Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

DOI10.1016/j.aim.2020.107452zbMath1464.37042arXiv1903.09831OpenAlexW3096268743WikidataQ124850302 ScholiaQ124850302MaRDI QIDQ2214093

Khadim War, Gerhard Knieper, Vaughn Climenhaga

Publication date: 4 December 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.09831

zbMATH Keywords

geodesic flowmixingconjugate pointmaximal metric entropy

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Geodesics in global differential geometry (53C22) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Topological entropy (37B40) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (12)

Existence and uniqueness of equilibrium states for systems with specification at a fixed scale: an improved Climenhaga–Thompson criterion* ⋮ Closed geodesics on surfaces without conjugate points ⋮ Effective intrinsic ergodicity for countable state Markov shifts ⋮ Geodesic flows modeled by expansive flows: compact surfaces without conjugate points and continuous Green bundles ⋮ Unique ergodicity of the horocycle flow of a higher genus compact surface with no conjugate points and continuous Green bundles ⋮ Anatole Katok ⋮ Properties of equilibrium states for geodesic flows over manifolds without focal points ⋮ Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps ⋮ Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature ⋮ Does the hyperbolicity of periodic orbits of a geodesic flow without conjugate points imply the Anosov property? ⋮ Symbolic dynamics for non-uniformly hyperbolic systems ⋮ Beyond Bowen’s Specification Property

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