpsLogEps,
author = {G. Keller and P. J. Howard and Klages, R.},
title = {Continuity properties of transport coefficients in simple maps},
journal = {Nonlinearity},
year = {2008},
volume = {21},
pages = {1719--1743},
doi = {10.1088/0951-7715/21/8/003},
}
@Article{KenHew87,
Title = {Necessary and sufficient conditions for balancing unstable systems},
Author = {Kenney, C. and Hewer, G.},
Journal = {IEEE Trans. Automatic Control},
Year = {1987},
Pages = {157},
Volume = {AC-32}
}
@Article{Kerswell05,
Title = {Recent progress in understanding the transition to turbulence in a pipe},
Author = {R. R. Kerswell},
Journal = {Nonlinearity},
Year = {2005},
Pages = {17--44},
Volume = {18},
Abstract = {The problem of understanding the nature of fluid
flow through a circular straight pipe remains one of the
oldest problems in fluid mechanics. So far no explanation
has been substantiated to rationalize the transition
process by which the steady unidirectional laminar flow
state gives way to a temporally and spatially disordered
three-dimensional (turbulent) solution as the flow rate
increases. Recently, new travelling wave solutions have
been discovered which are saddle points in phase space.
These plausibly represent the lowest level in a hierarchy
of spatio-temporal periodic flow solutions which may be
used to construct a cycle expansion theory of turbulent
pipe flows. We summarize this success against the backdrop
of past work and discuss its implications for future
research. }
}
@Article{ketzWeyl,
Title = {Hierarchical fractal {Weyl} laws for chaotic resonance states in open mixed systems},
Author = {K\"orber, M. J. and Michler, M. and B\"acker, A. and Ketzmerick, R.},
Journal = {Phys. Rev. Lett.},
Year = {2013},
Pages = {114102},
Volume = {111},
DOI = {10.1103/PhysRevLett.111.114102}
}
@Article{kev01ks,
Title = {The {Oseberg} transition: {Visualization} of global bifurcations for the {Kuramoto-Sivashinsky} equation},
Author = {M. E. Johnson and M. S. Jolly and I. G. Kevrekidis},
Journal = {Int. J. Bifur. Chaos},
Year = {2001},
Pages = {1--18},
Volume = {11}
}
@Inbook{Kiefer85,
chapter = {Design of Experiments},
pages = {718},
title = {{Jack Carl Kiefer Collected Papers}},
publisher = {Springer},
year = {1985},
editor = {Brown, L. D. and Olkin, I. and Sacks, J. and Wynn, H. P.},
volume = {III},
address = {Berlin},
}
@Article{Kif74,
Title = {On small random perturbations of some smooth dynamical systems},
Author = {Y. Kifer},
Journal = {Math. USSR-Izv.},
Year = {1974},
Pages = {1083--1107},
Volume = {8}
}
@Article{Kim87,
Title = {Turbulence statistics in fully developed channel flow at low {R}eynolds number},
Author = {J. Kim and P. Moin and R. Moser},
Journal = {J. Fluid Mech.},
Year = {1987},
Pages = {133--166},
Volume = {177}
}
@Article{Kitagawa77,
Title = {An algorithm for solving the matrix equation {X = F X F' + S}},
Author = {Kitagawa, G.},
Journal = {Int. J. Control},
Year = {1977},
Pages = {745--753},
Volume = {25}
}
@Incollection{Kitahara75,
Title = {{The Hamilton-Jacobi} equation approach to fluctuation phenomena},
Author = {Kitahara, K.},
Booktitle = {Advances in Chemical Physics: Membranes, Dissipative Structures and Evolution},
Publisher = {John Wiley \&\ Sons},
Year = {1975},
Address = {Hoboken, NJ},
Editor = {G. Nicolis and R. Lefever},
Volume = {29},
DOI = {10.1002/9780470143810.ch5}
}
@Book{Kitch98,
Title = {Symbolic Dynamics. One-sided, Two-sided, and Countable {Markov} shifts},
Editor = {B. Kitchens},
Publisher = {Springer},
Year = {1998},
Address = {Berlin}
}
@InProceedings{KK05,
Title = {Unstable periodic motion in plane {C}ouette system: The skeleton of turbulence},
Author = { G. Kawahara and S. Kida and M. Nagata},
Booktitle = {One Hundred Years of Boundary Layer Research},
Year = {2005},
Publisher = {Kluwer}
}
@InProceedings{Kleiser80,
Title = {Treatment of incompressibility and boundary conditions in {3-D} numerical spectral simulations of plane channel flows},
Author = {L. Kleiser and U. Schuman},
Booktitle = {Proc. 3\textsuperscript{rd} GAMM Conf. Numerical Methods in Fluid Mechanics},
Year = {1980},
Address = {Viewweg, Braunschweig},
Editor = {E. Hirschel},
Organization = {GAMM},
Pages = {165--173}
}
@Article{KLH94,
Title = {Bounds for threshold amplitudes in subcritical shear flows},
Author = {{Kreiss}, G. and {Lundbladh}, A. and {Henningson}, D. S.},
Journal = {J. Fluid Mech.},
Year = {1994},
Pages = {175--198},
Volume = {270}
}
@Article{KNSks90,
Title = {Back in the saddle again: a computer assisted study of the {Kuramoto-Sivashinsky} equation},
Author = {I. G. Kevrekidis and B. Nicolaenko and J. C. Scovel},
Journal = {Siam J. Appl. Math.},
Year = {1990},
Pages = {760--790},
Volume = {50},
Abstract = {The initial bifurcations of the KSe are examined analytically and
numerically. The heteroclinic connections between symmetric solutions proved to play
an important role in the dynamics.}
}
@Article{KoGrPo13,
Title = {Classifying and measuring geometry of a quantum ground state manifold},
Author = {Kolodrubetz, M. and Gritsev, V. and Polkovnikov, A.},
Journal = {Phys. Rev. B},
Year = {2013},
Pages = {064304},
Volume = {88},
DOI = {10.1103/PhysRevB.88.064304}
}
@Misc{KoKo11,
Title = {{Navier-Stokes} equation by stochastic variational method},
Author = {T. Koide and T. Kodama},
Note = {\arXiv:1105.6256}
}
@Article{kolm91,
Title = {The local structure of turbulence in incompressible viscous fluid for very large {Reynolds} numbers},
Author = {A. N. Kolmogorov},
Journal = {Proc. R. Soc. Lond. A},
Year = {1991},
Pages = {9--13},
Volume = {434},
Abstract = {Study the distribution of velocity difference of neighboring points
based on the locally homogeneous and locally isotropic hypothesized poperties of
turbulence motion. Two more similarity hypothesis suggested the existence of a
universal distribution for different viscosity and energy dissipation rate. The
large distance asymptotic behavior of the distribution is also deduced.}
}
@Article{Kolov94,
Title = {A remark on the problem of quantum-classical correspondence in the case of chaotic dynamics},
Author = {A. R. Kolovsky},
Journal = {Europhys. Lett.},
Year = {1994},
Pages = {79},
Volume = {27}
}
@Article{Kolov96,
Title = {Quantum coherence, evolution of the {Wigner} function, and transition from quantum to classical dynamics for a chaotic system},
Author = {A. R. Kolovsky},
Journal = {Chaos},
Year = {1996},
Pages = {534--542},
Volume = {6},
DOI = {10.1063/1.166201}
}
@Article{kook89,
Title = {Periodic orbits for reversible symplectic mappings},
Author = {H-T. Kook and J. D. Meiss},
Journal = {Physica D},
Year = {1989},
Pages = {65--86},
Volume = {35},
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.}
}
@Article{kooknewt,
Title = {Application of {N}ewton's method to {L}agrangian mappings},
Author = {H-T Kook and J. D. Meiss},
Journal = {Physica D},
Year = {1989},
Pages = {317--326},
Volume = {36},
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.}
}
@Misc{koopmania,
Author = {P. Cvitanovi\'{c}},
Note = {Appendix {\em ``Implementing evolution''}, in \refref{DasBuch}},
Year = {2013}
}
@Article{KoSch90,
Title = {Noise reduction--finding the simplest dynamical system consistent with the data},
Author = {Kostelich, E. and Yorke, J.},
Journal = {Physica D},
Year = {1990},
Pages = {183--196},
Volume = {41}
}
@Article{KoSch93,
Title = {Noise reduction in chaotic time-series data: a survey of common methods},
Author = {Kostelich, E. and Schreiber, T.},
Journal = {Phys. Rev. E},
Year = {1993},
Pages = {1752--1763},
Volume = {48}
}
@Article{kovalev,
Title = {Sur le probl\`eme de la rotation d'un corps solide d'un point fixe},
Author = {S. Kovalevskaia},
Journal = {Acta Math.},
Year = {1889},
Pages = {177},
Volume = {12}
}
@Article{Kras04,
Title = {Growing random sequences},
Author = {I. Krasikov and G. J. Rodgers and C. E. Tripp},
Journal = {J. Phys. A: Math. Gen.},
Year = {2004},
Pages = {2365--2370},
Volume = {37},
Abstract = {The random sequence has been generalized both in the form of
addition and in the probability distributions. Critical parameter values are
discovered around which the system has very different behavior.}
}
@Book{KrReBe10,
Title = {A Kinetic View of Statistical Physics},
Author = {Krapivsky, P. L. and Redner, S. and Ben-Naim, E.},
Publisher = {Cambridge Univ. Press},
Year = {2010},
Address = {Cambridge, UK}
}
@Article{KRSR67,
Title = {The structure of turbulent boundary layers},
Author = {Kline, S.J. and Reynolds, W.C. and Schraub, F.A. and Rundstadler, P.W. },
Journal = {J. Fluid Mech.},
Year = {1967},
Pages = {741--773},
Volume = {30}
}
@Article{kruskal62,
Title = {Asymptotic theory of {H}amiltonian and other systems with all solutons nearly periodic},
Author = {M. Kruskal},
Journal = {J. Math. Phys.},
Year = {1962},
Pages = {806},
Volume = {3},
Abstract = {Asymptotic expansion to all orders. A systematic way to
construct the adiabatic invariants.}
}
@Article{kruskal65,
Title = {Interaction of "solitons" in a collisionless plasma and the recurrence of initial states},
Author = {N. J. Zabusky and M. D. Kruskal},
Journal = {Phys. Rev. Lett.},
Year = {1965},
Pages = {240},
Volume = {15}
}
@Article{ks04com,
Title = {Fourth-order time stepping for stiff {PDE}s},
Author = {A. -K. Kassam and L. N. Trefethen},
Journal = {SIAM J. Sci. Comp.},
Year = {2004},
Abstract = {A contour integral method is presented to evaluate accurately
the matrix functions with removable singularities.}
}
@Article{kschang86,
Title = {Travelling waves on fluid interfaces: {N}ormal form analysis of the {K}uramoto-{S}ivashisky equation},
Author = {H.-C. Chang},
Journal = {Phys. Fluids},
Year = {1986},
Pages = {3142},
Volume = {29},
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.}
}
@Article{ksgreene88,
Title = {The steady states of the {Kuramoto-Sivashinsky} equation},
Author = {J. M. Greene and J. -S. Kim},
Journal = {Physica D},
Year = {1988},
Pages = {99--120},
Volume = {33},
Abtract = {Use Fourier modes to discuss the energy transport from long wavelength modes to short ones. The generation of steady states with periodic boundary condition is studied systematically with a bifurcation analysis. Their stability is investigated and the scaling in the limit of large system size is presented.}
}
@Article{ksgrim91,
Title = {The non-existence of a certain class of travelling wave solutions of the {K}uramoto-{S}ivashinsky equation},
Author = {R. Grimshaw and A. P. Hooper},
Journal = {Physica D},
Year = {1991},
Pages = {231--238},
Volume = {50},
Abstract = {If the effect of short-wave stability is small, there are no
regular shocks.}
}
@Article{ksham95,
Title = {Hamiltonian structure and integrability of the stationary {Kuramoto-Sivashinsky} equation},
Author = {S. Bouquet},
Journal = {J. Math. Phys.},
Year = {1995},
Pages = {1242},
Volume = {36},
Abstract = {The stationary KSe can be transformed into a time-depent 1-d
Hamiltonian system. There exist a large class of initial conditions under which
the system will explode in a finite time like 120/(x-x_0)^3.}
}
@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},
Abstract = {Numerically calculated connections of the KSe}
}
@Article{kskent92,
Title = {Travelling-waves of the {Kuramoto-Sivashinsky} equation: period-multiplying bifurcations},
Author = {P. Kent and J. Elgin},
Journal = {Nonlinearity},
Year = {1992},
Pages = {899--919},
Volume = {5},
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.}
}
@Article{kstroy89,
Title = {The existence of steady solutions of the {K}uramoto-{S}ivashinsky 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.}
}
@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},
Abstract = {Using asymptotic analysis (beyond all orders)in the weak
shock limit, the oscillatory
shocks and the solitary saves are constructed. It shows that the oscillatory
shocks can be only be anti-symmetric and numurical results support the
anlytical calculation.}
}
@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,
Title = {Persistent propagation of concentration waves in dissipative media far from thermal equilibrium},
Author = {Y. Kuramoto and T. Tsuzuki},
Journal = {Progr. Theor. Phys.},
Year = {1976},
Pages = {365},
Volume = {55},
Abstract = {The KSe is derived through the CGLe near the bifurcation point. Some
scaling argument is used to sort out the domiant terms.}
}
@Article{Kubo57,
Title = {Statistical mechanical theory of irreversible processes. {I}.},
Author = {K. Kubo},
Journal = {J. Phys. Soc. Japan},
Year = {1957},
Pages = {570--586},
Volume = {12}
}
@Article{Kuehn11,
Title = {Deterministic continutation of stochastic metastable equilibria via {Lyapunov} equations and ellipsoids},
Author = {Kuehn, C.},
Journal = {SIAM J. Sci. Comp.},
Year = {2012},
Pages = {A1635-A1658},
Volume = {34},
DOI = {10.1137/110839874}
}
@Article{KuMaKi73,
Title = {Fluctuation and relaxation of macrovariables},
Author = {Kubo, R. and Matsuo, K. and Kitahara, K.},
Journal = {J. Stat. Phys.},
Year = {1973},
Pages = {51--96},
Volume = {9},
DOI = {10.1007/BF01016797},
Keywords = {Relaxation and fluctuation; Markovian process; propagation of extensive property; birth and death process; kinetic Weiss-lsing model; Brownian motion; generalized Fokker-Planck equation; fluctuations far from equilibrium; relaxation spectrum in critical states; path integral}
}
@Book{kura84tur,
Title = {Chemical Oscillations, Waves and Turbulence},
Author = {Y. Kuramoto},
Publisher = {Springer},
Year = {1984},
Address = {Berlin}
}
@Article{Kurch98,
Title = {Fluctuation theorem for stochastic dynamics},
Author = {J. Kurchan},
Journal = {J. Phys. A},
Year = {1998},
Pages = {3719},
Volume = {31}
}
@Article{kuturb78,
Title = {Diffusion-Induced Chaos in Reaction Systems},
Author = {Y. Kuramoto},
Journal = {Suppl. Progr. Theor. Phys.},
Year = {1978},
Pages = {346--367},
Volume = {64},
Abstract = {Phase turbulence and amplitude turbulence are named and distinguished
from a dynamical systems point of view. The prototyped equations are derived.}
}
@Article{Lalley99,
Title = {Beneath the noise, chaos},
Author = {Lalley, S. P.},
Journal = {Ann. Statist.},
Year = {1999},
Pages = {461--479},
Volume = {27}
}
@Article{lamb98,
Title = {Time reversal symmetry in dynamical systems: A survey},
Author = {J. S. W. Lamb and J. A. G. Roberts},
Journal = {Physica D},
Year = {1998},
Pages = {1},
Volume = {112}
}
@Phdthesis{Lan:Thesis,
Title = {Dynamical systems approach to $1-d$ spatiotemporal chaos -- {A} cyclist's view},
Author = {Y. Lan},
School = {School of Physics, Geogia Institute of Technology},
Year = {2004},
Address = {Atlanta}
}
@Article{Lancaster70,
Title = {Explicit solutions of linear matrix equations},
Author = {Lancaster, P.},
Journal = {SIAM Review},
Year = {1970},
Pages = {544--566},
Volume = {12}
}
@Article{landau44,
Title = {On the problem of turbulence},
Author = {L. D. Landau},
Journal = {Dokl. Akad. Nauk SSSR},
Year = {1944},
Pages = {339},
Volume = {44}
}
@Article{lanmaw03,
Title = {Stationary modulated-amplitude waves in the {1D} complex {G}inzburg-{L}andau equation},
Author = {Y. Lan and N. Garnier and P. Cvitanovi\'{c}},
Journal = {Physica D},
Year = {2004},
Pages = {193--212},
Volume = {188}
}
@Article{lanVar1,
Title = {Variational method for finding periodic orbits in a general flow},
Author = {Y. Lan and P. Cvitanovi\'{c}},
Journal = {Phys. Rev. E},
Year = {2004},
Note = {\arXiv{nlin.CD/0308008}},
Pages = {016217},
Volume = {69}
}
@Article{Laplace1810,
Title = {M{\'e}moire sur les int{\'e}grales d{\'e}finies et leur application aux probabilit{\'e}s, et sp{\'e}cialement {\`a} la recherche du milieu qu'il faut choisir entre les r{\'e}sultats des observations},
Author = {Laplace, P. S.},
Journal = {Mem. Acad. Sci. (I), XI, Sec. V.},
Year = {1810},
Pages = {375--387},
Address = {Paris},
URL = {http://gallica.bnf.fr/ark:/12148/bpt6k77600r/f362}
}
@Article{laquey74,
Title = {Nonlinear saturation of the trapped-ion mode},
Author = {R. E. La Quey and S. M. Mahajan and P. H. Rutherford and W. M. Tang},
Journal = {Phys. Rev. Lett.},
Year = {1974},
Pages = {391--394},
Volume = {34}
}
@Book{LaTi85,
Title = {The Theory of Matrices},
Author = {P. Lancaster and M. Tismenetsky},
Publisher = {Academic},
Year = {1985},
Address = {New York}
}
@Book{latt,
Title = {Quantum Fields on the Computer},
Author = {M. Creutz},
Publisher = {World Scientific},
Year = {1992},
Address = {Singapore}
}
@Article{lattref,
Title = {A lattice refinement scheme for finding periodic orbits},
Author = {B. I. Henry and S. D. Watt and S. L. Wearne},
Journal = {Anziam J.},
Year = {2000},
Pages = {735--751},
Volume = {42E},
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.}
}
@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}
}
@Article{Laur91,
Title = {Discrete symmetries and the periodic-orbit expansions},
Author = {B. Lauritzen},
Journal = {Phys. Rev. A},
Year = {1991},
