Sinai’s Work on Markov Partitions and SRB Measures

[1]  Dominique Perrin,et al.  Symbolic dynamics , 2010, Handbook of Automata Theory.

[2]  Y. Sinai.  Markov partitions and C-diffeomorphisms , 2020, Hamiltonian Dynamical Systems.

[3]  C. Tsallis.  Entropy , 2022, Thermodynamic Weirdness.

[4]  D. Sz'asz.  Markov Approximations and Statistical Properties of Billiards , 2017, The Abel Prize.

[5]  Boris Marcovich Gurevich,et al.  Entropy Theory of Dynamical Systems , 2019, The Abel Prize.

[6]  A. Katok.  Dmitry viktorovich anosov: His life and mathematics , 2017 .

[7]  V. Climenhaga,et al.  Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps , 2014, 1405.6194.

[8]  SRB measures for partially hyperbolic systems whose central direction is weakly expanding , 2014 .

[9]  B. Hasselblatt,et al.  Pointwise hyperbolicity implies uniform hyperbolicity , 2013 .

[10]  Y. Pesin,et al.  The essential coexistence phenomenon in dynamics , 2013 .

[11]  L. Barreira,et al.  Introduction to Smooth Ergodic Theory , 2013, Graduate Studies in Mathematics.

[12]  Y. Pesin,et al.  A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents , 2013 .

[13]  O. Sarig.  Symbolic dynamics for surface diffeomorphisms with positive entropy , 2012 .

[14]  Y. Pesin,et al.  A volume preserving flow with essential coexistence of zero and non-zero Lyapunov exponents , 2012, Ergodic Theory and Dynamical Systems.

[15]  R. Ures,et al.  Uniqueness of SRB Measures for Transitive Diffeomorphisms on Surfaces , 2010, 1005.4149.

[16]  Ja. G. Sinaĭ.  Weak Isomorphism of Transformations with Invariant Measure , 2010 .

[17]  C. Vásquez.  Stable ergodicityfor partially hyperbolic attractors with positive central Lyapunov exponents , 2009 .

[18]  A. Katok.  Moscow dynamics seminars of the Nineteen seventies and the early career of Yasha Pesin , 2008 .

[19]  B. Marcus.  Symbolic Dynamics , 2008, Encyclopedia of Complexity and Systems Science.

[20]  Y. Pesin,et al.  Stable ergodicity for partially hyperbolic attractors with negative central exponents , 2007 .

[21]  S. Smale.  A Structurally Stable Differentiable Homeomorphism with an Infinite Number of Periodic Points , 2007 .

[22]  Yakov Pesin,et al.  Nonuniform Hyperbolicity: General Hyperbolic Measures , 2007 .

[23]  Yakov Pesin,et al.  Nonuniform Hyperbolicity: Ergodic Theory of Smooth and SRB Measures , 2007 .

[24]  L. Barreira,et al.  Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents , 2007 .

[25]  Rufus Bowen,et al.  Some systems with unique equilibrium states , 1974, Mathematical systems theory.

[26]  Yakov Pesin,et al.  Lectures on Partial Hyperbolicity and Stable Ergodicity , 2004 .

[27]  Yongluo Cao,et al.  A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem of Mañé , 2003, math/0309057.

[28]  Non­zero Lyapunov exponents and uniform hyperbolicity , 2003 .

[29]  Y. Pesin,et al.  Every compact manifold carries a completely hyperbolic diffeomorphism , 2002, Ergodic Theory and Dynamical Systems.

[30]  N. Chernov.  Chapter 4 Invariant measures for hyperbolic dynamical systems , 2002 .

[31]  Lai-Sang Young,et al.  Strange Attractors with One Direction of Instability , 2001 .

[32]  Lai-Sang Young,et al.  Markov Extensions and Decay of Correlations for Certain Hénon Maps , 2000, Astérisque.

[33]  C. Bonatti,et al.  SRB measures for partially hyperbolic systems whose central direction is mostly contracting , 2000 .

[34]  José F. Alves,et al.  SRB measures for partially hyperbolic systems whose central direction is mostly expanding , 2000, 1403.2937.

[35]  L. Young,et al.  STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS WITH SOME HYPERBOLICITY , 1998 .

