Maximal measure and entropic continuity of Lyapunov exponents for \({\mathcal{C}}^r\) surface diffeomorphisms with large entropy

DOI10.1007/s00023-023-01308-yarXiv2202.07266OpenAlexW4366579105MaRDI QIDQ6119780

David Burguet

Publication date: 20 February 2024

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.07266

zbMATH Keywords

Lyapunov exponentssurface diffeomorphismentropic continuity

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Topological entropy (37B40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Cites Work

• Large entropy implies existence of a maximal entropy measure for interval maps
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Volume growth and entropy
• Continuity properties of entropy
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Measures of maximal entropy for surface diffeomorphisms
• Continuity properties of Lyapunov exponents for surface diffeomorphisms
• Symbolic extensions in intermediate smoothness on surfaces
• surface diffeomorphisms with no maximal entropy measure
• Jumps of entropy for C^rinterval maps
• A proof of the estimation from below in Pesin's entropy formula
• Existence of measures of maximal entropy for 𝒞^{𝓇} interval maps
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