Pages = {603--606},
Volume = {43}
}
@Incollection{lauw86,
Title = {One-dimensional iterative maps},
Author = {H.A. Lauwerier},
Booktitle = {Chaos},
Publisher = {Princeton Univ. Press},
Year = {1986},
Editor = {A. V. Holden},
Pages = {58--96},
ISBN = {9780691610535}
}
@Incollection{lauw86II,
Title = {Two-dimensional iterative maps},
Author = {H.A. Lauwerier},
Booktitle = {Chaos},
Publisher = {Princeton Univ. Press},
Year = {1986},
Editor = {A. V. Holden},
Pages = {39--57},
ISBN = {9780691610535}
}
@Article{LaWe83,
Title = {Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters},
Author = {Lai, T. L. and Wei, C. Z.},
Journal = {J. Multivariate Analysis},
Year = {1983},
Pages = {1--23},
Volume = {13},
Abstract = {This paper establishes several almost sure asymptotic
properties of general autoregressive processes. By
making use of these properties, we obtain a proof of
the strong consistency of the least-squares estimates
of the parameters of the process without any assumption
on the roots of the characteristic polynomial.}
}
@Article{LecDenSol90,
Title = {Optimal brain damage},
Author = {LeCun, Yann and Denker, John S and Solla, Sara A},
Journal = {Advances in neural information processing systems, NIPS 1989},
Year = {1990},
Pages = {598--605},
Volume = {2},
Publisher = {Morgan Kaufmann Publishers}
}
@Article{Lega:holes,
Title = {Traveling hole solutions of the complex Ginzburg Landau equation: a review},
Author = {J. Lega},
Journal = {Physica D},
Year = {2001},
Pages = {152--153},
Volume = {269}
}
@Article{Lehrm97,
Title = {Symbolic analysis of chaotic signals and turbulent fluctuations},
Author = {M. Lehrman and A. B. Rechester and R. B. White},
Journal = {Phys. Rev. Lett.},
Year = {1997},
Pages = {54},
Volume = {78}
}
@Misc{LevnMezi08,
Title = {Ergodic theory and visualization {I}: {Visualization} of ergodic partition and invariant sets},
Author = {Levnaji\'c, Z. and Mezi\'c, I.},
Note = {\arXiv{0805.4221}},
Year = {2008},
Abstract = {We present a computational study of the
invariant sets visualization method based on ergodic
partition theory. The algorithms
for computation of the time averages of many L1 functions
are developed and employed producing the approximation of
the phase space ergodic partitioning. The method is
exposed in the context of discrete-time dynamical systems
producing a graphical representation of the phase space
in terms of the invariant set structure that gives a
substantial insight into the global and local properties
of the dynamics. We use the Chirikov standard map in
order to show the implementation of the method, followed
by applications to other multi-dimensional maps. We examine
the visualization of periodic sets using harmonic time
averages.}
}
@Article{Lewis84,
Title = {Descriptor systems: {Decomposition} into forward and backward subsystems},
Author = {Lewis, F.},
Journal = {IEEE Trans. Auto. Contr.},
Year = {1984},
Pages = {167--170},
Volume = {29}
}
@Article{lfind,
Title = {Systematic computation of the least unstable periodic orbits in chaotic attractors},
Author = {F. K. Diakonos and P. Schmelcher and O. Biham},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Note = {\arXiv{chao-dyn/9810022}},
Pages = {4349},
Volume = {81}
}
@Article{Liao09,
Title = {On the reliability of computed chaotic solutions of non-linear differential equations},
Author = {Liao, S. J.},
Journal = {Tellus A},
Year = {2009},
Note = {\arXiv{0901.2986}},
Pages = {550--564},
Volume = {61}
}
@Misc{Liao11,
Title = {Chaos: a bridge from microscopic uncertainty to macroscopic randomness},
Author = {Liao, S. J.},
Note = {\arXiv{1108.4472}},
Year = {2011}
}
@Book{Lichtenberg92,
Title = {Regular and Chaotic Dynamics},
Author = { A. J. Lichtenberg and M. A. Lieberman},
Publisher = {{S}pringer-{V}erlag},
Year = {1992},
Address = {N.Y.}
}
@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}
}
@Article{LiLi04,
Title = {The maximal {Lyapunov} exponent for a 3-d stochastic system},
Author = {Lie, K. M. and Liu, X. B},
Journal = {J. Appl. Mechanics},
Year = {2004},
Pages = {677--690},
Volume = {71},
Abstract = {a linear part of a co-dimension two-bifurcation system that
is on a three-dimensional central manifold and subjected to parametric
excitation by an ergodic real noise. an n-dimensional Ornstein-Uhlenbeck
vector process which is the output of a linear filter system, while both
the detailed balance condition and the strong mixing condition are
removed. Through a perturbation method and the spectrum representations of
the Fokker Planck operator and its adjoint operator of the linear filter
system, the explicit asymptotic expressions of the maximal Lyapunov
exponent for three case studies, in which different forms of the
coefficient matrix included in the noise excitation term are assumed, are
obtained.}
}
@Unpublished{LipCvi07,
Title = {Optimal resolution of the state space of a chaotic flow in presence of noise},
Author = {P. Cvitanovi\'c and D. Lippolis},
Note = {In preparation},
Year = {2013}
}
@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}
}
@InProceedings{Lippolis13,
author = {D. Lippolis},
title = {Mapping densities in a noisy state space},
booktitle = {{2013 International Symposium on Nonlinear Theory and its Applications, NOLTA2013}},
year = {2013},
volume = {2},
pages = {318--321},
address = {Japan},
publisher = {IEICE},
doi = {10.15248/proc.2.318},
}
@Phdthesis{LippolisThesis,
Title = {How well can one resolve the state space of a chaotic map?},
Author = {Lippolis, D.},
School = {School of Physics, Georgia Inst. of Technology},
Year = {2010},
Address = {Atlanta},
URL = {http://ChaosBook.org/projects/theses.html}
}
@Article{littlejohn86,
Title = {The semiclassical evolution of wave packets},
Author = {Littlejohn, R. G.},
Journal = {Phys. Rep.},
Year = {1986},
Pages = {193--291},
Volume = {138}
}
@Article{liuliupego05,
Title = {Divorcing pressure from viscosity in incompressible {N}avier-{S}tokes dynamics},
Author = {J.-G. Liu and J. Liu and R. L. Pego },
Journal = {ar{X}iv::math.{AP}/0502549},
Year = {2005}
}
@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{lorenz1,
Title = {Deterministic Nonperiodic Flow},
Author = {E. N. {L}orenz},
Journal = {J. Atmos. Sci.},
Year = {1963},
Pages = {130},
Volume = {20}
}
@Article{Lorenz63a,
Title = {The Mechanics of vacillation},
Author = {E. N. Lorenz},
Journal = {J. Meteorology},
Year = {1963},
Pages = {448--465},
Volume = {20},
DOI = {10.1175/1520-0469(1963)020<0448:TMOV>2.0.CO;2}
}
@Article{Lorenz65,
Title = {A study of the predictability of a 28-variable atmospheric model},
Author = {Lorenz, E. N.},
Journal = {Tellus},
Year = {1965},
Pages = {321--333},
Volume = {17},
Abstract = {A 28-variable model of the atmosphere is constructed by
expanding the equations of a two-level geostrophic model in truncated
double-Fourier series. The model includes the nonlinear interactions
among disturbances of three different wave lengths. Nonperiodic
time-dependent solutions are determined by numerical integration.By
comparing separate solutions with slightly different initial
conditions, the growth rate of small initial errors is studied. The
time required for errors comparable to observational errors in the
atmosphere to grow to intolerable errors is strongly dependent upon
the current circulation pattern, and varies from a few days to a few
weeks.Some statistical predictability of certain quantities seems to
be present even after errors in the complete circulation pattern are
no longer small. The feasibility of performing similar studies with
much larger atmospheric models is considered.},
DOI = {10.1111/j.2153-3490.1965.tb01424.x}
}
@Article{lorenz69,
Title = {The predictability of a flow which possessesmany scales of motion},
Author = {E. N. Lorenz},
Journal = {Tellus},
Year = {1969},
Pages = {289--307},
Volume = {21}
}
@Article{Lorenz84,
Title = {Irregularity: a fundamental property of the atmosphere*},
Author = {Lorenz, E. N.},
Journal = {Tellus A},
Year = {1984},
Pages = {98--110},
Volume = {36},
Abstract = {Some early ideas concerning the general circulation of
the atmosphere are reviewed. A model of the general circulation,
consisting of three ordinary differential equations, is introduced.
For different intensities of the axially symmetric and asymmetric
thermal forcing, the equations may possess one or two stable
steady-state solutions, one or two stable periodic solutions, or
irregular (aperiodic) solutions. Qualitative reasoning which has been
applied to the real atmosphere may sometimes be applied to the model,
and checked for soundness by comparing the conclusions with numerical
solutions. The implications of irregularity for the atmosphere and
for atmospheric science are discussed.},
DOI = {10.1111/j.1600-0870.1984.tb00230.x}
}
@Article{lozi2,
Title = {Un attracteur {\'e}trange (?) du type attracteur de {H\'enon}},
Author = {R. Lozi},
Journal = {J. Phys. (Paris) Colloq.},
Year = {1978},
Pages = {C5--9},
Volume = {39},
DOI = {10.1051/jphyscol:1978505}
}
@Article{LPRev,
Title = {Tunneling-induced transparency in a chaotic microcavity},
Author = {Xiao, Yun-Feng and Jiang, Xue-Feng and Yang, Qi-Fan and Wang, Li and Shi, Kebin and Li, Yan and Gong, Qihuang},
Journal = {Laser \& Photonics Reviews},
Year = {2013},
Pages = {51--54},
Volume = {7},
DOI = {10.1002/lpor.201300042}
}
@Article{LR98,
Title = {An adaptive {N}ewton-{P}icard 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}
}
@Misc{LSTvW14,
Title = {Large-scale fluctuations of {Lyapunov} exponents in diffusive systems},
Author = {{Laffargue}, T. and {Sollich}, P. and {Tailleur}, J. and {van Wijland}, F.},
Note = {\arXiv{1406.6370}},
Year = {2014}
}
@Article{LSZ,
Title = {Fractal Weyl laws for open systems},
Author = {W. T. Lu and S. Sridhar and M. Zworski},
Journal = {Phys. Rev. Lett.},
Year = {2003},
Pages = {154101},
Volume = {91}
}
@Article{luce95,
Title = {Homoclinic explosions in the complex {G}inzburg-{L}andau equation},
Author = {B. P. Luce},
Journal = {Physica D},
Year = {1995},
Pages = {553--581},
Volume = {84}
}
@Article{LundJohan91,
Title = {Direct simulation of turbulent spots in plane {C}ouette flow},
Author = {Lundbladh, A. and Johansson, A.},
Journal = {J. Fluid Mech.},
Year = {1991},
Pages = {499--516},
Volume = {229}
}
@Book{Lutk93,
Title = {Introduction to Multiple Time Series Analysis},
Author = {H. L{\"u}tkepohl},
Publisher = {Springer-Verlag},
Year = {1993},
Address = {Berlin, Germany}
}
@Article{LY75,
Title = {Period 3 implies chaos},
Author = {T. Li and J. A. Yorke},
Journal = {Amer. Math. Monthly},
Year = {1975},
Pages = {985},
Volume = {82}
}
@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{Lyapunov1892en,
Title = {The general problem of the stability of motion},
Author = {A. M. Lyapunov},
Journal = {Int. J. Control},
Year = {1992},
Pages = {531--534},
Volume = {55},
DOI = {10.1080/00207179208934253}
}
@Book{lyschm,
Title = {{Lyapunov-S}chmidt Methods in Nonlinear Analysis and Applications},
Author = {N. Sidorov and B. Loginov and A. Sinitsyn and M. Falaleev},
Publisher = {Kluwer},
Year = {2002},
Address = {Dordrecht},
Series = {mathematics and its applications},
Volume = {550}
}
@Article{M86,
Title = {Critical layers in shear flows},
Author = {Maslowe, S. A.},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1986},
Pages = {405--432},
Volume = {18}
}
@Article{MajBran12,
Title = {Lessons in uncertainty quantification for turbulent dynamical systems},
Author = {Majda, A. J. and Branicki, M.},
Journal = {Discrete Contin. Dyn. Syst.},
Year = {2012},
Pages = {3133--3221},
Volume = {32},
DOI = {10.3934/dcds.2012.32.3133}
}
@Misc{malinin07,
Title = {Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition},
Author = {S. V. Malinin and V. Y. Chernyak},
Note = {\arXiv{nlin/0703014}},
Year = {2007}
}
@Book{man90b,
Title = {Dissipative structures and weak turbulence},
Author = {P. Manneville},
Publisher = {Academic},
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}
}
@Article{Mann04,
Title = {Spots and turbulent domains in a model of transitional plane {C}ouette flow},
Author = {Manneville, P.},
Journal = {Theor. Comp. Fluid Dyn.},
Year = {2004},
Pages = {169--181},
Volume = {18}
}
@Article{marcio03,
Title = {Topological characterization of spatial-temporal chaos},
Author = {M. Gameiro and W. Kalies and K. Mischaikow},
Journal = {submitted},
Year = {2003},
Pages = {1},
Volume = {1},
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.}
}
@Book{marsdenbb,
Title = {The {H}opf Bifurcation and its Applications},
Author = {J. E. Marsden and M. McCracken},
Publisher = {Springer},
Year = {1976}
}
@Article{mart87lfa,
Title = {Local frequency analysis of chaotic motion in multidimensional systems: {Energy} transport and bottlenecks in planar {OCS}},
Author = {C. C. Martens and M. J. Davis and G. S. Ezra},
Journal = {Chem. Phys. Lett.},
Year = {1987},
Pages = {519},
Volume = {142},
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 "noble ratio" consideration.}
}
@Article{Martin73,
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,
Title = {Variational construction of orbits of twist difeomorphisms},
Author = {J. N. Mather},
Journal = {J. Am. Math. Soc.},
Year = {1991},
Pages = {207--263},
Volume = {4}
}
@Article{mawcgl,
Title = {Modulated amplitude waves and the transition from phase to defect chaos},
Author = {L. Brusch and M. G. Zimmermann and M. van Hecke and M. B\"{a}r and A. Torcini},
Journal = {Phys. Rev. Lett.},
Year = {2000},
Pages = {86},
Volume = {85},
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.}
}
@Article{May76,
Title = {Simple mathematical models with very complicated dynamics},
Author = {R. May},
Journal = {Nature},
Year = {1976},
Pages = {459--467},
Volume = {261}
}
@Article{Mayb_Amri,
Title = {Dynamic algorithm for parameter estimation and its applications},
Author = {A. Maybhate and R. E. Amritkar},
Journal = {Phys. Rev. E},
Year = {2000},
Number = {6},
Pages = {6461--6470},
Volume = {61}
}
@Article{MC96pha,
Title = {Phase turbulence in the two-dimensional complex {G}inzburg-{L}andau equation},
Author = {P. Manneville and H. Chat\'{e}},
Journal = {Physica D},
Year = {1996},
Pages = {30--46},
Volume = {96},
Abtract = {instability of plane waves}
}
@Article{McKeon04,
Title = {Further observations on the mean velocity in fully-developed pipe flow},
Author = {McKeon, B.J. and Li, J. and Jiang, W. and Morrison, J.F. and Smits, A.J.},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {135--147},
Volume = {501}
}
@Article{Mcoh03,
Title = {Coherent and incoherent structures in systems described by the {1D CGLE}: {Experiments} and identification},
Author = {M. van Hecke},
Journal = {Physica D},
Year = {2003},
Pages = {134},
Volume = {174},
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.}
}
@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}
}
@Article{MEF04,
Title = {Fractal lifetimes in the transition to turbulence},
Author = {Moehlis, J. and Eckhardt, B. and Faisst, H. },
Journal = {Chaos},
Year = {2004},
Pages = {S11},
Volume = {14}
}
@Article{Mein95s,
Title = {Elementary proof of the {Routh-Hurwitz} test},
Author = {G. Meinsma},
Journal = {Systems and Control Letters},
Year = {1995},
Pages = {237--242},
Volume = {25}
}
@Article{MFE04,
Title = {A low-dimensional model for turbulent shear flows},
Author = {Moehlis, J. and Faisst, H. and Eckhardt, B.},
Journal = {New J. of Physics},
Year = {2004},
Pages = {56+17},
Volume = {6}
}
@Article{MFE04b,
Title = {Periodic orbits and chaotic sets in a low-dimensional model for shear flows},
Author = {Moehlis, J. and Faisst, H. and Eckhardt, B.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2004},
Pages = {352--376},
Volume = {4}
}
@Article{mfind,
Title = {Efficient algorithm for detecting unstable periodic orbits in chaotic systems},
Author = {R. L. Davidchack and Y.-C. Lai},
Journal = {Phys. Rev. E},
Year = {1999},
Pages = {6172},
Volume = {60}
}
@Article{MHMwind96,
Title = {Winding number instability in the phase-turbulence regime of the complex {G}inzburg-{L}andau equation},
Author = {R. Montagne and E. Hern\'{a}ndez-Garc\'{i}a and M. S. Miguel},
Journal = {Phys. Rev. Lett.},
Year = {1996},
Pages = {267},
Volume = {77},
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.}
}
@Article{michsiv77,
Title = {Nonlinear analysis of hydrodynamic instability in laminar flames - II. Numerical experiments},
Author = {D. M. Michelson and G. I. Sivashinsky},
Journal = {Acta Astr.},
Year = {1977},
Pages = {1207--1221},
Volume = {4},
Abstract = {Consider the effect of hydrodynamics instability and diffusion thermal
instability through the numerical calculation of the KSe.}
}
@Misc{MiFeFl08,
Title = {Preservation of hyperbolic equilibrium points and synchronization in dynamical systems},
Author = {C. Miranda-Reyes and G. Fern and J. J. Flores-Godoy},
Year = {2008}
}
@Article{Milb_sqa,
