Empirical measures of partially hyperbolic attractors

DOI10.1007/s00220-019-03668-1OpenAlexW2998621556MaRDI QIDQ1986585

Sylvain Crovisier, Jinhua Zhang, Da-Wei Yang

Publication date: 8 April 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12472

zbMATH Keywords

large deviationsSRB measurespartially hyperbolic attractor

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (19)

GEOMETRICAL AND MEASURE-THEORETIC STRUCTURES OF MAPS WITH A MOSTLY EXPANDING CENTER ⋮ Abundance of observable Lyapunov irregular sets ⋮ On the abundance of Sinai-Ruelle-Bowen measures ⋮ Non-statistical rational maps ⋮ Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers ⋮ Topological transitivity of Kan-type partially hyperbolic diffeomorphisms ⋮ On multifractal analysis and large deviations of singular hyperbolic attractors ⋮ Persistent non-statistical dynamics in one-dimensional maps ⋮ Physical measures for ash attractors ⋮ Volume growth and topological entropy of partially hyperbolic systems ⋮ On the number of ergodic physical/SRB measures of singular-hyperbolic attracting sets ⋮ Physical measures for partially hyperbolic flows with mostly contracting centre ⋮ Entropy along expanding foliations ⋮ The dynamics of vector fields with singularities ⋮ Lyapunov exponents for random maps ⋮ Unstable entropy in smooth ergodic theory ^* ⋮ Historic behaviour vs. physical measures for irrational flows with multiple stopping points ⋮ Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability ⋮ Statistical properties of physical-like measures*

Cites Work

• Unnamed Item
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• On Pesin's entropy formula for dominated splittings without mixed behavior
• Existence and uniqueness of SRB measure on \(C^1\) generic hyperbolic attractors
• Quadratic maps without asymptotic measure
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Nonabsolutely continuous foliations for an Anosov diffeomorphism
• Stable ergodicity and julienne quasi-conformality
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• Formula of entropy along unstable foliations for \(C^1\) diffeomorphisms with dominated splitting
• Unstable entropies and variational principle for partially hyperbolic diffeomorphisms
• A \(C^1\) Anosov diffeomorphism with a horseshoe that attracts almost any point
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Decay of correlations
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Entropy along expanding foliations
• Propriétés ergodiques des mesures de Sinaï
• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• SRB measures for partially hyperbolic systems whose central direction is weakly expanding
• SRB-like Measures for C⁰Dynamics
• Approximation by Brownian motion for Gibbs measures and flows under a function
• A proof of the estimation from below in Pesin's entropy formula
• Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
• Gibbs measures for partially hyperbolic attractors
• An inequality for the entropy of differentiable maps
• A proof of Pesin's formula
• A Measure Associated with Axiom-A Attractors
• Heteroclinic attractors: Time averages and moduli of topological conjugacy
• Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin
• Limit theorems for partially hyperbolic systems
• SRB measures for higher dimensional singular partially hyperbolic attractors
• Measure-theoretical properties of center foliations
• A new criterion of physical measures for partially hyperbolic diffeomorphisms
• The Pesin entropy formula for diffeomorphisms with dominated splitting
• Orbits with historic behaviour, or non-existence of averages
• LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS
• GIBBS MEASURES IN ERGODIC THEORY
• SRB measures as zero-noise limits
• A generic \(C^1\) expanding map has a singular S-R-B measure

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