Ergodic properties of equilibrium measures for smooth three dimensional flows

DOI10.4171/CMH/378zbMath1366.37087arXiv1504.00048OpenAlexW3102339652MaRDI QIDQ268281

François Ledrappier, Yuri Lima, Omri M. Sarig

Publication date: 14 April 2016

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.00048

zbMATH Keywords

geodesic flowsymbolic dynamicsMarkov partitionReeb flow

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Orbit growth in dynamical systems (37C35) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Symbolic dynamics (37B10) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (16)

Building thermodynamics for non-uniformly hyperbolic maps ⋮ The K-property for some unique equilibrium states in flows and homeomorphisms ⋮ Invariant family of leaf measures and the Ledrappier–Young property for hyperbolic equilibrium states ⋮ Bernoulli property of subadditive equilibrium states ⋮ Equilibrium states for self‐products of flows and the mixing properties of rank 1 geodesic flows ⋮ Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points ⋮ Properties of equilibrium states for geodesic flows over manifolds without focal points ⋮ On the Bernoulli property for certain partially hyperbolic diffeomorphisms ⋮ Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature ⋮ Symbolic dynamics for three-dimensional flows with positive topological entropy ⋮ Unique equilibrium states for geodesic flows in nonpositive curvature ⋮ On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points ⋮ Measures of maximal entropy on subsystems of topological suspension semiflows ⋮ Measures of maximal entropy for surface diffeomorphisms ⋮ Symbolic dynamics for non-uniformly hyperbolic systems ⋮ Beyond Bowen’s Specification Property

Cites Work

• Unnamed Item
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• Bernoullicity of equilibrium measures on countable Markov shifts
• Bernoulli equilibrium states for surface diffeomorphisms
• Structure of manifolds of nonpositive curvature. I
• Continuity properties of entropy
• Bernoulli flows over maps of the interval
• Anosov flows with Gibbs measures are also Bernoullian
• The ergodic theory of axiom A flows
• Unique ergodicity for horocycle foliations
• Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points
• The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds
• Symbolic dynamics. One-sided, two-sided and countable state Markov shifts
• Propriétés ergodiques des mesures de Sinaï
• Bernoulli shifts with the same entropy are isomorphic
• Factors of Bernoulli shifts are Bernoulli shifts
• Strongly mixing g-measures
• Expansive one-parameter flows
• Geodesic flows are Bernoullian
• The isomorphism theorem for Bernoulli flows
• Markov partitions for Anosov flows on \(n\)-dimensional manifolds
• An inequality for the entropy of differentiable maps
• Bernoulli equilibrium states for axiom A diffeomorphisms
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• On the Bernoulli nature of systems with some hyperbolic structure
• Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems
• [https://portal.mardi4nfdi.de/wiki/Publication:4401805 Principe variationnel et syst�mes dynamiques symboliques]
• Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Thermodynamic formalism for null recurrent potentials

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