Title = {Quantum and classical Liouville dynamics in the anharmonic oscillator},
Author = {G. J. Milburn},
Journal = {Phys. Rev. A},
Year = {1986},
Number = {1},
Pages = {674--685},
Volume = {33}
}
@Article{Milb_sqa2,
Title = {Dissipative quantum and classical Liouville dynamics in the anharmonic oscillator},
Author = {G. J. Milburn and C. A. Holmes},
Journal = {Phys. Rev. Lett.},
Year = {1986},
Number = {21},
Pages = {2237--2240},
Volume = {56}
}
@Book{MiraGum80,
Title = {Recurrances and Discrete Dynamical Systems},
Author = {I. Gumowski and C. Mira},
Publisher = {Springer},
Year = {1980},
Address = {Berlin}
}
@Article{mis01ks,
Title = {Rigorous Numerics for Partial Differential Equations: the {Kuramoto-Sivashinsky} equation},
Author = {P. Zgliczynski and K. Mischaikow},
Journal = {Foundations of Comp. Math.},
Year = {2001},
Pages = {255--288},
Volume = {1}
}
@Article{misdis,
Title = {Construction of symbolic dynamics from experimental time series},
Author = {K. Mischaikow and M. Mrozek and J. Reiss and A. Szymczak},
Journal = {Phys. Rev. Lett.},
Year = {1999},
Pages = {1144},
Volume = {82}
}
@Article{Misiurewicz80,
Title = {Strange attractors for the {Lozi} mappings},
Author = {Misiurewicz, Michal},
Journal = {Ann. New York Acad. Sci.},
Year = {1980},
Pages = {348--358},
Volume = {357}
}
@Article{mislor1,
Title = {Chaos in the {L}orenz equations: A computer assisted proof Part II: Details},
Author = {K. Mischaikow and M. Mrozek},
Journal = {Math. Comp.},
Year = {1998},
Pages = {1023--1046},
Volume = {67}
}
@Article{Mks86,
Title = {Steady solutions of the {Kuramoto-Sivashinsky} equation},
Author = {D. Michelson},
Journal = {Physica D},
Year = {1986},
Pages = {89--111},
Volume = {19},
Abtract = {The variety of steady solution of the KSe is discussed. For large c, there is only one odd front-like bounded solution. In decreasing c, odd solutions with more zeros are born until finally a periodic solution is born. Associated with the periodic solution, infinite many tori will appear in the elliptic case and Cantor-type set of chaotic solutions, with infinite many homoclinic odd solutions.},
DOI = {10.1016/0167-2789(86)90055-2}
}
@Misc{MoMiAo14,
Title = {Optimal colored noise for estimating phase response curves},
Author = {{Morinaga}, K. and {Miyata}, R. and {Aonishi}, T.},
Note = {\arXiv{1409.1637}},
Year = {2014}
}
@Article{Moore81,
Title = {Principal component analysis in linear systems: {Controllability}, observability, and model reduction},
Author = {B. Moore},
Journal = {IEEE Trans. Automat. Contr.},
Year = {1981},
Pages = {17--32},
Volume = {26}
}
@InProceedings{Morkovin69,
Title = {On the many faces of transition},
Author = {Morkovin, M.V},
Booktitle = {Viscous Drag Reduction},
Year = {1969},
Editor = {Wells, C.S.},
Pages = {1--31},
Publisher = {Plenum, New York}
}
@Article{Morrison02,
Title = {Reynolds number dependence of streamwise velocity spectra in turbulent pipe flow},
Author = {J.F. Morrison and W. Jiang and B.J. McKeon and A.J. Smits},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Pages = {214501},
Volume = {88}
}
@Article{Morrison04,
Title = {Scaling of the streamwise velocity component in turbulent pipe flow},
Author = {J.F. Morrison and B.J. McKeon and W. Jiang and A.J. Smits},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {99--131},
Volume = {508}
}
@Book{Morse73,
Title = {Variational Analysis: Critical Extremals and Sturmian Extensions},
Author = {M. Morse},
Publisher = {Wiley},
Year = {1973},
Address = {New York}
}
@Article{moser96,
Title = {A rapidly converging iteration method and nonlinear partial differential equations -{I}},
Author = {J. Moser},
Journal = {Ann. Scuola Norm. Super. Pisa},
Year = {1966},
Pages = {265--315},
Volume = {20},
URL = {http://archive.numdam.org/ARCHIVE/ASNSP/ASNSP_1966_3_20_2/ASNSP_1966_3_20_2_265_0/ASNSP_1966_3_20_2_265_0.pdf}
}
@Article{moser96a,
Title = {A rapidly convergent iteration method and non-linear differential equations - {II}},
Author = {J. Moser},
Journal = {Ann. Scuola Norm. Super. Pisa},
Year = {1966},
Pages = {499--535},
Volume = {20},
URL = {http://archive.numdam.org/ARCHIVE/ASNSP/ASNSP_1966_3_20_3/ASNSP_1966_3_20_3_499_0/ASNSP_1966_3_20_3_499_0.pdf}
}
@Book{mosersr,
Title = {Stable and Random Motions in Dynamical Systems},
Author = {J. Moser},
Publisher = {Princeton Univ. Press},
Year = {1973},
Address = {Princeton}
}
@Article{MR94,
Title = {Periodic orbit expansions for the {Lorentz} gas},
Author = {G. P. Morriss and L. Rondoni},
Journal = {J. Stat. Phys.},
Year = {1994},
Pages = {553--584},
Volume = {75},
DOI = {10.1007/BF02186872}
}
@Article{MS66,
Title = {A thermally excited nonlinear oscillator},
Author = {D. W. Moore and E. A. Spiegel},
Journal = {Astrophys. J.},
Year = {1966},
Pages = {871},
Volume = {143}
}
@Article{MTYYA14,
Title = {Potential function in a continuous dissipative chaotic system: {Decomposition} scheme and role of strange attractor},
Author = {Ma, Y. and Tan, Q. and Yuan, R. and Yuan, B. and Ao, P.},
Journal = {Int. J. Bifur. Chaos},
Year = {2014},
Pages = {1450015},
Volume = {24},
DOI = {10.1142/S0218127414500151}
}
@Article{MvH98,
Title = {Building blocks of spatiotemporal intermittency},
Author = {M. van Hecke},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {1896},
Volume = {80}
}
@Article{MvHhole01,
Title = {Ordered and Self-disordered dynamics of holes and defects in the one-dimensional complex {G}inzburg-{L}andau equation},
Author = {M. van Hecke and M. Howard},
Journal = {Phys. Rev. Lett.},
Year = {2001},
Pages = {2018},
Volume = {86},
Abtract = {Ordered hole-defect dynamics happens when an unstable hole invade a plane wave state and periodically nucleates defects from which new holes are born. The interaction between the holes and a self-disordered background are essential for the occurrence of spatiotemporal chaos in hole-defect states.}
}
@Article{N90,
Title = {Three-dimensional finite-amplitude solutions in plane {Couette} flow: bifurcation from infinity},
Author = {Nagata, M.},
Journal = {J. Fluid Mech.},
Year = {1990},
Pages = {519--527},
Volume = {217},
DOI = {10.1017/S0022112090000829}
}
@Article{name,
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},
Abstract = {The article demonstrates the existence of a nonuniform stationary measure
associated with the space-filling properties of the unstable invariant foliation in 2D
differentiable area-preserving systems and derives a sequence of analytical approximations
for it. In fluid convection systems, it is just the convected material line.}
}
@Article{NaSaWa13,
Title = {{Hamilton-Jacobi} method for molecular distribution function in a chemical oscillator},
Author = {Nakanishi, H. and Sakaue, T. and Wakou, J.},
Journal = {J. Chem. Phys.},
Year = {2013},
Pages = {214105},
Volume = {139},
DOI = {10.1063/1.4834636}
}
@Misc{natmsr,
Author = {P. Cvitanovi\'{c} and R. Artuso and L. Rondoni and E. A. Spiegel},
Note = {Chapter {\em Transporting densities}, in \refref{DasBuch}},
Year = {2012}
}
@Article{NeSa11,
Title = {Thermodynamic formula for the cumulant generating function of time-averaged current},
Author = {Nemoto, T. and Sasa, S.-i.},
Journal = {Phys. Rev. E},
Year = {2011},
Pages = {061113},
Volume = {84},
DOI = {10.1103/PhysRevE.84.061113},
Numpages = {18}
}
@Article{NeuSch01,
Title = {Estimation of parameters and eigenmodes of multivariate autoregressive models},
Author = {A. Neumaier and T. Schneider},
Journal = {A.C.M. Trans. Math. Softw.},
Year = {2001},
Pages = {27--57},
Volume = {27},
Abstract = {Dynamical characteristics of a complex system can
often be inferred from analyses of a stochastic time
series model fitted to observations of the system.
Oscillations in geophysical systems, for example, are
sometimes characterized by principal oscillation
patterns, eigenmodes of estimated autoregressive (AR)
models of first order. This paper describes the
estimation of eigenmodes of AR models of arbitrary
order. AR processes of any order can be decomposed into
eigenmodes with characteristic oscillation periods,
damping times, and excitations. Estimated eigenmodes
and confidence intervals for the eigenmodes and their
oscillation periods and damping times can be computed
from estimated model parameters. As a computationally
efficient method of estimating the parameters of AR
models from high-dimensional data, a stepwise least
squares algorithm is proposed. This algorithm computes
model coefficients and evaluates criteria for the
selection of the model order stepwise for AR models of
successively decreasing order. Numerical simulations
indicate that, with the least squares algorithm, the AR
model coefficients and the eigenmodes derived from the
coefficients are estimated reliably and that the
approximate 95\% confidence intervals for the
coefficients and eigenmodes are rough approximations of
the confidence intervals inferred from the
simulations.}
}
@Misc{NeuSch97,
Title = {Multivariate autoregressive and {Ornstein-Uhlenbeck} processes: {Estimates} for order, parameters, spectral information, and confidence regions},
Author = {A. Neumaier and T. Schneider},
Note = {Submitted to A.C.M. Trans. Math. Softw., unpublished}
}
@Article{newcgl1,
Title = {Instabilities of {G}inzburg-{L}andau 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}
}
@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}
}
@Misc{Nico90,
Title = {Chaotic dynamics and markovian coarse-graining in nonlinear dynamical systems},
Author = {G. Nicolis},
Note = {in \textit{Noise and Chaos in Nonlinear Dynamical Systems}, edited by F. Moss, L. A. Lugiato, and W. Schleich (Cambridge Univ. Pres)},
Year = {1990}
}
@Article{Nico95,
Title = {Chaotic dynamics applied to information processing},
Author = {J. S. Nicolis},
Journal = {Rep. Prog. Phys.},
Year = {1986},
Pages = {1109--1196},
Volume = {49}
}
@Article{nlin0001013,
Title = {{Frobenius-Perron} resonances for maps with a mixed phase space},
Author = {{Weber}, J. and {Haake}, F. and {{\v S}eba}, P.},
Journal = {Phys. Rev. Lett.},
Year = {2000},
Note = {\arXiv{nlin/0001013}},
Pages = {3620--3623},
Volume = {85}
}
@Article{nlin0102039,
Title = {Periodic orbit quantization of a {Hamiltonian} map on the sphere},
Author = {A. J. Scott and G. J. Milburn},
Journal = {J. Phys. A},
Year = {2001},
Note = {\arXiv{nlin/0102039}},
Pages = {7541},
Volume = {34},
Abstract = {In a previous paper we introduced examples of
Hamiltonian mappings with phase space structures
resembling circle packings. It was shown that a vast
number of periodic orbits can be found using special
properties. We now use this information to explore the
semiclassical quantization of one of these maps.}
}
@Article{nlin0105047,
Title = {Resonances of the {Frobenius-Perron} operator for a {Hamiltonian} map with a mixed phase space},
Author = {{Weber}, J. and {Haake}, F. and {Braun}, P.~A. and {Manderfeld}, C. and {Seba}, P.},
Journal = {J. Phys. A},
Year = {2001},
Note = {\arXiv{nlin/0105047}},
Pages = {7195--7211},
Volume = {34}
}
@Article{nlin0107020,
Title = {Classical versus quantum time evolution of (quasi-) probability densities at limited phase-space resolution},
Author = {{Manderfeld}, C. and {Weber}, J. and {Haake}, F.},
Journal = {J. Phys. A},
Year = {2001},
Note = {\arXiv{nlin/0107020}},
Pages = {9893--9905},
Volume = {34}
}
@Article{nlin0312062,
Title = {Spectral properties and classical decays in quantum open systems},
Author = {Garc{\'{\i}}a-Mata, I. and {Saraceno}, M.},
Journal = {Phys. Rev. E},
Year = {2004},
Note = {\arXiv{nlin/0312062}},
Pages = {056211},
Volume = {69}
}
@Article{NLSmal91,
Title = {Modulational instabilities and soliton solutions of a generalized nonlinear {S}chr\"{o}dinger equation},
Author = {B. A. Malomed and L. Stenflo},
Journal = {J. Phys. A},
Year = {1991},
Pages = {1149--1153},
Volume = {24},
Abtract = {A Hamiltonian equation is proposed for the generalized nonlinear Schr\"{o}dinger equation. Soliton solutions are found and the stability of the plane waves is investigated.}
}
@Article{NLSper77,
Title = {Nonlinear Schr\"{o}dinger equation including growth and damping},
Author = {N. R. Pereira and L. Stenflo},
Journal = {Phys. Fluids},
Year = {1977},
Pages = {1733--1734},
Volume = {20},
Abstract = {A nonlinear Schr\"{o}dinger equation is found with growth and damping
terms in the weakly nonlinear regime. An exact solitary solution is found for the
equation.}
}
@Article{NLSstn03,
Title = {Oscillons at a plasma surface},
Author = {L. Stenflo and M. Y. Yu},
Journal = {Phys. Plasmas},
Year = {2003},
Pages = {912--913},
Volume = {10},
Abstract = {Under the external driving force, an oscillon solutions is found.}
}
@Article{NockelStone,
Title = {Ray and wave chaos in asymmetric resonant optical cavities},
Author = {Nockel, J. U. and Stone, A. D.},
Journal = {Nature},
Year = {1997},
Number = {6611},
Pages = {45--47},
Volume = {385},
Abstract = {OPTICAL resonators are essential components of lasers and
other optical devices, A resonator is characterized by a set of modes,
each with a resonant frequency omega and resonance width delta omega =
1/tau, where tau is the lifetime of a photon in the mode, Cylindrical
or spherical dielectric resonators have extremely long-lived
resonances(1) due to 'whispering gallery' modes in which light
circulates around the perimeter trapped by total internal reflection,
These resonators emit light isotropically, Recently a new category of
asymmetric resonant cavities has been proposed in which substantial
deformation of the cavity from cylindrical or spherical symmetry leads
to partially chaotic ray dynamics, This has been predicted(2-4) to
give rise to a universal, frequency-independent broadening of
the,whispering-gallery resonances, and to highly anisotropic emission,
Here we present solutions of the wave equation for asymmetric resonant
cavities which confirm these predictions but also reveal interesting
frequency-dependent effects characteristic of quantum chaos, For small
deformations the lifetime is controlled by evanescent leakage, the
optical analogue of quantum tunnelling(5); here the lifetime is
significantly shortened by a process known as 'chaos-assisted
tunnelling'(6-7). In contrast, for large deformations (similar to 10%)
some resonances are found to have longer lifetimes than predicted by
the ray chaos model due to the phenomenon of 'dynamical
localization'(8).},
DOI = {Doi 10.1038/385045a0}
}
@InProceedings{NoeckChang,
Title = {{2D} microcavities: {Theory} and experiemtns},
Author = {N\"ockel, J. U. and Chang, R. K.},
Booktitle = {Cavity-Enhanced Spectroscopies},
Year = {2002},
Editor = {Van Zee, R. D. and Looney, J. P.},
Pages = {185--226},
Publisher = {Academic},
ISBN = {9780124759879}
}
@Article{noisy_Fred,
Title = {Trace formulas for stochastic evolution operators: {Weak} noise perturbation theory},
Author = {P. Cvitanovi\'{c} and C. P. Dettmann and R. Mainieri and G. Vattay },
Journal = {J. Stat. Phys.},
Year = {1998},
Note = {\arXiv{chao-dyn/9807034}},
Pages = {981},
Volume = {93}
}
@Article{nongal89,
Title = {Nonlinear {G}\"{a}lerkin methods},
Author = {M. Martine and R. Temam},
Journal = {SIAM J. Numer. Anal.},
Year = {1989},
Pages = {1139--1157},
Volume = {26},
Abstract = {nonlinear {G}\"{a}lerkin methods}
}
@Book{nr,
Title = {Numerical Recipes in {C}},
Author = {W. H. Press and S. A. Teukolsky and W. T. Vetterling and B. P. Flannery},
Publisher = {Cambridge Univ. Press},
Year = {1992},
Address = {Cambridge, England}
}
@Book{ns,
Title = {Numerical Partial Differential Equations},
Author = {J. W. Thomas},
Publisher = {Spring-Verlag},
Year = {1995},
Address = {New York}
}
@Article{NSTks85,
Title = {Some global dynamical properties of the {Kuramoto-Sivashinsky} equations: nonlinear stability and attractors},
Author = {B. Nicolaenko and B. Scheurer and R. Temam},
Journal = {Physica D},
Year = {1985},
Pages = {155--183},
Volume = {16},
Abstract = {The KSe shows coherent spatial patterns but temporal chaos. The
anti-diffusion term destablizes the solutin while stability is achived by the collective
action of all modes through the nonlinear convection term. An estimate of the L^2 norm of
the solution in the antisymmetric periodic function space is given. The number of
determining Fourier modes is calculated together with fractal dimension of the strange
attractor.}
}
@Article{OcToHe92,
Title = {Accuracy of semiclassical dynamics in the presence of chaos},
Author = {P. W. Oconnor and S. Tomsovic and Heller, E. J. },
Journal = {J. Stat. Phys.},
Year = {1992},
Pages = {131--152},
Volume = {68}
}
@Article{OHSZKCKY04,
Title = {A local ensemble {Kalman} filter for atmospheric data assimilation},
Author = {Ott, E. and Hunt, B. and Szunyogh, I. and Zimin, A. and Kostelich, E. and Corrazza, M. and Kalnay, E. and Yorke, J.},
Journal = {Tellus A},
Year = {2004},
Pages = {415--428},
Volume = {56}
}
