Existence of measures of maximal entropy for 𝒞^{𝓇} interval maps

DOI10.1090/S0002-9939-2013-12067-8zbMath1290.37020OpenAlexW1521893058MaRDI QIDQ5401677

David Burguet

Publication date: 11 March 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/journals/proc/2014-142-03/S0002-9939-2013-12067-8

zbMATH Keywords

topological entropyinterval mapmaximal measureintrinsically ergodic

Mathematics Subject Classification ID

Topological entropy (37B40) Dynamical systems involving maps of the interval (37E05)

Related Items (4)

Jumps of entropy for C^rinterval maps ⋮ Maximal measure and entropic continuity of Lyapunov exponents for \({\mathcal{C}}^r\) surface diffeomorphisms with large entropy ⋮ Smooth parametrizations in dynamics, analysis, diophantine and computational geometry ⋮ Measures of maximal entropy for surface diffeomorphisms

Cites Work

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• Large entropy implies existence of a maximal entropy measure for interval maps
• Smooth interval maps have symbolic extensions
• Volume growth and entropy
• Continuity properties of entropy
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Intrinsic ergodicity of smooth interval maps
• Mixing \(C^r\) maps of the interval without maximal measure.
• Examples of \({\mathcal C}^r\) interval map with large symbolic extension entropy
• Symbolic extensions in intermediate smoothness on surfaces
• Symbolic extensions for nonuniformly entropy expanding maps
• Thermodynamic formalism for countable symbolic Markov chains
• Topological Entropy Bounds Measure-Theoretic Entropy
• Relating Topological Entropy and Measure Entropy

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