Yakov B. Pesin


State College, PA





Articles (selected)

Smooth Dynamical Systems

  • Families of invariant manifolds corresponding to non-zero characteristic exponents (pdf), Math. USSR Izvestija, v. 40, N6 (1976) 1261–1305

  • Geodesic flows on closed Riemannian manifolds without focal points (pdf), Math. USSR Izvestija, v. 11, N6 (1977) 1195–1228.

  • Formulas for the entropy of the geodesic flow on a compact Riemannian manifold without conjugate points (pdf), Math. USSR Izvestija, v. 40, N6 (1976) 1261–1305

  • (with Ya. Sinai) Gibbs measures for partially hyperbolic attractors (pdf), ETDS, v. 2, N3-4 (1983) 417-438

  • Dynamical Systems With Generalized Hyperbolic Attractors: Hyperbolic, Ergodic and Topological Properties (pdf), ETDS, v. 12, N1 (1992) 123-152

  • (with R. de la Llave and M. Jiang) On the Integrability of Intermediate Foliations for Anosov Diffeomorphisms (pdf), ETDS, v.15, N2 (1995) 317-331

  • (with M. Brin) On Morse-Smale Endomorphisms (pdf), Amer. Math. Soc. Transl., v. 171, N2 (1996) 35-43

  • (with D. Dolgopyat and H. Hu) An Example of a Smooth Hyperbolic Measure with Countably Many Ergodic Components (pdf), Appendix to "Lectures on Lyapunov Exponents and Smooth Ergodic Theory" (pdf) in the book: "Smooth Ergodic Theory and Its Applications", Proceedings of Symposia in Pure Mathematics (2001) 95-106

  • (with K. Burns and D. Dolgopyat) Partial Hyperbolicity, Lyapunov Exponents and Stable Ergodicity (pdf), J. Stat. Phys., v. 108, N5-6 (2002) 927-942

  • (with M. Hirayama) Non-absolutely Continuous Foliations (pdf), Israel Journal of Math., v. 160 (2007) 173-187

  • (with K. Burns, D. Dolgopyat, and M. Pollicott) Stable Ergodicity For Partially Hyperbolic Attractors With Negative Central Exponents (pdf), Journal of Modern Dynamics, v. 2, N1 (2008) 1-19

  • On the Work of Dolgopyat on Partial and Nonuniform Hyperbolicity (pdf), Journal of Modern Dynamics v. 4, N2 (2010) 227-241

  • On the Work of Sarig on Countable Markov Chains and Thermodynamic Formalism (pdf), Journal of Modern Dynamics v. 8, N1 (2014) 1-14

  • (with B. Hasselblatt, J. Schmeling) Pointwise hyperbolicity implies uniform hyperbolicity (pdf), Discrete Contin. Dyn. Syst. v. 34, N7 (2014) 2819-2827

  • (with V. Climenhaga, D. Dolgopyat) Non-stationary Non-uniform Hyperbolicity: SRB Measures for Dissipative Maps (pdf), Comm. Math. Phys., v. 346, N2 (2016) 553-602

  • (with V. Climenhaga) Hadamard--Perron Theorems and Effective Hyperbolicity (pdf), ETDS, v. 36, N1 (2016) 23-63

  • (with M. Brin) D.V. Anosov and our road to partial hyperbolicity (pdf), "Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov", AMS, Contemporary Mathematics Series, 692 (2017) 23--28

  • (with A. Gorodetski), Path Connectedness and Entropy Density of the Space of Hyperbolic Ergodic Measures (pdf), "Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov", AMS, Contemporary Mathematics Series, 692 (2017) 111-121

  • Sinai's work on Markov partitions and SRB measures (pdf), The Abel Prize Laureates book series, Springer-Verlag, 2018

  • Anatole Katok's works on hyperbolicity, entropy and geodesic flows (pdf), in "Anatole Katok Collective Works", World Scientific Publ., 2023

Genericity and Coexistence

  • (with D. Dolgopyat), Every Compact Manifold Carries a Completely Hyperbolic Diffeomorphism (pdf), ETDS, v. 22 (2002) 1-27

  • (with H. Hu and A. Talitskaya), Every Compact Manifold Carries a Hyperbolic Bernoulli Flow (pdf), in the book: "Modern Dynamical Systems and Applications", Cambridge Univ. Press, 2004, pp. 347-358

  • (with H. Hu and A. Talitskaya), A Volume Preserving Diffeomorphism With Essential Coexistence of Zero and Nonzero Lyapunov Exponents (pdf), CMP, v. 319, N2 (2013) 331-378

  • (with J. Chen and H. Hu), A Volume Preserving Flow With Essential Coexistence of Zero and Nonzero Lyapunov Exponents (pdf), ETDS, v. 33, N6 (2013) 1748-1785

  • (with J. Chen and H. Hu and K. Zhang), The essential coexistence phenomenon in Hamiltonian dynamics (pdf), ETDS special issue in memory of A. Katok, Ergodic Theory Dynam. Systems, 42, no. 2 (2022) 592--613.