@Article{OkEckThiDoe08,
Title = {Mixing effectiveness depends on the source--sink structure: simulation results},
Author = {Okabe, T. and Eckhardt, B. and Thiffeault, J.-L. and Doering, C. R.},
Journal = {J. Stat. Phys},
Year = {2008},
Pages = {P07018},
Volume = {2008},
DOI = {10.1088/1742-5468/2008/07/P07018}
}
@Book{Oksendal03,
Title = {Stochastic Differential Equations: An Introduction with Applications},
Author = {{\O}ksendal, B.K.},
Publisher = {Springer},
Year = {1998},
Address = {New York},
ISBN = {9783540637202}
}
@Article{OlGo92,
Title = {Isotropic-nematic transition in shear flow: {State} selection, coexistence, phase transitions, and critical behavior},
Author = {Olmsted, P. D. and Goldbart, P. M.},
Journal = {Phys. Rev. A},
Year = {1992},
Pages = {4966--4993},
Volume = {46},
DOI = {10.1103/PhysRevA.46.4966}
}
@Article{Olmsted94,
Title = {Rotational invariance and {Goldstone modes} in nematic elastomers and gels},
Author = {Olmsted, P. D.},
Journal = {J. Phys. II France},
Year = {1994},
Pages = {2215--2230},
Volume = {4},
DOI = {10.1051/jp2:1994257}
}
@Article{OnKa79,
Title = {Nonequilibrium steady state of critical fluids under shear flow: {A} renormalization group approach},
Author = {A. Onuki and K. Kawasaki},
Journal = {Ann. Phys.},
Year = {1979},
Pages = {456--528},
Volume = {121},
DOI = {10.1016/0003-4916(79)90105-2}
}
@Article{Onsager53,
Title = {Fluctuations and irreversible processes},
Author = {L. Onsager and S. Machlup},
Journal = {Phys. Rev.},
Year = {1953},
Pages = {1505--1512},
Volume = {91},
DOI = {10.1103/PhysRev.91.1505}
}
@Article{Onsager53II,
Title = {Fluctuations and irreversible processess. {II. Systems} with kinetic energy},
Author = {Machlup, S. and Onsager, L.},
Journal = {Phys. Rev.},
Year = {1953},
Pages = {1512--1515},
Volume = {91},
DOI = {10.1103/PhysRev.91.1512}
}
@Article{Onuki87,
Title = {Homogeneous block copolymer systems under shear flow},
Author = {A. Onuki},
Journal = {J. Chem. Phys.},
Year = {1987},
Pages = {3692--3697},
Volume = {87},
DOI = {10.1063/1.452967}
}
@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,
Title = {Optimal periodic orbits of continuous time chaotic systems},
Author = {T.-H. Yang and B. R. Hunt and E. Ott},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {1950},
Volume = {62}
}
@Article{Ordonez96,
Title = {Spectral decomposition of tent maps using symmetry considerations},
Author = {G. E. Ordonez and D. J. Driebe},
Journal = {J. Stat. Phys.},
Year = {1996},
Pages = {269--276},
Volume = {84},
Keywords = {Frobenius-Perron, coupled systems, tent map, symmetry}
}
@Article{Orland11,
Title = {Generating transition paths for {Langevin} bridges},
Author = {H. Orland},
Journal = {J. Chem. Phys.},
Year = {2011},
Pages = {174114},
Volume = {134},
DOI = {10.1063/1.3586036}
}
@Article{OrlMaj15,
Title = {Effective Langevin equations for constrained stochastic processes},
Author = {S. N. Majumdar and H. Orland},
Journal = {J. Stat. Mech.},
Year = {2015},
Pages = {P06039},
DOI = {10.1088/1742-5468/2015/06/P06039}
}
@Article{OrnUhl30,
Title = {On the theory of the {Brownian} motion},
Author = {Uhlenbeck, G. E. and Ornstein, L. S.},
Journal = {Phys. Rev.},
Year = {1930},
Pages = {823--841},
Volume = {36},
DOI = {10.1103/PhysRev.36.823}
}
@Article{Orszag1,
Title = {Boundary conditions for incompressible flows},
Author = {S. A. Orszag and M. Israeli and M. Deville},
Journal = {J. Sci. Comput.},
Year = {1986},
Pages = {75--111},
Volume = {1}
}
@Article{Orszag71,
Title = {Accurate solution of the {O}rr-{S}ommerfeld stability equation},
Author = {Steven A.\ Orszag},
Journal = {J. Fluid Mech.},
Year = {1971},
Pages = {689--703},
Volume = {50}
}
@Article{OsSchn62,
Title = {Some theorems on the inertia of general matrices},
Author = {A. Ostrowski and H. Schneider},
Journal = {J. Math. Anal. Appl.},
Year = {1962},
Pages = {72--84},
Volume = {4}
}
@Article{ostruszka01,
Title = {Spectrum of the {Frobenius-Perron} operator for systems with stochastic perturbation},
Author = {A. Ostruszka and K. Zyczkowski},
Journal = {Phys. Lett. A},
Year = {2001},
Note = {\arXiv{nlin/0106003}},
Pages = {306},
Volume = {289}
}
@Book{ottbook,
Title = {Chaos and Dynamical Systems},
Author = {E. Ott},
Publisher = {Cambridge Univ. Pres},
Year = {2002}
}
@Article{Ozorio,
author = {Ozorio de Almeida, A. M. and Hannay, J. H.},
title = {Resonant periodic orbits and the semiclassical energy spectrum},
journal = {J. Phys. A},
year = {1987},
volume = {20},
pages = {5873},
doi = {10.1088/0305-4470/20/17/021},
}
@Article{PaCrFaSh80,
Title = {Geometry from a Time Series},
Author = {Packard, N. H. and Crutchfield, J. P. and Farmer, J. D. and Shaw, R. S.},
Journal = {Phys. Rev. Lett.},
Year = {1980},
Pages = {712--716},
Volume = {45}
}
@Article{Paul05,
Title = {Models of stochastic gene expression},
Author = {Paulsson, J.},
Journal = {Phys. Life Rev.},
Year = {2005},
Pages = {157--175},
Volume = {2}
}
@Article{Pauls04,
Title = {Summing up noise in gene expression},
Author = {Paulsson, J.},
Journal = {Nature},
Year = {2004},
Pages = {415--418},
Volume = {427}
}
@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.}
}
@Article{Penzl98,
Title = {Numerical solution of generalized {Lyapunov} equations},
Author = {Penzl, T.},
Journal = {Advances in Comp. Math.},
Year = {1998},
Pages = {33--48},
Volume = {8}
}
@Article{PePaVr08,
Title = {Stochastic optimization for detecting periodic orbits of nonlinear mappings},
Author = {Petalas, Y. G. and Parsopoulos, K. E. and Vrahatis, M. N.},
Journal = {Nonlin. Phenom. Complex Sys.},
Year = {2008},
Pages = {285 -- 291},
Volume = {11}
}
@Article{percgl,
Title = {Exact periodic solutions of the complex {G}inzburg-{L}andau equation},
Author = {A. V. Porubov and M. G. Velarde},
Journal = {J. Math. Phys.},
Year = {1999},
Pages = {884},
Volume = {40}
}
@Book{perg,
Title = {An Introduction to Ergodic Theory},
Author = {P. Walters},
Publisher = {Springer},
Year = {1981},
Address = {New York}
}
@Book{perkob,
Title = {Differential Equations and Dynamical Systems},
Author = {L. Perko},
Publisher = {Springer},
Year = {1991},
Address = {New York}
}
@Article{Petermann79,
Title = {Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding},
Author = {Petermann, K.},
Journal = {IEEE J. Quantum Electron.},
Year = {1979},
Pages = {566--570},
Volume = {15}
}
@Article{pexp,
Title = {Periodic orbit expansions for classical smooth flows},
Author = {P. Cvitanovi\'{c} and B. Eckhardt},
Journal = {J. Phys. A},
Year = {1991},
Pages = {L237},
Volume = {24}
}
@Book{Peyret02,
Title = {Spectral Methods for Incompressible Flows},
Author = {R. Peyret},
Publisher = {Springer},
Year = {2002},
Addr = {New York}
}
@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 = {Fitzgerald, Richard},
Journal = {Physics Today},
Year = {2004},
Number = {2},
Pages = {21--23},
Volume = {57}
}
@Article{PhysWorld04,
Title = {Turbulent transition for fluids},
Author = {Barenghi, Carlo},
Journal = {Physics World},
Year = {2004},
Number = {12},
Volume = {17}
}
@Article{pimsimp,
Title = {The {PIM}-simplex method: an extension of the {PIM}-triple method to saddles with an arbitrary number of expanding directions},
Author = {P. Moresco and S. P. Dawson},
Journal = {Physica},
Year = {1999},
Pages = {38},
Volume = {126D},
Abstract = {They generilized 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.}
}
@Article{pimstag,
Title = {Stagger-and-step method: {Detecting} and computing chaotic saddles in higher dimensions},
Author = {D. Sweet and H. E. Nusse. and J. A. Yorke},
Journal = {Phys. Rev. Lett.},
Year = {2001},
Pages = {2261},
Volume = {86},
Abstract = {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.}
}
@Article{pimyk,
Title = {A procedure for finding numerical trajectories on chaotic saddles},
Author = {H. E. Nusse and J. A. York},
Journal = {Physica},
Year = {1989},
Pages = {137},
Volume = {36D},
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{Plume_Lef1,
Title = {From template analysis to generating partitions {I}: {Periodic} orbits, knots and symbolic encodings},
Author = {Plumecoq, J. and Lefranc, M.},
Journal = {Physica D},
Year = {2000},
Pages = {231},
Volume = {144}
}
@Article{Plume_Lef2,
Title = {From template analysis to generating partitions {II}: {Characterization} of the symbolic encodings},
Author = {Plumecoq, J. and Lefranc, M.},
Journal = {Physica D},
Year = {2000},
Pages = {259},
Volume = {144}
}
@Book{poincare,
Title = {Les M\'ethodes Nouvelles de la M\'echanique C\'eleste},
Author = {H. Poincar\'e},
Publisher = {Guthier-Villars},
Year = {1899},
Address = {Paris},
Note = {For a very readable exposition of Poincar\'e's work and the development of the dynamical systems theory up to 1920's see \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{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{Pontr62,
Title = {{Mathematical Theory of Optimal Processes}},
Author = {Pontryagin, L. S. and V. Boltyanskii and R. Gamkrelidge and E. Mishenko},
Publisher = {Interscience},
Year = {1962},
Address = {New York}
}
@Book{popebook,
Title = {Turbulent Flows},
Author = {Stephen B.\ Pope},
Publisher = {Cambridge Univ. Press},
Year = {2000},
Address = {Cambridge, UK}
}
@Article{postgal89,
Title = {Postprocessing the {G}\"{a}lerkin method: a novel approach to approximate inertial manifolds},
Author = {B. Garc\'{i}a-Archilla and J. Novo and E. S. Titi},
Journal = {SIAM J. Numer. Anal.},
Year = {1998},
Pages = {941--972},
Volume = {35},
Abstract = {{G}\"{a}lerkin method}
}
@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. of Math. (2)},
Year = {1983},
Pages = {573--591},
Volume = {118}
}
@Article{PolVyt16,
author = {M. Pollicott and P. Vytnova},
title = {Linear response and periodic points},
journal = {Nonlinearity},
year = {2016},
volume = {29},
pages = {3047--3066},
doi = {10.1088/0951-7715/29/10/3047},
}
@Article{pre88top,
Title = {Topological and metric properties of {H\'{e}non}-type strange attractors},
Author = {P. Cvitanovi\'{c} and G. H. Gunaratne and I. Procaccia},
Journal = {Phys. Rev. A},
Year = {1988},
Pages = {1503},
Volume = {38}
}
@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{ProvVall80,
Title = {Riemannian structure on manifolds of quantum states},
Author = {Provost, J.P. and Vallee, G.},
Journal = {Commun. Math. Phys.},
Year = {1980},
Pages = {289--301},
Volume = {76},
DOI = {10.1007/BF02193559}
}
@Article{PrPr09,
Title = {The {Lyapunov} operator equation for the exponential dichotomy of one-parameter semigroups},
Author = {C. Preda and P. Preda},
Journal = {Systems \& Control Lett.},
Year = {2009},
Pages = {259--262},
Volume = {58}
}
@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/0006011}},
Pages = {2119},
Volume = {62}
}
@Article{pugh67cl,
Title = {An improved closing lemma and a general density theorem},
Author = {C. Pugh},
Journal = {Amer. J. Math.},
Year = {1967},
Volume = {89}
}
@Article{PyRuTy12,
Title = {Stochastic semigroups and their applications to biological models},
Author = {Pich{\'o}r, K. and Rudnicki, R. and Tyran-Kami{\'n}ska, M.},
Journal = {Demonstratio Math},
Year = {2012},
Pages = {463--494},
Volume = {45}
}
@Article{QF_dyntun,
Title = {Dynamical tunneling-assisted coupling of high-Q deformed microcavities using a free-space beam},
Author = {Yang, Q. F. and Jiang, X. F. and Cui, Y. L. and Shao, L. B. and Xiao, Y. F.},
Journal = {Phys. Rev. A},
Year = {2013},
Volume = {88},
DOI = {10.1103/PhysRevA.88.023810}
}
@Article{Qmaps,
Title = {Quantum Maps},
Author = {M.V. Berry and N.L. Balazs and M. Tabor and A. Voros},
Journal = {Ann. Physics},
Year = {1979},
Pages = {26},
Volume = {122}
}
@Article{QuAb09,
Title = {State and parameter estimation using {Monte Carlo} evaluation of path integrals},
Author = {Quinn, J. C. and Abarbanel, H. D. I.},
Journal = {Quart. J. Royal Meteor. Soc.},
Year = {2009},
Note = {\arXiv{0912.1581}},
Pages = {19},
Volume = {136},
Abstract = {Transferring information from observations of a dynamical system to estimate
the fixed parameters and unobserved states of a system model can be formulated
as the evaluation of a discrete time path integral in model state space. The
observations serve as a guiding potential working with the dynamical rules of
the model to direct system orbits in state space. The path integral
representation permits direct numerical evaluation of the conditional mean path
through the state space as well as conditional moments about this mean.}
}
@Article{R1883,
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},
Author = {Reynolds, O.},
Journal = {Proc. Roy. Soc. Lond. Ser A},
Year = {1883},
Pages = {935--982},
Volume = {174}
}
@Article{R1894,
Title = {On the dynamical theory of incompressible viscous flows and the determination of the criterion},
Author = {Reynolds, Osborne},
Journal = {Proc. Roy. Soc. Lond. Ser A},
Year = {1894},
Pages = {123--161},
Volume = {186}
}
@Article{Re08,
Title = {A path integral method for data assimilation},
Author = {Restrepo, J. M.},
Journal = {Physica D},
Year = {2008},
Pages = {14--27},
Volume = {237}
}
@Article{RechWhi91,
Title = {Symbolic Kinetic-Equation for a Chaotic Attractor},
Author = {A. B. Rechester and R. B. White },
Journal = {Phys. Lett. A},
Year = {1991},
Pages = {419--424},
Volume = {156}
}
@Article{RechWhi91maps,
Title = {Symbolic Kinetic Analysis of Two-Dimensional Maps},
Author = {A. B. Rechester and R. B. White },
Journal = {Phys. Lett. A},
Year = {1991},
Pages = {51--56},
Volume = {158}
}
@Article{Reick_lr,
author = {Reick, C. H.},
title = {Linear response of the {Lorenz} system},
journal = {Phys. Rev. E},
year = {2002},
volume = {66},
pages = {036103},
doi = {10.1103/physreve.66.036103},
}
@Article{reimann1,
Title = {Noisy one-dimensional maps near a crisis 1: Weak {Gauss}ian white and colored noise},
Author = {P. Reimann},
Journal = {J. Stat. Phys.},
Year = {1996},
Pages = {1467--1501},
Volume = {82}
}
@Article{reimann2,
Title = {Noisy one-dimensional maps near a crisis 2: General uncorrelated weak noise},
Author = {P. Reimann},
Journal = {J. Stat. Phys.},
Year = {1996},
Pages = {403--425},
Volume = {85}
}
@Article{ReiTal99,
Title = {Invariant densities for noisy maps},
Author = {Reimann, P. and Talkner, P.},
Journal = {Phys. Rev. A},
Year = {1991},
Pages = {6348--6363},
Volume = {44},
DOI = {10.1103/PhysRevA.44.6348}
}
@Article{Ren57,
Title = {Representation for real numbers and their ergodic propoerties},
Author = {A. R\'nyi},
Journal = {Acta Math. Acad. Sci. Hungar.},
Year = {1957},
Pages = {477--493},
Volume = {8}
}
@Article{ReOtt96,
Title = {Quasi-two-dimensional fast kinematic dynamo instabilities of chaotic fluid flows},
Author = {Reyl, C. and Antonsen, T.M. and Ott, E.},
Journal = {Phys. Plasmas},
Year = {1996},
Pages = {2564},
Volume = {3}
}
@Article{Risken72,
Title = {Solutions of the {Fokker-Planck} equations in detailed balance},
Author = {H. Risken},
Journal = {Z. Physik},
Year = {1972},
Pages = {251},
Volume = {231}
}
@Book{Risken96,
Title = {The {Fokker-Planck} Equation},
Author = {H. Risken},
Publisher = {Springer},
Year = {1996},
Address = {New York},
ISBN = {978-3-540-61530-9}
}
@Misc{RMChaosHist,
Author = {R. Mainieri and P. Cvitanovi\'c},
Note = {Appendix {\em ``A brief history of chaos''}, in \refref{DasBuch}},
Year = {2012}
}
@Article{Robinson91,
Title = {Coherent motions in the turbulent boundary layer},
Author = {Robinson, S. K.},
Journal = {Ann. Rev. Fluid Mech.},
Year = {1991},
Pages = {601--639},
Volume = {23}
}
@Article{Romanov73,
Title = {Stability of plane-parallel {C}ouette flow},
Author = {Romanov, V.A.},
Journal = {Functional Anal.\ \& its Applic.},
Year = {1973},
Pages = {137--146},
Volume = {7}
}
@Article{Rome69,
Title = {A direct solution to the linear variance equation of a time-invariant linear system},
Author = {Rome, H.},
Journal = {IEEE Transactions on Automatic Control},
Year = {1969},
Pages = {592--593},
Volume = {14}
}
@Article{RoMeBaSchHe09,
Title = {Spectral analysis of nonlinear flows},
Author = {Rowley, C. W. and Mezi\'c, I. and Bagheri, S. and Schlatter, P. and Henningson, D. S.},
Journal = {J. Fluid Mech.},
Year = {2009},
Pages = {115},
Volume = {641}
}
@Article{Ronc95,
Title = {Small-fluctuation expansion of the transition probability for a diffusion process},
Author = {M. Roncadelli},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {4661},
Volume = {52},
DOI = {10.1103/PhysRevE.52.4661}
}
@Article{ross,
Title = {An equation for continuous chaos},
Author = {O. E. R\"{o}ssler},
Journal = {Phys. Lett. A},
Year = {1976},
Pages = {397},
Volume = {57}
}
@Article{roth99,
Title = {Persistent patterns in transient chaotic fluid mixing},
Author = {D. Rothstein and E. Henry and J. P. Gollub},
Journal = {Nature},
Year = {1999},
Pages = {770--772},
Volume = {401},
Abstract = {Experimentally generate a 2-d periodic(or weakly turbulent)
velocity field using glycerol-water on magnets driven by electric current.
