A note on partially hyperbolic attractors: entropy conjecture and SRB measures

DOI10.3934/dcds.2015.35.341zbMath1351.37138OpenAlexW2091260494MaRDI QIDQ479978

Kening Lu, Pei-Dong Liu

Publication date: 8 December 2014

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

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.341

zbMATH Keywords

random perturbationsSRB measuresentropy conjecturepartially hyperbolic attractors

Mathematics Subject Classification ID

Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (9)

On the abundance of Sinai-Ruelle-Bowen measures ⋮ SRB measures for a class of partially hyperbolic attractors in Hilbert spaces ⋮ On Pesin's entropy formula for dominated splittings without mixed behavior ⋮ The entropy conjecture for dominated splitting with multi 1D centers via upper semi-continuity of the metric entropy ⋮ Random Gibbs \(u\)-state for partially hyperbolic on fibers system ⋮ SRB measures for attractors with continuous invariant splittings ⋮ A forward ergodic closing lemma and the entropy conjecture for nonsingular endomorphisms away from tangencies ⋮ Random entropy expansiveness for diffeomorphisms with dominated splittings ⋮ Lower bound in Pesin formula of C ¹ interval maps*

Cites Work

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• The entropy conjecture for diffeomorphisms away from tangencies
• Estimates of the topological entropy from below for continuous self-maps on some compact manifolds
• The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Entropy formula for random transformations
• Volume growth and entropy
• A remark on the topological entropy of homeomorphisms
• Currents, flows and diffeomorphisms
• Entropy and stability
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• On differentiability of SRB states for partially hyperbolic systems
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Dynamics of random transformations: smooth ergodic theory
• Gibbs measures for partially hyperbolic attractors
• An inequality for the entropy of differentiable maps
• Dynamical systems, filtrations and entropy
• Topological conditional entropy
• Generating partitions for random transformations
• Entropy-Expansive Maps
• SRB measures as zero-noise limits

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