Existence of SRB measures for hyperbolic maps with weak regularity

DOI10.1080/14689367.2023.2230917arXiv2205.15590OpenAlexW4307225835MaRDI QIDQ6181627

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Publication date: 22 January 2024

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.15590

zbMATH Keywords

modulus of continuityhyperbolic dynamicsweak regularity

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Cites Work

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• Un exemple de transformation dilatante et C¹ par morceaux de l'intervalle, sans probabilité absolument continue invariante
• Ruelle's Operator Theorem and g-Measures
• Most expanding maps have no absolutely continuous invariant measure
• Properties of invariant measures for piecewise expanding one-dimensional transformations with summable oscillations of derivative
• Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’
• Introduction to Dynamical Systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• A generic \(C^1\) expanding map has a singular S-R-B measure
• On Ruelle-Perron-Frobenius operators. I: Ruelle theorem
• On Ruelle-Perron-Frobenius operators. II: Convergence speeds

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