Persistent spatial patterns are observed, which decays exponentially.}
}
@Article{rowley_reduction_2003,
Title = {Reduction and reconstruction for self-similar dynamical systems},
Author = {Rowley, C. W. and Kevrekidis, I. G. and Marsden, J. E. and Lust, K.},
Journal = {Nonlinearity},
Year = {2003},
Pages = {1257--1275},
Volume = {16}
}
@Article{Rowley05,
Title = {Model reduction for fluids using balanced proper orthogonal decomposition},
Author = {C. W. Rowley},
Journal = {Int. J. Bifur. Chaos},
Year = {2005},
Pages = {997--1013},
Volume = {15}
}
@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},
Address = {Philadelphia},
Publisher = {SIAM}
}
@Article{RSBH98,
Title = {On stability of streamwise streaks and transition thresholds in plane channel flows},
Author = {Reddy, S. C. and Schmid, P. J. and Baggett, J. S. and Henningson, D. S. },
Journal = {J. Fluid Mech.},
Year = {1998},
Pages = {269--303},
Volume = {365}
}
@Book{rtb,
Title = {Theory of Orbits},
Author = {V. Szebehely},
Publisher = {Academic},
Year = {1967},
Address = {New York}
}
@Article{rue04ne,
Title = {Conversations on nonequilibrium physics with an extraterrestrial},
Author = {D. Ruelle},
Journal = {Physics Today},
Year = {2004},
Pages = {48--53},
Volume = {57},
Abstract = {New ideas of nonequilibrium physics are introduced. Emphasize
the SRB measure approach and energy fluctuation theorem.}
}
@Article{ruell68,
author = {D. Ruelle},
title = {Statistical mechanics of a one-dimensional lattice gas},
journal = {Commun. Math. Phys.},
year = {1968},
volume = {9},
pages = {267--278},
doi = {10.1007/BF01654281},
}
@Article{ruelext,
Title = {Large volume limit of the distribution of characteristic exponents in turbulence},
Author = {D. Ruelle},
Journal = {Commun. Math. Phys.},
Year = {1982},
Pages = {287--302},
Volume = {87}
}
@Article{ruell71,
Title = {On the nature of turbulence},
Author = {D. Ruelle and F. Takens},
Journal = {Commun. Math. Phys.},
Year = {1971},
Pages = {167},
Volume = {20}
}
@Book{ruelle,
Title = {Statistical Mechanics, Thermodynamic Formalism},
Author = {D. Ruelle},
Publisher = {Addison-Wesley},
Year = {1978},
Address = {Reading, MA}
}
@Article{Ruelle09,
author = {D. Ruelle},
title = {A review of linear response theory for general differentiable dynamical systems},
journal = {Nonlinearity},
year = {2009},
volume = {22},
pages = {855--870},
doi = {10.1088/0951-7715/22/4/009},
}
@Article{Ruelle76,
Title = {Zeta functions for expanding maps and {Anosov} flows},
Author = {D. Ruelle},
Journal = {Invent. Math.},
Year = {1976},
Pages = {231},
Volume = {34},
DOI = {10.1007/BF01403069}
}
@Article{Ruelle76b,
Title = {A measure associated with {Axiom-A} attractors},
Author = {Ruelle, D.},
Journal = {Amer. J. Math.},
Year = {1976},
Pages = {619--654},
Volume = {98},
Abstract = {The future orbits of a diffeomorphism near an Axiom-A
attractor are investigated. It is found that their asymptotic
behavior is in general described by a fixed probability measure �
carried by the attactor. The measure has an exponential cluster
property, and satisfies a variational principle.}
}
@Article{ruelle79,
Title = {Ergodic theory of differentiable dynamical systems},
Author = {D. Ruelle},
Journal = {Publ. Math. IHES},
Year = {1979},
Pages = {275},
Volume = {50}
}
@Article{Ruelle80,
Title = {Measures describing a turbulent flow},
Author = {Ruelle, D.},
Journal = {Ann. N. Y. Acad. Sci.},
Year = {1980},
Pages = {1--9},
Volume = {357},
DOI = {10.1111/j.1749-6632.1980.tb29669.x}
}
@Article{ruelle86,
Title = {Resonances of chaotic dynamical systems},
Author = {D. Ruelle},
Journal = {Phys. Rev. Lett.},
Year = {1986},
Pages = {405},
Volume = {56},
Abstract = {We present analytic properties of the power spectrum for
a class of chaotic dynamical systems (Axiom-A systems). The power spectrum
is meromorphic in a strip; the position of the poles (resonances) depends
on the system considered, but only their residues depend on
the observable monitored. In relation with these results we also discuss
the exponential or nonexponential decay of correlation functions at infinity.
In conclusion, it appears desirable to analyze the decay of correlation functions
and the possible analyticity of power spectra for physical time evolutions,
and for computer generated simple dynamical systems (non-Axiom-A in general).}
}
@Article{Ruelle97,
Title = {Differentiation of {SRB} states},
Author = {D. Ruelle},
Journal = {Commun. Math. Phys.},
Year = {1997},
Pages = {227},
Volume = {187}
}
@Article{Ruelle98,
Title = {Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics},
Author = {D. Ruelle},
Journal = {J. Stat. Phys.},
Year = {1999},
Note = {\arXiv{chao-dyn/9812032}},
Pages = {393--468},
Volume = {95}
}
@Article{Ruelle98a,
Title = {Nonequilibrium statistical mechanics near equilibrium: {Computing} higher order terms},
Author = {D. Ruelle},
Journal = {Nonlinearity},
Year = {1998},
Note = {\arXiv{arXiv.org:0901.0484}},
Pages = {5--18},
Volume = {11}
}
@Misc{SaGoGh11,
Title = {Two novel costs for determining the tuning parameters of the {Kalman} filter},
Author = {{Saha}, M. and {Goswami}, B. and {Ghosh}, R.},
Note = {\arXiv{1110.3895}},
Year = {2011}
}
@Article{SaitoMatsu,
author = {N. Saito and Y. Matsunaga},
title = {Linear response theory formulated from the chaotic dynamics},
journal = {J. Phys. Soc. Japan},
year = {1989},
volume = {58},
pages = {3089--3105},
doi = {10.1143/jpsj.58.3089},
}
@Article{SaiYam98,
Title = {Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems},
Author = {Y. Saiki and M. Yamada},
Journal = {Nonlin. Proc. Geophys.},
Year = {2008},
Pages = {675--680},
Volume = {15},
DOI = {10.5194/npg-15-675-2008}
}
@Article{saka90br,
Title = {Breakdown of the phase dynamics},
Author = {H. Sakaguchi},
Journal = {Prog. Theor. Phys.},
Year = {1990},
Pages = {792--800},
Volume = {84}
}
@Book{sakurai,
Title = {Modern Quantum Mechanics},
Author = {J. J. Sakurai},
Publisher = {Addison-Wesley-Longman},
Year = {1994},
Address = {Reading, Mass.}
}
@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. A},
Year = {2013},
Volume = {469},
Abstract = {We examine the geometry of the finite-dimensional
attractor associated with fluid flows described by
Navier-Stokes equations and relate its nonlinear
dimensionality to energy exchanges between dynamical components (modes)
of the flow. Specifically, we use a stochastic framework based on the
dynamically orthogonal equations to perform efficient order-reduction and
describe the stochastic attractor in the reduced-order phase space in
terms of the associated probability measure. We introduce the notion of
local fractal dimensionality to describe the geometry of the attractor
and we establish a connection with the number of positive finite-time
Lyapunov exponents. Subsequently, we illustrate in specific fluid flows
that the low dimensionality of the stochastic attractor is caused by the
synergistic activity of linearly unstable and stable modes as well as the
action of the quadratic terms. In particular, we illustrate the
connection of the low-dimensionality of the attractor with the
circulation of energy: (i) from the mean flow to the unstable modes (due
to their linearly unstable character), (ii) from the unstable modes to
the stable ones (due to a nonlinear energy transfer mechanism) and (iii)
from the stable modes back to the mean (due to the linearly stable
character of these modes).},
DOI = {10.1098/rspa.2012.0550}
}
@Article{SCD07,
Title = {On the state space geometry of the {Kuramoto-Sivashinsky} flow in a periodic domain},
Author = {Cvitanovi{\'c}, P. and Davidchack, R. L. and Siminos, E.},
Journal = {SIAM J. Appl. Dyn. Syst.},
Year = {2010},
Note = {\arXiv{0709.2944}},
Pages = {1--33},
Volume = {9}
}
@Article{SchomTwor,
Title = {Quantum-to-Classical Crossover of Quasibound States in Open Quantum Systems},
Author = {H. Schomerus and J. Tworzydlo},
Journal = {Phys. Rev. Lett},
Year = {2004},
Pages = {154102},
Volume = {93},
DOI = {10.1103/PhysRevLett.93.154102}
}
@Article{science04,
Title = {Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow},
Author = {Hof, B. and van Doorne, C. W. H. and Westerweel, J. and Nieuwstadt, F. T. M. and Faisst, H. and Eckhardt, B. and Wedin, H. and Kerswell, R. R. and Waleffe, F.},
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.
