On Pesin's entropy formula for dominated splittings without mixed behavior

DOI10.1016/j.jde.2016.06.012zbMath1366.37014arXiv1512.08541OpenAlexW2963002814MaRDI QIDQ305414

Da-Wei Yang, Yong-Luo Cao

Publication date: 29 August 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08541

zbMATH Keywords

dominated splittingPesin's entropy formulaShub's entropy conjecturetopological attractor

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Ergodicity, mixing, rates of mixing (37A25) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (13)

On the abundance of Sinai-Ruelle-Bowen measures ⋮ Pesin's entropy formula for \(C^1\) non-uniformly expanding maps ⋮ Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers ⋮ The entropy conjecture for dominated splitting with multi 1D centers via upper semi-continuity of the metric entropy ⋮ Upper bounds on measure-theoretic tail entropy for dominated splittings ⋮ Empirical measures of partially hyperbolic attractors ⋮ A forward ergodic closing lemma and the entropy conjecture for nonsingular endomorphisms away from tangencies ⋮ Weak pseudo-physical measures and Pesin’s entropy formula for Anosov 𝐶¹-diffeomorphisms. ⋮ Entropy of partially hyperbolic flows with center dimension two ⋮ Random entropy expansiveness for diffeomorphisms with dominated splittings ⋮ Unstable entropy in smooth ergodic theory ^* ⋮ On the continuity of topological entropy of certain partially hyperbolic diffeomorphisms ⋮ Lower bound in Pesin formula of C ¹ interval maps*

Cites Work

• The entropy conjecture for diffeomorphisms away from tangencies
• A note on partially hyperbolic attractors: entropy conjecture and SRB measures
• Existence and uniqueness of SRB measure on \(C^1\) generic hyperbolic attractors
• Dominated splitting and Pesin's entropy formula
• The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center
• Volume growth and entropy
• The ergodic theory of axiom A flows
• Currents, flows and diffeomorphisms
• Entropy and stability
• \(C^{1}\)-generic Pesin's entropy formula
• Residual entropy, conditional entropy and subshift covers
• Dynamical systems, filtrations and entropy
• Non-zero Lyapunov exponents and uniform hyperbolicity
• The Pesin entropy formula for diffeomorphisms with dominated splitting
• Entropy-Expansive Maps
• SRB measures as zero-noise limits
• Invariant manifolds
• A generic \(C^1\) expanding map has a singular S-R-B measure
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