The Pesin entropy formula for diffeomorphisms with dominated splitting

DOI10.1017/etds.2013.93zbMath1356.37047arXiv1209.5784OpenAlexW3121228685MaRDI QIDQ5262241

Eleonora Catsigeras, Marcelo Cerminara, Heber Enrich

Publication date: 13 July 2015

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

Full work available at URL: https://arxiv.org/abs/1209.5784

zbMATH Keywords

Lyapunov exponentsdominated splittingPesin entropy

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (23)

GEOMETRICAL AND MEASURE-THEORETIC STRUCTURES OF MAPS WITH A MOSTLY EXPANDING CENTER ⋮ Dirac physical measures on saddle-type fixed points ⋮ On Pesin's entropy formula for dominated splittings without mixed behavior ⋮ Pesin's entropy formula for \(C^1\) non-uniformly expanding maps ⋮ Homoclinic classes for sectional-hyperbolic sets ⋮ Dominated splitting, partial hyperbolicity and positive entropy ⋮ When a physical-like measure is physical or SRB? ⋮ Formula of entropy along unstable foliations for \(C^1\) diffeomorphisms with dominated splitting ⋮ Entropy of physical measures for \(C^\infty\) dynamical systems ⋮ Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers ⋮ Volume growth and topological entropy of partially hyperbolic systems ⋮ Pesin's entropy formula for systems between \(C^1\) and \(C^{1+\alpha}\) ⋮ Dirac physical measures for generic diffeomorphisms ⋮ Empirical measures of partially hyperbolic attractors ⋮ Invariant measures for typical continuous maps on manifolds ⋮ Weak pseudo-physical measures and Pesin’s entropy formula for Anosov 𝐶¹-diffeomorphisms. ⋮ A new criterion of physical measures for partially hyperbolic diffeomorphisms ⋮ Entropy along expanding foliations ⋮ Topological entropy on points without physical-like behaviour ⋮ Unstable entropy in smooth ergodic theory ^* ⋮ Statistical properties of physical-like measures* ⋮ Non-dense orbits of systems with the approximate product property ⋮ Lower bound in Pesin formula of C ¹ interval maps*

Cites Work

• Existence and uniqueness of SRB measure on \(C^1\) generic hyperbolic attractors
• Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms
• The \(C^{1+\alpha}\) hypothesis in Pesin theory
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• \(C^{1}\)-generic Pesin's entropy formula
• SRB-like Measures for C⁰Dynamics
• A proof of the estimation from below in Pesin's entropy formula
• A genericC¹map has no absolutely continuous invariant probability measure
• Errata to ‘A proof of Pesin's formula’
• An inequality for the entropy of differentiable maps
• A proof of Pesin's formula
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY

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