},
Eprint = {http://www.sciencemag.org/cgi/reprint/305/5690/1594.pdf},
URL = {http://www.sciencemag.org/cgi/content/abstract/305/5690/1594}
}
@Article{SCYYA12,
Title = {Relation of a new interpretation of stochastic differential equations to {Ito} process},
Author = {Shi, J. and Chen, T. and Yuan, R. and Yuan, B. and Ao, P.},
Journal = {J. Stat. Phys.},
Year = {2012},
Pages = {579--590},
Volume = {148},
DOI = {10.1007/s10955-012-0532-8},
Keywords = {Stochastic differential equation; Boltzmann-Gibbs distribution; Fokker-Planck equation; Potential function}
}
@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 {C}ouette flow},
Author = {Schmiegel, A. and Eckhardt, B.},
Journal = {Europhys.\ Lett.},
Year = {2000},
Pages = {395--400},
Volume = {51}
}
@Article{SeToHe92,
Title = {Semiclassical propagation - how long can it last},
Author = {M. A. Sepulveda and S. Tomsovic and Heller, E. J. },
Journal = {Phys. Rev. Lett.},
Year = {1992},
Pages = {402--405},
Volume = {69}
}
@Article{ShaTah12,
Title = {Optimal sensor and actuator location for unstable systems},
Author = {Shaker, H. R. and Tahavori, M.},
Journal = {J. Vibration and Control},
Year = {2012},
Abstract = {... In industrial practice it is often the case that the
system, which is to be controlled, is not stable. The method
proposed supports both stable and unstable systems.},
DOI = {10.1177/1077546312451302}
}
@Article{SHcgl90,
Title = {Pulses and fronts in the complex {G}inzburg-{L}andau equation near a subcritical bifurcation},
Author = {W. van Saarloos and P. C. Hohenberg},
Journal = {Phys. Rev. Lett.},
Year = {1990},
Pages = {749},
Volume = {64}
}
@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,
Title = {Fronts, pulses, sources and sinks in generalized complex {G}inzburg-{L}andau equations},
Author = {W. van Saarloos and P. C. Hohenberg},
Journal = {Physica D},
Year = {1992},
Pages = {303--367},
Volume = {56},
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.}
}
@Article{ShiFreMan08,
Title = {Can we make a robot ballerina perform a pirouette? {Orbital} stabilization of periodic motions of underactuated mechanical systems},
Author = {A.S. Shiriaev and L.B. Freidovich and I.R. Manchester},
Journal = {Ann. Rev. Control},
Year = {2008},
Pages = {200--211},
Volume = {32},
Abstract = {This paper provides an introduction to several problems
and techniques related to controlling periodic motions of dynamical
systems. In particular, we consider planning periodic motions and
designing feedback controllers for orbital stabilization. We review
classical and recent design methods based on the Poincare
first-return map and the transverse linearization. We begin with
general nonlinear systems and then specialize to a class of
underactuated mechanical systems for which a particularly rich
structure allows many of the problems to be solved analytically.},
DOI = {10.1016/j.arcontrol.2008.07.001}
}
@Article{Shim1,
Title = {Perturbation theory analysis of chaos {I}.},
Author = {Shimizu, T.},
Journal = {Physica A},
Year = {1987},
Pages = {75--102},
Volume = {142}
}
@Article{Shim2,
Title = {Perturbation theory analysis of chaos {II}.},
Author = {Shimizu, T.},
Journal = {Physica A},
Year = {1987},
Pages = {341--360},
Volume = {145}
}
@Article{Shim3,
Title = {Perturbation theory analysis of chaos {III}.},
Author = {Shimizu, T.},
Journal = {Physica A},
Year = {1991},
Pages = {101--122},
Volume = {178}
}
@Article{ShiNag79,
Title = {A numerical approach to ergodic problem of dissipative dynamical systems},
Author = {Shimada, I. and Nagashima, T.},
Journal = {Prog. Theor. Phys.},
Year = {1979},
Pages = {1605--1615},
Volume = {61},
DOI = {10.1143/PTP.61.1605}
}
@Article{Shraiman81,
Title = {Scaling theory for noisy period-doubling transitions to chaos},
Author = {B. Shraiman and C. E. Wayne and P. C. Martin},
Journal = {Phys. Rev. Lett.},
Year = {1981},
Pages = {935--939},
Volume = {46},
DOI = {10.1103/PhysRevLett.46.935}
}
@Article{SiCvi10,
Title = {Continuous symmetry reduction and return maps for high-dimensional flows},
Author = {Siminos, E. and Cvitanovi{\'c}, P.},
Journal = {Physica D},
Year = {2011},
Pages = {187--198},
Volume = {240},
DOI = {10.1016/j.physd.2010.07.01}
}
@Article{SiebRich,
Title = {Correlations between periodic orbits and their r�le in spectral statistics},
Author = {M. Sieber and K. Richter},
Journal = {Phys. Scr.},
Year = {2001},
Pages = {128--133},
Volume = {T90}
}
@Article{siegel42,
Title = {Iteration of analytic functions},
Author = {C. L. Siegel},
Journal = {Ann. Math.},
Year = {1942},
Pages = {607--612},
Volume = {43}
}
@Article{sinai,
Title = {Gibbs measures in ergodic theory},
Author = {Ya. G. Sinai},
Journal = {Russian Math. Surveys},
Year = {1972},
Pages = {21},
Volume = {27},
DOI = {10.1070/RM1972v027n04ABEH001383}
}
@Book{sinai76,
Title = {Introduction to Ergodic Theory},
Author = {Ya. G. Sinai},
Publisher = {Princeton Univ. Press},
Year = {1976},
Address = {Princeton}
}
@Article{sirovcgl90,
Title = {Low-dimensional dynamics for the complex {G}inzburg-{L}andau equation},
Author = {J. D. Rodriguez and L. Sirovich},
Journal = {Physica D},
Year = {1990},
Pages = {77--86},
Volume = {43}
}
@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 Astr.},
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 = {Prog. Theor. Phys. Suppl.},
Year = {1980},
Pages = {2112},
Volume = {66}
}
@Article{Sjo97,
Title = {Operators associated with the {Hermite} semigroup - a survey},
Author = {Sj\"ogren, P.},
Journal = {J. Fourier Anal. Appl.},
Year = {1997},
Pages = {813--823},
Volume = {3}
}
@Article{Skazka05,
Title = {On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. {II. Differential} equations},
Author = {V. V. Skazka},
Journal = {Siberian Math. J.},
Year = {2005},
Pages = {935--947},
Volume = {46}
}
@Article{Skazka96,
Title = {On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. {I. Solvability} of the {Lyapunov} equation},
Author = {V. V. Skazka},
Journal = {Siberian Math. J.},
Year = {1996},
Pages = {573--590},
Volume = {37}
}
@Article{skeleton,
Title = {Periodic Orbits as the skeleton of classical and quantum chaos},
Author = {P. Cvitanovi\'{c}},
Journal = {Physica D},
Year = {1991},
Pages = {138},
Volume = {51}
}
@Article{slg93,
Title = {Application of {Bogomolny} transfer operator to semiclassical quantization of a chaotic system},
Author = {T. Szeredi and J. H. Lefebvre and D. A. Goodings },
Journal = {Phys. Rev. Lett.},
Year = {1993},
Pages = {2891--2894},
Volume = {71}
}
@Article{smale,
Title = {Differentiable dynamical systems},
Author = {S. Smale},
Journal = {Bull. Amer. Math. Soc.},
Year = {1967},
Pages = {747--817},
Volume = {73}
}
@Article{SMcgl02,
Title = {Stable and chaotic solutions of the complex {G}inzburg-{L}andau equation with periodic boundary conditions},
Author = {J. Scheuer and B. A. Malomed},
Journal = {Physica D},
Year = {2002},
Pages = {102--115},
Volume = {161},
Abstrac = {The behavior of the solutions of the CGLe without diffusion is studied with a periodic boundary condition.}
}
@Article{SmiKap09,
Title = {Method to modify {Random Matrix Theory} using short-time behavior in chaotic systems},
Author = {Smith, A. M. and Kaplan, L.},
Journal = {Phys. Rev. E},
Year = {2009},
Note = {\arXiv{0907.5037}},
Pages = {035205(R)},
Volume = {80}
}
@Article{SmiKap10,
Title = {Integrating {Random Matrix Theory} predictions with short-time dynamical effects in chaotic systems},
Author = {Smith, A. M. and Kaplan, L.},
Journal = {Phys. Rev. E},
Year = {2010},
Note = {\arXiv{1006.5733}},
Pages = {016214},
Volume = {82}
}
@Inproceedings{SoCoCv16,
author = {Solla, S. A. and Cohen, Y. and Cvitanovi{\'c}, P.},
title = {Learning in a noisy environment: {A Lyapunov} equation approach},
booktitle = {APS Meeting Abstracts},
year = {2016},
url = {http://meetings.aps.org/Meeting/MAR16/Event/263385},
}
@Article{SongCao,
Title = {Channeling chaotic rays into waveguides for efficient collection of microcavity emission},
Author = {Song, Q. H. and Ge, L. and Redding, B. and Cao, H.},
Journal = {Phys. Rev. Lett.},
Year = {2012},
Volume = {108},
Abstract = {We demonstrate a robust and generic mechanism, which we
term "chaos-assisted channeling," to achieve unidirectional output
from wave-chaotic microcavities with long-lived resonances. It
utilizes the coexistence of regular and chaotic ray dynamics in most
deformed microcavities. Long-lived resonances are formed by total
internal reflection on classical periodic orbits, and their leakage
into the chaotic region of the phase space is efficiently channeled
into an attached waveguide without additional loss. We explain this
behavior using a ray dynamics analysis which is confirmed via
numerical simulations and experimental demonstration.},
DOI = {10.1103/PhysRevLett.108.243902}
}
@Article{Spalart91,
Title = {Spectral Methods for the {N}avier-{S}tokes Equations with One Infinite and Two Periodic Directions},
Author = {P.R. Spalart and R.D. Moser and M.M. Rogers},
Journal = {J. Comput. Physics},
Year = {1990},
Pages = {297--324},
Volume = {96}
}
@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.}
}
@Article{spercgl,
Title = {Small-amplitude periodic and chaotic solutions of the complex {G}inzburg-{L}andau 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},
Author = {N. M. Temme},
Publisher = {Wiley},
Year = {1996},
Address = {New York}
}
@Article{SPScgl92,
Title = {Spatiotemporal chaos in the one-dimensional complex {G}inzburg-{L}andau 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{SrHe92,
Title = {Physical and numerical experiments on the wave mechanics of classically chaotic systems},
Author = {S. Sridhar and Heller, E. J. },
Journal = {Phys. Rev. A},
Year = {1992},
Pages = {1728--1731},
Volume = {46}
}
@Article{stabpcgl,
Title = {Stability of plane wave solutions of complex {G}inzburg-{L}andau equations},
Author = {B. J. Matkowsky and V. Volpert},
Journal = {Quart. Appl. Math.},
Year = {1993},
Pages = {265--281},
Volume = {LI}
}
@Article{StanTas11,
Title = {Computing generalized inverses using {LU} factorization of matrix product},
Author = {P. S. Stanimirovi\'c and M. B. Tasi\'c},
Journal = {International Journal of Computer Mathematics},
Year = {2008},
Number = {12},
Pages = {1865-1878},
Volume = {85},
DOI = {10.1080/00207160701582077}
}
@Article{sten94sol,
Title = {Solitary surface-wave deformation of a plasma boundary},
Author = {L. Stenflo and O. M. Gradov},
Journal = {Phys. Plasmas},
Year = {1994},
Pages = {2804},
Volume = {1},
Abstract = {A nonlinear equation of the plasma surface is derived for the
small deformation. Possible solitary solutions are discussed.}
}
@Article{sten98osc,
Title = {Plasma oscillons in spherically bounded magnetized plasmas},
Author = {L. Stenflo and M. Y. Yu},
Journal = {Phys. Plasmas},
Year = {1998},
Pages = {3122},
Volume = {5}
}
@Article{sternb57,
Title = {Local contractions and a theorem of {Poincar\'e}},
Author = {S. Sternberg},
Journal = {Amer. J. Math.},
Year = {1957},
Pages = {809-824},
Volume = {79},
DOI = {10.2307/2372437}
}
@Article{sternb58,
Title = {On the structure of local homeomorphisms of {Euclidean} n-space, {II}},
Author = {S. Sternberg},
Journal = {Amer. J. Math.},
Year = {1958},
Pages = {623--631},
Volume = {80},
DOI = {10.2307/2372774}
}
@Article{sternb59,
Title = {The structure of local homeomorphisms},
Author = {S. Sternberg},
Journal = {Amer. J. Math.},
Year = {1959},
Pages = {578},
Volume = {81},
DOI = {10.2307/2372915}
}
@Book{StGo09,
Title = {Mathematics for Physics: A Guided Tour for Graduate Students},
Author = {Stone, M. and Goldbart, P.},
Publisher = {Cambridge Univ. Press},
Year = {2009},
Address = {Cambridge}
}
@Article{StMeiss98,
Title = {Computing periodic orbits using the anti-integrable limit},
Author = {D. Sterling and J. D. Meiss},
Journal = {Phys. Lett. A},
Year = {1998},
Pages = {46--52},
Volume = {241},
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.}
}
@Book{stoeck,
Title = {Quantum Chaos: An Introduction},
Author = {H. J. St\"ockmann},
Publisher = {Cambridge Univ. Press},
Year = {1999},
Address = {Cambridge}
}
@Book{Stratonovich,
Title = {Conditional {Markov} Processes and Their Application to the Theory of Control},
Author = {R. L. Stratonovich},
Publisher = {Elsevier},
Year = {1968},
Address = {New York}
}
@Book{strogb,
Title = {Nonlinear Dynamics and Chaos},
Author = {S. H. Strogatz},
Publisher = {Perseus Publishing},
Year = {2000},
Address = {Cambridge, Mass.},
Series = {Studies in Nonlinearity}
}
@Book{StuOttWigg06,
Title = {The mathematical foundations of mixing: the linked twist map as a paradigm in applications: micro to macro, fluids to solids},
Author = {Sturman, Rob and Ottino, Julio M and Wiggins, Stephen},
Publisher = {Cambridge Univ. Pres},
Year = {2006},
Volume = {22}
}
@Article{Subbiah98,
Title = {Spectral decomposition of the tent map with varying height},
Author = {S. Subbiah and D. J. Driebe},
Journal = {Chaos},
Year = {1998},
Pages = {741--756},
Volume = {8},
Keywords = {nonlinear dynamics, tent map}
}
@Article{Suhl94,
Title = {Chaos and the {Kubo} formula},
Author = {Suhl, H.},
Journal = {Physica B},
Year = {1994},
Pages = {1--7},
Volume = {199/200}
}
@Article{SWG02,
Title = {Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows},
Author = {Stone, P.A. and Waleffe, F. and Graham, M.D.},
Journal = {Phys. Rev. Lett.},
Year = {2002},
Pages = {20831},
Volume = {89}
}
@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 = {Philosophical Magazine},
Year = {1852},
Pages = {138--142},
Volume = {4}
}
@Misc{symb_dyn,
Author = {P. Cvitanovi\'{c}},
Note = {Chapter {\em ``Charting the state space''}, in \refref{DasBuch}},
Year = {2012}
}
@Article{symmcgl,
Title = {Breaking the hidden symmetry in the {G}inzburg-{L}andau equation},
Author = {A. Doelman},
Journal = {Physica D},
Year = {1996},
Pages = {398--428},
Volume = {97}
}
@Article{tajima02,
Title = {Microextensive chaos of a spatially extended system},
Author = {S. Tajima and H. S. Greenside},
Journal = {Phys. Rev. E},
Year = {2002},
Pages = {017205},
Volume = {66}
}
@Article{Takada01,
Title = {Mathematical index and model in stabirometry},
Author = {Takada, H. AND Kitaoka, Y. AND Shimizua, Y.},
Journal = {Forma},
Year = {2001},
Pages = {17--46},
Volume = {16},
URL = {http://ci.nii.ac.jp/naid/10006657190/en/}
}
@Unpublished{Tan12,
Title = {A tentative method for computing probabilities of extremely rare outcomes of a stochastic process},
Author = {S. Tan},
Note = {Working notes},
Year = {2012}
}
@Article{Tanner_cars,
Title = {Discrete flow mapping: transport of phase space densities on triangulated surfaces},
Author = {Chappell, D. J. and Tanner, G. and L\"ochel, D. and S{\o}ndergaard, N. },
Journal = {Proc. R. Soc. A},
Year = {2013},
Pages = {20130153},
Volume = {469},
DOI = {10.1098/rspa.2013.0153}
}
@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{Taussky61,
Title = {A generalization of a theorem of {Lyapunov}},
Author = {Taussky, O.},
Journal = {J. SIAM},
Year = {1961},
Pages = {640--643},
Volume = {9}
}
@Article{tbohr,
Title = {The diversity of Steady state solutions of the complex {G}inzburg-{L}andau equation},
Author = {M. Bazhenov and T. Bohr and K. Gorshkov and M. Rabinovich},
Journal = {Phys. Lett. A},
Year = {1996},
Pages = {104},
Volume = {217}
}
@Book{TelGr06,
Title = {Chaotic Dynamics: An Introduction Based on Classical Mechanics},
Author = {T\'el, T. and Gruiz, M.},
Publisher = {Cambridge Univ. Pres},
Year = {2006},
Address = {Cambridge}
}
@Article{temam91edd,
Title = {Approximation of attractors, large eddy simulations and multiscale methods},
Author = {R. Temam},
Journal = {Proc. R. Soc. Lond. A},
Year = {1991},
Pages = {23--39},
Volume = {434},
Abstract = {Estimates on the dimension of the attractors and the decay rates of
Fourier mode of NSe are given. By approximation of the inertial manifold, the
interaction between the large and small eddies are derived. Such laws open the way to
numerically efficient algorithms via multiscale mthods.}
}
@Article{TFGphase97,
Title = {Studies of Phase Turbulence in the One Dimensional Complex {G}inzburg-{L}andau Equation},
Author = {A. Torcini and 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{Therapos89,
Title = {Balancing transformation for unstable nonminimal linear systems},
Author = {Therapos, C. P.},
Journal = {IEEE Trans. Automatic Control},
Year = {1989},
Pages = {455},
Volume = {34}
}
@Article{Thomas2014,
Title = {Self-sustaining turbulence in a restricted nonlinear model of plane {Couette} flow},
Author = {Thomas, V.L. and Lieu, B.K. and Jovanovi\'c, M.R. and Farrell, B.F. and Ioannou, P.J. and Gayme, D.F.},
Journal = {Phys. Fluids},
Year = {2014},
Volume = {26},
DOI = {10.1063/1.4898159}
}
@Article{TiCo01,
Title = {Adjoints and low-rank covariance representation},
Author = {M. K. Tippett and S. E. Cohn},
Journal = {Nonlinear Proc. Geoph.},
Year = {2001},
Pages = {331--340},
Volume = {8},
URL = {https://hal.archives-ouvertes.fr/hal-00302042}
}
@Article{ToHe93,
Title = {Long-time semiclassical dynamics of chaos --- the stadium billiard},
Author = {S. Tomsovic and Heller, E. J. },
Journal = {Phys. Rev. E},
Year = {1993},
Pages = {282 -- 299},
Volume = {47}
}
@Article{ToHe93a,
Title = {Semiclassical construction of chaotic eigenstates},
Author = {S. Tomsovic and Heller, E. J. },
Journal = {Phys. Rev. Lett.},
Year = {1993},
Pages = {1405--1408},
Volume = {70}
}
@Article{ToHe93b,
Title = {Postmodern quantum mechanics},
Author = {Heller, E. J. and S. Tomsovic },
Journal = {Physics Today},
Year = {1993},
Pages = {38--46},
Volume = {46}
}
@Article{Tomita74,
Title = {Irreversible circulation of fluctuation},
Author = {Tomita, K. and Tomita, H.},
Journal = {Prog. Theor. Phys.},
Year = {1974},
Pages = {1731--1749},
Volume = {51},
Abstract = {The notion of irreversible circulation of fluctuation around
the steady state, or cyclic balance, is proposed. In addition to the
shape of the probability distribution function this concept is necessary
in describing the behaviour of the thermodynamically coupled degrees of
freedom at off-equilibrium situation. When the circulation entails
instability, a macroscopic orbital revolution, i.e. limit cycle, may
appear, which is characteristic of a far from equilibrium situation.
