Counting closed geodesics in a compact rank-one locally CAT(0) space

DOI10.1017/etds.2021.83zbMath1490.37045arXiv1903.07635OpenAlexW3196815945WikidataQ114118689 ScholiaQ114118689MaRDI QIDQ5027317

Russell Ricks

Publication date: 4 February 2022

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.07635

zbMATH Keywords

entropynon-positive curvatureclassical ergodic theory

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Geodesics in global differential geometry (53C22) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (1)

Closed geodesics on surfaces without conjugate points

Cites Work

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• Boundaries and JSJ decompositions of \(\text{CAT}(0)\)-groups.
• The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds
• Unique equilibrium states for geodesic flows in nonpositive curvature
• The unique measure of maximal entropy for a compact rank one locally CAT(0) space
• Equidistribution and counting of orbit points for discrete rank one isometry groups of Hadamard spaces
• On the Patterson-Sullivan measure for geodesic flows on rank 1 manifolds without focal points
• Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces
• Ergodicité et équidistribution en courbure négative

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