Mathematical Physics. Coupled Map Lattices

  • (with Ya. Sinai), Space-time Chaos in the System of Weakly Interacting Hyperbolic Systems (pdf), Journal of Geometry and Physics, v. 3 (1988) 483-492

  • (with V. Afraimovich), Traveling Waves in Lattice Models of Multi-Dimensional and Multi-Component Media: Part I. General Hyperbolic Properties (pdf), Nonlinearity, v. 6 (1993) 429-455

  • (with V. Afraimovich and A. Tempelman), Traveling Waves in Lattice Models of Multi-Dimensional and Multi-Component Media: Part II. Ergodic Properties and Dimension (pdf), Chaos v. 3 (1993) 233-241

  • (with M. Jiang), Equilibrium Measures for Coupled Map Lattices: Existence, Uniqueness, and Finite-Dimensional Approximations (pdf), Comm. Math. Phys., v. 193, N3 (1998) 675-711

  • (with D. R. Orendovici), Chaos in Traveling Waves of Lattice Systems of Unbounded Media (pdf), Proceedings of the IMA Volumes in Mathematics and its Applications, v. 119, "Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems", Springer-Verlag (1999) 327-359

  • (with A. Yurchenko), Some Physical Models of The Reaction-Diffusion Equation and Coupled Map Lattices (pdf), Russian Math. Surveys, 59, n.3, 2004

  • (with H. Kang), Dynamics of a Discrete Brusselator Model: Escape to infinity and Julia set (pdf), Milan Journal of Mathematics, v. 73 (2004), 1-15

Thermodynamic Formalism

  • (with Ke Zhang), Phase Transitions For Uniformly Expanding Maps (pdf), J. Stat. Phys., v. 122, N6 (2006), 1095-1110

  • (with Ke Zhang), Thermodynamics Associated with Inducing Schemes and Liftability of Measures (pdf), Proc. Fields Inst., 51 (2007) 289-305

  • (with S. Senti), Thermodynamical formalism associated with inducing schemes for one-dimensional maps (pdf), Moscow Math. Journal, 5:3 (2005) 669--678

  • (with S. Senti), Equilibrium Measures for Maps with Inducing Schemes (pdf), Journal of Modern Dynamics v. 2, N3 (2008) 1-31

  • (with S. Senti and Ke Zhang), Lifting Measures to Inducing Schemes (pdf), ETDS, v. 28, N2 (2008) 553-574

  • (with S. Senti and Ke Zhang), Thermodynamics of Towers of Hyperbolic Type (revised version)(pdf), Trans. Amer. Math. Soc., v. 368, N12 (2016) 8519-8552

  • (with S. Senti and Ke Zhang), Thermodynamics of the Katok Map (pdf), ETDS (2018) v. 39, n. 3 (2019) 764--794; corrigendum (pdf)

  • (with V. Climenhaga and A. Zelerowicz), Equilibrium States in Dynamical Systems via Geometric Measure Theory (pdf), Bulletin of the AMS, 2019 v. 56, n. 4 (2019) 569--610

  • (with V. Climenhaga and A. Zelerowicz), Equilibrium measures for some partially hyperbolic systems (pdf), Journal of Modern Dynamics, 16 (2020) 155--205

  • (with V. Climenhaga and S. Luzzatto), SRB measures and Young Towers for surface diffeomorphisms (pdf), Ann. Henri Poincar\'e, 23 (2022) 973--1059

  • (with S. Senti and F. Shahidi), Area preserving surface diffeomorphisms with polynomial decay of correlations are ubiquitous (pdf), in "Vision for Dynamics in the 21st Century: the Legacy of Anatole Katok", Cambridge University Press, 2023

Dimension Theory. Multifractal Formalism

  • On Rigorous Mathematical Definition of Correlation Dimension and Generalized Spectrum For Dimensions (pdf), J. Stat. Phys., v. 71, N3-4 (1993) 529-547

  • (with H. Weiss), On the Dimension of Deterministic and Random Cantor-like Sets, Symbolic Dynamics, and the Eckmann-Ruelle Conjecture (pdf), Comm. Math. Phys., v. 182, N1 (1996) 105-153

  • (with L. Barreira and J. Schmeling), On a General Concept of Multifractality: Multifractal Spectra for Dimensions, Entropies, and Lyapunov Exponents. Multifractal Rigidity (pdf), Chaos, v. 7, N1 (1997) 27-30

  • (with L. Barreira and J. Schmeling), Multifractal Spectra and Multifractal Rigidity for Horseshoes (pdf), Journal of Dynamical and Control Systems, v. 3, N1 (1997) 33-49

  • (with H. Weiss), A Multifractal Analysis of Equilibrium Measures For Conformal Expanding Maps and Markov Moran Geometric Constructions (pdf), J. Stat. Phys., v. 86, N1-2 (1997) 233-275

  • (with H. Weiss), The Multifractal Analysis of Gibbs Measures: Motivation, Mathematical Foundation, and Examples (pdf), Chaos, v. 7, N1 (1997) 89-106

  • (with L. Barreira and J. Schmeling) Dimension and Product Structure of Hyperbolic Measures (pdf), Annals of Math., v. 149, N3 (1999) 755-783

  • (with V. Sadovskaya) Multifractal Analysis of Conformal Axion A Flows (pdf), Comm. Math. Phys., v. 216, N2 (2001) 277-312

  • (with H. Weiss) The Multifractal Analysis of Birkhoff Averages and Large Deviations (pdf), in the book "Global Analysis of Dynamical Systems", Editors: H. Broer, B. Krauskopf, G. Vegter. IoP Publishing, Bristol, UK, 2001

  • (with Y. Zhao) Scaled Entropy for Dynamical Systems (pdf), J. Stat. Phys. 158, N2 (2015) 447-475; Erratum (pdf): J. Stat. Phys. 162, N6 (2016) 1654-1660

  • (with Y. Zhao), Q-Entropy for Symbolic Dynamical Systems (pdf), J. Physica A, v. 48, N49 (2015) 17 pp

  • (with A. Zelerowicz and Y. Zhao), Time Rescaling of Lyapunov Exponents (pdf), in the book "Advances in Dynamics, Patterns, Cognition", Ed.: I Aaronson, at all, ``Nonlinear Systems and Complexity'' series, Springer, v. 20 (2017) 29--40

  • (with Y. Cao and Y. Zhao), Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure (pdf), GAFA, v. 29, n. 5 (2019) 1325--1368