[36]  M. Viana.  Dynamics: A Probabilistic and Geometric Perspective , 1998 .

[37]  L. Bunimovich,et al.  Sinai's Moscow Seminar on Dynamical Systems , 1995 .

[38]  A. Katok,et al.  Introduction to the Modern Theory of Dynamical Systems: Low-dimensional phenomena , 1995 .

[39]  Lai-Sang Young,et al.  Sinai-Bowen-Ruelle measures for certain Hénon maps , 1993 .

[40]  Y. Sinai.  Finite-dimensional randomness , 1991 .

[41]  Lennart Carleson,et al.  The Dynamics of the Henon Map , 1991 .

[42]  L. Bunimovich,et al.  Markov partitions for two-dimensional hyperbolic billiards , 1990 .

[43]  F. Ledrappier,et al.  The metric entropy of diffeomorphisms Part I: Characterization of measures satisfying Pesin's entropy formula , 1985 .

[44]  F. Ledrappier,et al.  The metric entropy of diffeomorphisms Part II: Relations between entropy, exponents and dimension , 1985 .

[45]  F. Ledrappier.  Propriétés Ergodiques Des Mesures De Sinaï , 1984 .

[46]  F. Ledrappier,et al.  The metric entropy of diffeomorphisms , 1984 .

[47]  Yakov Pesin,et al.  Gibbs measures for partially hyperbolic attractors , 1982, Ergodic Theory and Dynamical Systems.

[48]  F. Ledrappier,et al.  A proof of the estimation from below in Pesin's entropy formula , 1982, Ergodic Theory and Dynamical Systems.

[49]  L. Bunimovich,et al.  Markov Partitions for dispersed billiards , 1980 .

[50]  A. Katok.  Bernoulli Diffeomorphisms on surfaces , 1979 .

[51]  Y. Pesin.  CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY , 1977 .

[52]  Y. Pesin.  Description of π-partition of a diffeomorphism with invariant measure , 1977 .

[53]  R. Mañé.  Quasi-Anosov diffeomorphisms and hyperbolic manifolds , 1977 .

[54]  Ja B Pesin.  FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS , 1976 .

[55]  David Ruelle,et al.  A MEASURE ASSOCIATED WITH AXIOM-A ATTRACTORS. , 1976 .

[56]  D. Ruelle,et al.  The ergodic theory of AxiomA flows , 1975 .

[57]  D. Ruelle,et al.  The Ergodic Theory of Axiom A Flows. , 1975 .

[58]  R. Bowen.  Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms , 1975 .

[59]  M. Brin,et al.  PARTIALLY HYPERBOLIC DYNAMICAL SYSTEMS , 1974 .

[60]  D. Ornstein.  Ergodic theory, randomness, and dynamical systems , 1974 .

[61]  Benjamin Weiss,et al.  Geodesic flows are Bernoullian , 1973 .

[62]  M. Ratner.  Markov partitions for anosov flows onn-dimensional manifolds , 1973 .

[63]  Rufus Bowen,et al.  SYMBOLIC DYNAMICS FOR HYPERBOLIC FLOWS. , 1973 .

[64]  Y. Sinai.  GIBBS MEASURES IN ERGODIC THEORY , 1972 .

[65]  R. Bowen,et al.  MARKOV PARTITIONS FOR AXIOM A DIFFEOMORPHISMS. , 1970 .

[66]  D. Ornstein.  Bernoulli shifts with the same entropy are isomorphic , 1970 .

[67]  D. V. Anosov,et al.  Geodesic flows on closed Riemann manifolds with negative curvature , 1969 .

[68]  David Ruelle,et al.  Observables at infinity and states with short range correlations in statistical mechanics , 1969 .

[69]  P. L. Dobruschin.  The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity , 1968 .

[70]  Y. Sinai,et al.  Construction of Markov partitions , 1968 .

[71]  S. Smale.  Differentiable dynamical systems , 1967 .

[72]  Y. Sinai,et al.  SOME SMOOTH ERGODIC SYSTEMS , 1967 .

[73]  R. Adler,et al.  Entropy, a complete metric invariant for automorphisms of the torus. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[74]  C. Caramanis.  What is ergodic theory , 1963 .

[75]  W. Kyner.  Invariant Manifolds , 1961 .