Regularity of entropy, geodesic currents and entropy at infinity

DOI10.24033/asens.2455zbMath1475.37025arXiv1802.04991OpenAlexW3009890283WikidataQ114042135 ScholiaQ114042135MaRDI QIDQ4994388

Samuel Tapie, Barbara Schapira

Publication date: 18 June 2021

Published in: Annales Scientifiques de l'École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.04991

zbMATH Keywords

entropygeodesic flownegative curvaturegeodesic currentsentropy gapnoncompact dynamicsstrongly positive recurrentvariation of metrics

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) 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) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10)

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\(C^0\)-robustness of topological entropy for geodesic flows ⋮ Escape of entropy for countable Markov shifts ⋮ Ergodic optimization and zero temperature limits in negative curvature ⋮ Ergodicity and equidistribution in Hilbert geometry ⋮ Pressure metrics for deformation spaces of quasifuchsian groups with parabolics ⋮ Pressure at infinity and strong positive recurrence in negative curvature ⋮ Hitchin representations of Fuchsian groups ⋮ Escaping geodesics in Riemannian surfaces with variable negative curvature ⋮ Narrow equidistribution and counting of closed geodesics on noncompact manifolds ⋮ Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations ⋮ Geodesic stretch, pressure metric and marked length spectrum rigidity

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