Examples are mentioned, including chemical oscillations and undamped
spiking in lasers.},
DOI = {10.1143/PTP.51.1731}
}
@Article{tompaid96,
Title = {Numerical study of invariant sets of a quasi-periodic perturbation of a symplectic map},
Author = {S. Tompaidis},
Journal = {Experimental Mathematics},
Year = {1996},
Pages = {211--230},
Volume = {5},
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.}
}
@Article{torc96,
Title = {Order Parameter for the Transition from Phase to Amplitude Turbulence},
Author = {A. Torcini},
Journal = {Phys. Rev. Lett.},
Year = {1996},
Pages = {1047},
Volume = {77},
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.}
}
@Article{toricgl,
Title = {Invariant 2-tori in the time-dependent {G}inzburg-{L}andau equation},
Author = {P. Tak\'{a}\v{c}},
Journal = {Nonlinearity},
Year = {1992},
Pages = {289--321},
Volume = {5}
}
@Book{Townsend76,
Title = {The Structure of Turbulent Shear Flows, 2\textsuperscript{nd} Edn.},
Author = {Townsend, A.A.},
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}
}
@Book{Trefethen97,
Title = {Numerical Linear Algebra},
Author = {L. N. Trefethen and D. Bau},
Publisher = {SIAM},
Year = {1997},
Addr = {Philadelphia}
}
@Article{TrePan98,
Title = {Periodic orbits, {Lyapunov} vectors, and singular vectors in the {L}orenz system},
Author = {Trevisan, A. and Pancotti, F.},
Journal = {J. Atmos. Sci.},
Year = {1998},
Pages = {390},
Volume = {55},
Abstract = {A periodic orbit analysis in the Lorenz system
and the study of the properties of the associated tangent
linear equations are performed. A set of vectors are found
that satisfy the Oseledec (1968) theorem and reduce to
Floquet eigenvectors in the particular case of a periodic
orbit. These vectors, called Lyapunov vectors, can be
considered the generalization to aperiodic orbits of the
normal modes of the instability problem and are not
necessarily mutually orthogonal. The relation between
singular vectors and Lyapunov vectors is clarified. The
mechanism responsible for super-Lyapunov growth is shown to
be related to the nonorthogonality of Lyapunov vectors. The
leading Lyapunov vectors, as defined here, as well as the
asymptotic final singular vectors, are tangent to the
attractor, while the leading initial singular vectors, in
general, point away from it. Perturbations that are on the
attractor can be found in the subspace of the leading
Lyapunov vectors.}
}
@Book{Truesdell91,
Title = {A First Course in Rational Continuum Mechanics: {General} concepts},
Author = {Truesdell, C.},
Publisher = {Academic},
Year = {1991},
Address = {New York},
Volume = {1}
}
@Article{TTRD93,
Title = {Hydrodynamic stability without eigenvalues},
Author = {Trefethen, N. and Trefethen, A. E. and Reddy, S. C. and Driscoll, T. A.},
Journal = {Science},
Year = {1993},
Pages = {578--584},
Volume = {261}
}
@Article{TuckBar03,
Title = {Symmetry breaking and turbulence in perturbed plane {Couette} flow},
Author = {L. S. Tuckerman and D. Barkley},
Journal = {Theor. Comp. Fluid Dyn.},
Year = {2002},
Note = {\arXiv{physics/0312051}},
Pages = {91--97},
Volume = {16},
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.}
}
@Article{Uhlig73,
Title = {Simultaneous block diagonalization of two real symmetric matrices},
Author = {F. Uhlig},
Journal = {Linear Algebra Appl.},
Year = {1973},
Pages = {281--289},
Volume = {7},
Abstract = {The simultaneous diagonalization of two real symmetric
(r.s.) matrices has long been of interest. This subject is
generalized here to the following problem raised by Taussky-Tod: What
is the first simultaneous block diagonal structure of a nonsingular
pair of r.s. matrices S and T? If the number of blocks is maximal,
then one can speak of the finest simultaneous block diagonalization
of S and T.},
DOI = {10.1016/S0024-3795(73)80001-1}
}
@Book{Ulam60,
title = {{A Collection of Mathematical Problems}},
publisher = {Interscience},
year = {1960},
author = {Ulam, S. M.},
address = {New York},
}
@Article{umb94pat,
Title = {Transition to parametric wave patterns in a vertically oscillated granular layer},
Author = {F. Melo and P. Umbanhowar and H. L. Swinney},
Journal = {Phys. Rev. Lett.},
Year = {1994},
Pages = {172--175},
Volume = {72}
}
@Book{VanZeeLooney2002,
Title = {Cavity-enhanced Spectroscopies},
Author = {Van Zee, R.D. and Looney, J.P.},
Publisher = {Academic Press},
Year = {2002},
ISBN = {9780124759879},
Series = {Experimental methods in the physical sciences},
URL = {https://books.google.com/books?id=NQU8vTYJt1UC}
}
@InProceedings{Varga01,
Title = {On balancing and order reduction of unstable periodic systems},
Author = {Varga, A.},
Booktitle = {Periodic Control Systems 2001},
Year = {2001},
Address = {New York},
Editor = {S. Bittanti and P. Colaneri},
Organization = {IFAC Workshop},
Pages = {177--182},
Publisher = {Elsevier},
ISBN = {978-0-08-043682-1},
URL = {http://elib.dlr.de/22687/1/varga_como01p2.pdf}
}
@InProceedings{Varga05,
Title = {A periodic systems toolbox for {MATLAB}},
Author = {Varga, A},
Booktitle = {Proc. of IFAC Workshop on Periodic Control Systems},
Year = {2005},
Pages = {474--474},
Volume = {16}
}
@InProceedings{Varga11,
Title = {An overview of recent developments in computational methods for periodic system},
Author = {Varga, A.},
Booktitle = {Proc. of IFAC Workshop on Periodic Control Systems},
Year = {2011}
}
@Article{Varga97,
Title = {Periodic {Lyapunov} equations: {Some} applications and new algorithms},
Author = {Varga, A.},
Journal = {Int. J. Control},
Year = {1997},
Pages = {69--88},
Volume = {67},
DOI = {10.1080/002071797224360}
}
@InProceedings{VarVanD01,
Title = {Computational methods for periodic systems-an overview},
Author = {Varga, A. and Van Dooren, P.},
Booktitle = {Periodic Control Systems 2001},
Year = {2001},
Address = {New York},
Editor = {S. Bittanti and P. Colaneri},
Organization = {IFAC Workshop},
Pages = {171--176},
Publisher = {Elsevier},
ISBN = {978-0-08-043682-1},
URL = {http://elib.dlr.de/11743/1/varga_como01p1.pdf}
}
@Article{Vasi77,
Title = {An equilibrium characterization of the term structure},
Author = {Vasicek, O.},
Journal = {J. Financial Econ.},
Year = {1977},
Pages = {177--188},
Volume = {5},
Abstract = {The paper derives a general form of the term
structure of interest rates. The following assumptions are
made: (A.1) The instantaneous (spot) interest rate follows a
diffusion process; (A.2) the price of a discount bond depends
only on the spot rate over its term; and (A.3) the market is
efficient. Under these assumptions, it is shown by means of an
arbitrage argument that the expected rate of return on any bond
in excess of the spot rate is proportional to its standard
deviation. This property is then used to derive a partial
differential equation for bond prices. The solution to that
equation is given in the form of a stochastic integral
representation. An interpretation of the bond pricing formula
is provided. The model is illustrated on a specific case.}
}
@Misc{Vattay,
Author = {G. Vattay and P. Cvitanovi\'{c}},
Note = {Chapter {\em ``Noise''}, in \refref{DasBuch}},
Year = {2012}
}
@Article{VeQi10,
Title = {On the {Poincar{\'e}-Hill} cycle map of rotational random walk: locating the stochastic limit cycle in a reversible {Schnakenberg} model},
Author = {Vellela, M. and Qian, H.},
Journal = {Proc. Roy. Soc. Lond. Ser A},
Year = {2010},
Pages = {771--788},
Volume = {466},
Abstract = {Recent studies on stochastic oscillations mostly focus on
the power spectral analysis. However, the power spectrum yields
information only on the frequency of oscillation and cannot differentiate
between a stable limit cycle and a stable focus. The cycle flux,
introduced by Hill (Hill 1989 Free energy transduction and biochemical
cycle kinetics), is a quantitative measure of the net movement over a
closed path, but it is impractical to compute for all possible cycles in
systems with a large state space. Through simple examples, we introduce
concepts used to quantify stochastic oscillation, such as the cycle flux,
the Hill{\textendash}Qian stochastic circulation and rotation number. We
introduce a novel device, the Poincar{\'e}{\textendash}Hill cycle map
(PHCM), which combines the concept of Hill{\textquoteright}s cycle flux
with the Poincar{\'e} map from nonlinear dynamics. Applying the PHCM to a
reversible extension of an oscillatory chemical system, the Schnakenberg
model, reveals stable oscillations outside the Hopf bifurcation region in
which the deterministic system contains a limit cycle. Bistable behaviour
is found on the small volume scale with high probabilities around both
the fixed point and the limit cycle. Convergence to the deterministic
system is found in the thermodynamic~limit. },
DOI = {10.1098/rspa.2009.0346}
}
@Article{VerCar_scar,
Title = {Semiclassical construction of resonances with hyperbolic structure: the scar function},
Author = {Vergini, E. G. and G. Carlo},
Journal = {J. Phys. A},
Year = {2000},
Pages = {4525--4552},
Volume = {34}
}
@Article{VentKar14,
Title = {Convolutionless {Nakajima-Zwanzig} equations for stochastic analysis in nonlinear dynamical systems},
Author = {D. Venturi and G. E. Karniadakis},
Journal = {Proc. R. Soc. A},
Year = {2014},
Pages = {20130754},
Volume = {470},
DOI = {10.1098/rspa.2013.0754}
}
@Article{VerCar00,
Title = {Semiclassical quantization with short periodic orbits},
Author = {Vergini, E. G. and G. Carlo},
Journal = {J. Phys. A},
Year = {2000},
Note = {\arXiv{chao-dyn/9904039}},
Pages = {4717--4724},
Volume = {33}
}
@Article{Verg00,
Title = {Semiclassical theory of short periodic orbits in quantum chaos},
Author = {Vergini, E. G.},
Journal = {J. Phys. A},
Year = {2000},
Note = {\arXiv{chao-dyn/9904038}},
Pages = {4709--4716},
Volume = {33}
}
@Article{VeSchRi08,
Title = {The short periodic orbit approach for {Quantum Cat Maps}},
Author = {Vergini, E. G. and D. M. Schneider and A. M. F. Rivas},
Journal = {J. Phys. A},
Year = {2008},
Pages = {405102},
Volume = {41}
}
@Unpublished{ViSeLi11,
Title = {Metric entropy and the optimal prediction of chaotic signals},
Author = {D. Viswanath and X. Liang and K. Serkh},
Note = {\arXiv{nlin/1102.3202}},
Year = {2011}
}
@Article{VK79,
Title = {Eigenvalues of a diffusion process with a critical point},
Author = {H. Dekker and N. G. Van Kampen},
Journal = {Phys. Lett. A},
Year = {1979},
Pages = {374--376},
Volume = {73},
DOI = {10.1016/0375-9601(79)90088-4}
}
@Book{vKampen92,
Title = {Stochastic Processes in Physics and Chemistry},
Author = {N. G. van Kampen},
Publisher = {North-Holland},
Year = {1992},
Address = {Amsterdam}
}
@Article{vN32,
Title = {{Zur Operatorenmethode in der klassischen Mechanik}. ({German}) [{On} the operator methods of classical mechanics]},
Author = {J. von Neumann},
Journal = {Ann. Math.},
Year = {1932},
Note = {See additions \cite{vonNeum32}. Reprinted in \cite{Taub61}.},
Pages = {587--642},
Volume = {33}
}
@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{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},
Abstract = {Based on the experimentally generated velocity field, fixed points on
poincar\'{e} section are identified as well as their stable and unstable manifolds.
These information can be related to the gradient of the stretching field and the
distribution of passive scalar quantities. It seems that on these manifolds the
stretching field gains its maximum.}
}
@Article{vp98,
Title = {Gradient-based approach to solve optimal periodic output feedback control problems},
Author = {A. Varga and S. Pieters},
Journal = {Automatica},
Year = {1998},
Pages = {477--481},
Volume = {34},
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.}
}
@Article{W01,
Title = {Exact Coherent Structures in Channel Flow},
Author = {Waleffe, F. },
Journal = {J. Fluid Mech.},
Year = {2001},
Pages = {93--102},
Volume = {435}
}
@InProceedings{W02,
Title = {Exact coherent structures and their instabilities: {Toward} a dynamical-system theory of shear turbulence},
Author = {Waleffe, F. },
Booktitle = {Proceedings of the International Symposium on ``Dynamics and Statistics of Coherent Structures in Turbulence: Roles of Elementary Vortices''},
Year = {2002},
Editor = {Kida, Shigeo},
Pages = {115--128},
Publisher = {National Center of Sciences, Tokyo, Japan}
}
@Article{W03,
Title = {Homotopy of exact coherent structures in plane shear flows},
Author = {Waleffe, F.},
Journal = {Phys. Fluids},
Year = {2003},
Pages = {1517--1543},
Volume = {15}
}
@Article{W90,
Title = {Proposal for a self-sustaining process in shear flows},
Author = {Waleffe, F.},
Journal = {Working paper, available at \verb+www.math.wisc.edu/~waleffe/ECS/sspctr90.pdf+},
Year = {1990}
}
@InProceedings{W90b,
Title = {On the origin of the streak spacing in turbulent shear flow},
Author = {Waleffe, F.},
Booktitle = {Annual Research Briefs},
Year = {1990},
Pages = {159--168},
Publisher = {Center for Turbulence Research, Stanford Univ.}
}
@Article{W95a,
Title = {Hydrodynamic Stability and Turbulence: Beyond transients to a self-sustaining process},
Author = {Waleffe, F.},
Journal = {Stud. Appl. Math.},
Year = {1995},
Pages = {319--343},
Volume = {95}
}
@Article{W95b,
Title = {Transition in shear flows: Nonlinear normality versus non-normal linearity},
Author = {Waleffe, F.},
Journal = {Phys. Fluids},
Year = {1995},
Pages = {3060--3066},
Volume = {7}
}
@Article{W98,
Title = {Three-Dimensional Coherent States in Plane Shear Flows},
Author = {Waleffe, F.},
Journal = {Phys. Rev. Lett.},
Year = {1998},
Pages = {4140--4148},
Volume = {81}
}
@Misc{WaKo12,
author = {G. M. Wadsworth and D. T. Kovari},
title = {Optimal resolution of state space in chaotic hyperbolic 2-dimensional maps},
year = {2012},
note = {ChaosBook.org project},
url = {http://ChaosBook.org/projects/Lippolis/WaKo12.pdf},
}
@Unpublished{Waleffe90,
Title = {Proposal for a self-sustaining mechanism in shear flows},
Author = {F. Waleffe},
Note = {Center for Turbulence Research, Stanford Univ./NASA Ames, unpublished preprint (1990)}
}
@Article{Waleffe97,
Title = {On a self-sustaining process in shear flows},
Author = {Waleffe, F.},
Journal = {Phys. Fluids},
Year = {1997},
Pages = {883--900},
Volume = {9}
}
@Article{WaLiLi11,
Title = {Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of {Lorenz } equations},
Author = {Wang, P. F. and Li, J. P. and Li, Q.},
Journal = {Numerical Algorithms},
Year = {2011},
DOI = {10.1007/s11075-011-9481-6}
}
@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},
Note = {www.math.wisc.edu/~waleffe/ECS/WK97.pdf},
Pages = {385--422}
}
@Article{Wan11,
Title = {An adaptive high-order minimum action method},
Author = {X. Wan},
Journal = {J. Comput. Physics},
Year = {2011},
Pages = { - },
DOI = {10.1016/j.jcp.2011.08.006}
}
@Article{Wang13,
Title = {Forward and adjoint sensitivity computation of chaotic dynamical systems},
Author = {Wang, Q.},
Journal = {J. Comput. Phys.},
Year = {2013},
Addendum = {http://arXiv.org/abs/1202.5229},
Pages = {1--13},
Volume = {235},
DOI = {10.1016/j.jcp.2012.09.007}
}
@Article{WanZhoE10,
Title = {Study of the noise-induced transition and the exploration of the phase space for the {Kuramoto-Sivashinsky} equation using the minimum action method},
Author = {X. Wan and X. Zhou and W. E},
Journal = {Nonlinearity},
Year = {2010},
Pages = {475},
Volume = {23}
}
@Book{Wax,
Title = {Selected Papers on Noise and Stochastic Processes},
Author = {E. N. Wax},
Publisher = {Dover},
Year = {1954},
Address = {New York},
ISBN = {9780486495354}
}
@Article{WeezCoupLas,
Title = {Coherence between two coupled lasers from a dynamics perspective},
Author = {Ray, W. and Rogers, J. L. and Wiesenfeld, K.},
Journal = {Opt. Expr.},
Year = {2009},
Pages = {9357--68},
Volume = {17},
DOI = {10.1364/OE.17.009357}
}
@Article{WeezNonlInst,
Title = {Noisy precursors of nonlinear instabilities},
Author = {K. Wiesenfeld},
Journal = {J. Stat. Phys.},
Year = {1985},
Pages = {1071--1097},
Volume = {38}
}
@Article{weiss82,
Title = {The {P}ainlev\'{e} property for partial differential equations},
Author = {J. Weiss and M. Tabor and G. Carnevale},
Journal = {J. Math. Phys.},
Year = {1983},
Pages = {522},
Volume = {24}
}
@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,
Title = {{B}\"{a}cklund transformation and the {P}ainlev\'{e} property},
Author = {J. Weiss},
Journal = {J. Math. Phys.},
Year = {1986},
Pages = {1293},
