Equilibrium states and SRB-like measures of \(C^1\)-expanding maps of the circle

DOI10.4171/PM/1913zbMath1405.37042arXiv1202.6584MaRDI QIDQ692858

Heber Enrich, Eleonora Catsigeras

Publication date: 6 December 2012

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.6584

zbMATH Keywords

equilibrium statesergodic theorySRB measuresPesin's entropy formulaphysical measures

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical systems involving maps of the circle (37E10)

Related Items (5)

Pesin's entropy formula for \(C^1\) non-uniformly expanding maps ⋮ Empiric Stochastic Stability of Physical and Pseudo-physical Measures ⋮ On Ilyashenko’s statistical attractors ⋮ Invariant measures for typical continuous maps on manifolds ⋮ Lower bound in Pesin formula of C ¹ interval maps*

Cites Work

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• The Lyapunov exponents of generic volume-preserving and symplectic maps
• Physical measures at the boundary of hyperbolic maps
• Examples of expanding \(C^1\) maps having no \(\sigma\)-finite invariant measure equivalent to Lebesgue
• Semicontinuity of entropy, existence of equilibrium states and continuity of physical measures
• Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure
• SRB-like Measures for C⁰Dynamics
• Relations between natural and observable measures
• Multicomponent dynamical systems: SRB measures and phase transitions
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• A generic \(C^1\) expanding map has a singular S-R-B measure

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