Open problems in the theory of non-uniform hyperbolicity

DOI10.3934/dcds.2010.27.589zbMath1200.37001arXiv1303.2375OpenAlexW1966780936MaRDI QIDQ972042

Vaughn Climenhaga, Ya. B. Pesin

Publication date: 25 May 2010

Published in: Discrete and Continuous Dynamical Systems, Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2375

zbMATH Keywords

dissipative systemsconservative systemsSRB measuresgeneric propertiesstable and unstable manifoldsnon-uniform hyperbolicityeffective hyperbolicityHadamard-Perron theorem\(u\)-measuresmixed hyperbolicity

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Invariant manifold theory for dynamical systems (37D10) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10)

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Cites Work

• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• SRB measures for non-hyperbolic systems with multidimensional expansion

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