Volume = {27}
}
@Misc{WeissFeig,
Title = {Feigenbaum constant},
Author = {Weisstein, E. W.},
Note = {mathworld.wolfram.com/FeigenbaumConstant.html},
Year = {2012}
}
@Article{Weyl,
Title = {The asymptotic distribution law for the eigenvalues of linear partial differential equations (with applications to the theory of black body radiation)},
Author = {H. Weyl},
Journal = {Math. Ann.},
Year = {1912},
Pages = {441--479},
Volume = {71}
}
@Article{WierMain,
Title = {Fractal {Weyl} law for chaotic microcavities: {Fresnel}'s laws imply multifractal scattering},
Author = {Wiersig, J. and Main, J.},
Journal = {Phys. Rev. E},
Year = {2008},
Pages = {036205},
Volume = {77},
DOI = {10.1103/PhysRevE.77.036205}
}
@Book{wiggb,
Title = {Global Bifurcations and Chaos},
Author = {S. Wiggins},
Publisher = {Springer},
Year = {1988},
Address = {New York}
}
@Book{wiggins,
Title = {Normally Hyperbolic Invariant Manifolds in Dynamical Systems},
Author = {S. Wiggins },
Publisher = {Springer},
Year = {1994},
Address = {New York}
}
@Book{wiggins2,
Title = {Chaotic Transport in Dynamical Systems},
Author = {S. Wiggins},
Publisher = {Springer},
Year = {1991},
Address = {New York}
}
@Unpublished{wikiHermite,
Title = {{Hermit}e polynomials},
Author = {Wikipedia},
Note = {{en.wikipedia.org/wiki/Hermite\_polynomials}}
}
@Article{Wimmer73,
Title = {On the {Ostrowski-Schneider Inertia Theorem}},
Author = {H. K. Wimmer},
Journal = {J. Math. Anal. Appl.},
Year = {1973},
Pages = {164--169},
Volume = {41}
}
@Article{witt99hol,
Title = {Scale and space localization in the {Kuramoto-Sivashinsky} equation},
Author = {R. W. Wittenberg and P. Holmes},
Journal = {Chaos},
Year = {1999},
Pages = {452},
Volume = {9},
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.}
}
@Article{WK04,
Title = {Exact coherent structures in Pipe flow},
Author = {Wedin, H. and Kerswell, R.R.},
Journal = {J. Fluid Mech.},
Year = {2004},
Pages = {333--371},
Volume = {508}
}
@InProceedings{WKH93,
Title = {On the origin of streaks in turbulent shear flows},
Author = {Waleffe, F. and Kim, J. and Hamilton, J.},
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 = {Durst, F. and Friedrich, R. and Launder, B.E. and Schmidt, F.W. and Schumann, U. and Whitelaw, J.H.},
Pages = {37--49},
Publisher = {Springer}
}
@Article{WoSa07,
Title = {An efficient method for recovering {Lyapunov} vectors from singular vectors},
Author = {Wolfe, C. L. and Samelson, R. M.},
Journal = {Tellus A},
Year = {2007},
Pages = {355--366},
Volume = {59},
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.}
}
@InProceedings{WW05,
Title = {Transition threshold and the Self-Sustaining Process},
Author = {Waleffe, F. and Wang, J.},
Booktitle = {Non-uniqueness of Solutions to the Navier-Stokes Equations and their Connection with Laminar-Turbulent Transition},
Year = {2005},
Editor = {Mullin, T. and Kerswell, R.R.},
Pages = {85--106},
Publisher = {Kluwer}
}
@Article{XueFengUni,
Title = {Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-{Q} microcavities},
Author = {Jiang, X. F. and Xiao, Y. F. and Zou, C. L. and He, L. N. and Dong, C. H. and Li, B. B. and Li, Y. and Sun, F. W. and Yang, L. and Gong, Q. H.},
Journal = {Advanced Materials},
Year = {2012},
Pages = {260--264},
Volume = {24},
DOI = {10.1002/adma.201201229}
}
@Article{XZTang95,
Title = {Symbol sequence statistics in noisy chaotic signal reconstruction},
Author = {Tang, X. Z. AND Tracy, E. R. AND Boozer, A. D. AND deBrauw, A. AND Brown, R.},
Journal = {Phys. Rev. E},
Year = {1995},
Pages = {3871--3889},
Volume = {51}
}
@Article{YadIsAkh14,
Title = {Stability analysis of large-scale dynamical systems by sub-{Gramian} approach},
Author = {Yadykin, I. B. and Iskakov, A. B. and Akhmetzyanov, A. V.},
Journal = {Intl. J. Robust Nonlin. Control},
Year = {2014},
Pages = {1361--1379},
Volume = {24},
DOI = {10.1002/rnc.3116}
}
@Misc{YaLeGoCoFr10,
Title = {Diffusive realization of a {Lyapunov} equation solution, and its {FPGA} implementation},
Author = {Y. Yakoubi and M. Lenczner and G. Goavec-Merou and R. Couturier and J. M. Friedt},
Year = {2011}
}
@Article{Yang_dyntun,
Author = {J. Yang and S.-B. Lee and S. Moon and S.-Y. Lee and S. W. Kim and T. T. A. Dao and J.-H. Lee and K. An},
Journal = {Phys. Rev. Lett.},
Year = {2010},
Pages = {243601},
Volume = {104}
}
@Article{YinAo06,
Title = {Existence and construction of dynamical potential in nonequilibrium processes without detailed balance},
Author = {L. Yin and P. Ao},
Journal = {J. Phys. A},
Year = {2006},
Pages = {8593},
Volume = {39},
Abstract = {The existence of a dynamical potential with both local and
global meanings in general nonequilibrium processes has been
controversial. Following an earlier heuristic argument in a letter by
one of us, in the present paper we show rigorously its existence for a
generic class of situations in physical and biological sciences. The
local dynamical meaning of this potential function is demonstrated via
a special stochastic differential equation and its global steady-state
meaning via a novel and explicit form of the Fokker--Planck equation. We
also give a procedure to obtain the special stochastic differential
equation for any given Fokker--Planck equation. No detailed balance
condition is required in our demonstration. For the first time we
obtain here a formula to describe the noise-induced shift in drift
force compared to the steady-state distribution, a phenomenon
extensively observed in numerical studies.},
DOI = {10.1088/0305-4470/39/27/003}
}
@Article{YMYA14,
Title = {{Lyapunov} function as potential function: {A} dynamical equivalence},
Author = {Yuan, R. and Ma, Y. and Yuan, B. and Ao, P.},
Journal = {Chinese Physics B},
Year = {2014},
Note = {\arXiv{1012.2721}},
Pages = {010505},
Volume = {23},
Abstract = {For a physical system, regardless of time reversal symmetry,
a potential function serves also as a Lyapunov function, providing
convergence and stability information. In this paper, the converse is
constructively proved that any dynamics with a Lyapunov function has a
corresponding physical realization: a friction force, a Lorentz force,
and a potential function. Such construction establishes a set of
equations with physical meaning for Lyapunov function and suggests new
approaches on the significant unsolved problem namely to construct
Lyapunov functions for general nonlinear systems. In addition, a
connection is found that the Lyapunov equation is a reduced form of a
generalized Einstein relation for linear systems, revealing further
insights of the construction.},
DOI = {10.1088/1674-1056/23/1/010505}
}
@Article{YoNo93,
Title = {Finite-time {Lyapunov} stability analysis and its application to atmospheric predictability},
Author = {Yoden, S. and Nomura, M.},
Journal = {J. Atmos. Sci.},
Year = {1993},
Pages = {1531--1543},
Volume = {50}
}
@Article{yorke2,
Title = {Unstable periodic orbits and the dimensions of multifractal chaotic attractors},
Author = {C. Grebogi and E. Ott and J. A. Yorke},
Journal = {Phys. Rev. A},
Year = {1988},
Pages = {1711--1724},
Volume = {37},
Abstract = {The probability measure generated by typical chaotic orbits of a dynamical
system can have an arbitrarily fine-scaled interwoven structure of
points with different singularity scalings. Recent work has characterized
such measures via a spectrum of fractal dimension values. In this
paper we pursue the idea that the infinite number of unstable periodic
orbits embedded in the support of the measure provides the key to
an understanding of the structure of the subsets with different singularity
scalings. In particular, a formulation relating the spectrum of dimensions
to unstable periodic orbits is presented for hyperbolic maps of arbitrary
dimensionality. Both chaotic attractors and chaotic repellers are
considered.},
DOI = {10.1103/PhysRevA.37.1711}
}
@Book{Yosida80,
Title = {Functional Analysis},
Author = {K. Yosida},
Publisher = {Springer},
Year = {1980},
Address = {New York}
}
@Article{yu93bd,
Title = {Boundary Effects on the Nonlinear Interactions of Surface Waves},
Author = {S. V. Vladimirov and M. Y. Yu},
Journal = {Phys. Fluids B},
Year = {1993},
Pages = {2888},
Volume = {5}
}
@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,
Title = {Testing whether two chaotic one- dimensional processes are dynamically identical},
Author = {G.-C. Yuan and J. A. Yorke and T. L. Carroll and E. Ott and L. M. Pecora},
Journal = {Phys. Rev. Lett.},
Year = {2000},
Pages = {4265},
Volume = {85},
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.}
}
@Article{YWMYA13,
Title = {Exploring a noisy van der Pol type oscillator with a stochastic approach},
Author = {Yuan, R. and Wang, X. and Ma, Y. and Yuan, B. and Ao, P.},
Journal = {Phys. Rev. E},
Year = {2013},
Pages = {062109},
Volume = {87},
DOI = {10.1103/PhysRevE.87.062109}
}
@Article{Zagarola98,
Title = {Mean flow scaling of turbulent pipe flow},
Author = {Zagarola, M.V. and Smits, A.J.},
Journal = {J. Fluid Mech.},
Year = {1998},
Pages = {33--79},
Volume = {373}
}
@Article{ZakGol10,
Title = {Comment on ``{Time-averaged} properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems''},
Author = {Zaks, M. A. and Goldobin, D. S.},
Journal = {Phys. Rev. E},
Year = {2010},
Note = {\arXiv{0912.0596}},
Pages = {018201},
Volume = {81},
DOI = {10.1103/PhysRevE.81.018201}
}
@Article{Zang91,
Title = {On the rotation and skew-symmetric forms for incompressible flow simulations},
Author = {T.A. Zang},
Journal = {Appl. Numer. Math.},
Year = {1991},
Pages = {27--40},
Volume = {7}
}
@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},
Pages = {R2511},
Volume = {57}
}
@Article{ZhoRenE08,
Title = {Adaptive minimum action method for the study of rare events},
Author = {X. Zhou and W. Ren and W. E},
Journal = {J. Chem. Phys.},
Year = {2008},
Pages = {104111},
Volume = {128},
DOI = {10.1063/1.2830717}
}
@Article{ZhoSalWu99,
Title = {Balanced realization and model reduction for unstable systems},
Author = {Zhou, K. and Salomon, G. and Wu, E.},
Journal = {Intl. J. Robust Nonlin. Control},
Year = {1999},
Pages = {183--198},
Volume = {9},
DOI = {10.1002/(SICI)1099-1239(199903)9:3¡183::AID-RNC399¿3.0.CO;2-E}
}
@Article{Zhou92,
Title = {Coherence and chaos in a model of turbulent boundary layer},
Author = {X. Zhou and L. Sirovich},
Journal = {Phys. Fluids A},
Year = {1992},
Pages = {2855--2874},
Volume = {4}
}
@Book{ZhouDoyle,
Title = {Essentials of Robust Control},
Author = {Zhou, K. and Doyle, J. C.},
Publisher = {Prentice Hall},
Year = {1998},
Address = {Upper Saddle River, NJ}
}
@Article{ZhuLai03,
Title = {Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics},
Author = {Zhu, L. and {Lai}, Y.-C. and {Hoppensteadt}, F.~C. and {Bollt}, E.~M.},
Journal = {Chaos},
Year = {2003},
Pages = {410--419},
Volume = {13},
DOI = {10.1063/1.1520090}
}
@Article{ZhYiAo06,
Title = {Limit cycle and conserved dynamics},
Author = {Zhu, X.-M. and Yin, L. and Ao, P.},
Journal = {Int. J. Mod. Phys. B},
Year = {2006},
Pages = {817--827},
Volume = {20},
DOI = {10.1142/S0217979206033607}
}
@Article{ZuPaz,
Title = {Decoherence, chaos, and the second law},
Author = {W. H. Zurek and J. P. Paz},
Journal = {Phys. Rev. Lett.},
Year = {1994},
Pages = {2508},
Volume = {72}
}
@Book{Zwil92,
Title = {Handbook of Differential Equations},
Author = {Zwillinger, D.},
Publisher = {Academic},
Year = {1992},
Address = {New York}
}
@Book{Zwil92HI,
Title = {Handbook of Integration},
Author = {Zwillinger, D.},
Publisher = {Jones and Bartlett},
Year = {1992},
Address = {Boston}
}
@Book{Zwil96,
Title = {Standard Mathematical Tables and Formulae},
Author = {Zwillinger, D.},
Publisher = {CRC Press, Inc.},
Year = {1996},
Address = {Boca Raton, FL}
}
@Article{Zwor_pre,
Title = {Weyl asymptotics: From closed to open systems},
Author = { A. Potzuweit and T. Weich and S. Barkhofen and U. Kuhl and H.-J. St\"ockmann and M. Zworski},
Journal = {Phys. Rev. E},
Year = {2012},
Pages = {066205},
Volume = {86},
DOI = {10.1103/PhysRevE.86.066205}
}
@Article{Zwor_prl,
Title = {Experimental observation of the spectral gap in microwave $n$-disk systems},
Author = {Barkhofen, S. and Weich, T. and Potzuweit, A. and St\"ockmann, H.-J. and Kuhl, U. and Zworski, M.},
Journal = {Phys. Rev. Lett.},
Year = {2013},
Pages = {164102},
Volume = {110},
DOI = {10.1103/PhysRevLett.110.164102}
}
@Article{ZycSom,
Title = {Truncations of random unitary matrices},
Author = {K. Zyczkowski and H. J. Sommers},
Journal = {J. Phys. A},
Year = {2000},
Pages = {2045--2057},
Volume = {33},
Abstract = {We analyse properties of non-Hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N > M , distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M / N . For the truncated CUE we analytically derive the joint density of eigenvalues and all correlation functions. In the strongly non-unitary case universal Ginibre behaviour is found. For N - M fixed and N to {infty} the universal resonance-width distribution with N - M open channels is recovered.},
DOI = {10.1088/0305-4470/33/10/307}
}
@Article{OzoHan84,
author = {Ozorio de Almeida, A. M. and Hannay, J. H.},
title = {Periodic orbits and a correlation function for the semiclassical density of states},
journal = {J. Phys. A},
year = {1984},
volume = {17},
pages = {3429},
doi = {10.1088/0305-4470/17/18/013},
}
@Article{Farrell_1996,
author = {Brian F. Farrell and Petros J. Ioannou},
title = {Generalized Stability Theory. Part {II}: Nonautonomous Operators},
journal = {Journal of the Atmospheric Sciences},
year = {1996},
volume = {53},
number = {14},
pages = {2041--2053},
month = {jul},
doi = {10.1175/1520-0469(1996)053<2041:gstpin>2.0.co;2},
publisher = {American Meteorological Society},
}
@Misc{HuSv15,
author = {{Hu}, W. and {Sverak}, V.},
title = {Dynamics of geodesic flows with random forcing on Lie groups with left-invariant metrics},
year = {2015},
url = {http://arxiv.org/abs/1510.05279},
}
@Article{DaOsSa00,
author = {Davydychev, A. I. and Osland, P. and Saks, L.},
title = {Quark-gluon vertex in arbitrary gauge and dimension},
journal = {Phys. Rev. D},
year = {2000},
volume = {63},
pages = {014022},
doi = {10.1103/PhysRevD.63.014022},
}
@Article{DR91a,
author = {P. Dahlqvist and G. Russberg},
title = {Periodic orbit quantization of bound chaotic systems},
journal = {J. Phys. A},
year = {1991},
volume = {24},
pages = {4763--4778},
doi = {10.1088/0305-4470/24/20/012},
}
@Article{AllMar16,
author = {Allawala, Altan and Marston, J. B.},
title = {Statistics of the stochastically forced Lorenz attractor by the {Fokker-Planck} equation and cumulant expansions},
journal = {Phys. Rev. E},
year = {2016},
volume = {94},
pages = {052218},
doi = {10.1103/PhysRevE.94.052218},
}
@Inproceedings{BajCha17,
author = {J. Bajars and D. J. Chappell},
title = {On discretisation schemes for a boundary integral model of stochastic ray propagation},
booktitle = {Proc. 11. UK Conference on Boundary Integral Methods UKBIM11},
year = {2017},
editor = {D. J. Chappell},
isbn = {9780993111297},
pages = {25--32},
address = {Nottingham UK},
publisher = {Nottingham Trent Univ.},
url = {http://irep.ntu.ac.uk/id/eprint/31465/},
}
@Article{ChaTan14,
author = {Chappell, D. J. and Tanner, G.},
title = {A boundary integral formalism for stochastic ray tracing in billiards},
journal = {Chaos},
year = {2014},
volume = {24},
pages = {043137},
doi = {10.1063/1.4903064},
}
@Article{Goldobin14b,
author = {Goldobin, Denis S.},
title = {Noise can reduce disorder in chaotic dynamics},
journal = {European Physical Journal Special Topics},
year = {2014},
volume = {223},
pages = {1699--1709},
doi = {10.1140/epjst/e2014-02179-9},
abstract = {We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.},
day = {01},
issn = {1951-6401},
}
@Article{BihKva92,
author = {Biham, O. and Kvale, M.},
title = {Unstable periodic orbits in the stadium billiard},
journal = {Phys. Rev. A},
year = {1992},
volume = {46},
pages = {6334--6339},
doi = {10.1103/PhysRevA.46.6334},
}
@Inproceedings{SoCoCv19,
author = {S. A. Solla and Y. Cohen and P. Cvitanovi{\'c}},
title = {A novel approach to the empirical characterization of learning in biological systems},
booktitle = {{Comp. Systems Neuroscience (Cosyne), Lisbon, Portugal}},
year = {2019},
editor = {E. Chiappe et. al.},
publisher = {Cosyne},
url = {http://www.cosyne.org},
}
@Comment{jabref-meta: databaseType:bibtex;}