Otal-Peigné's Theorem for Gromov-hyperbolic spaces

Fuente: arXiv
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Main Author: Cavallucci, Nicola
Format: Preprint
Published: 2024
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author Cavallucci, Nicola
author_facet Cavallucci, Nicola
contents We extend the classical Otal-Peigné's Theorem to the class of proper, Gromov-hyperbolic spaces that are line-convex. Namely, we prove that when a group acts discretely and virtually freely by isometries on a metric space in this class then its critical exponent equals the topological entropy of the geodesic flow of the quotient metric space. We also show examples of proper, Gromov-hyperbolic spaces that are not line-convex and for which the statement fails.
format Preprint
id arxiv_https___arxiv_org_abs_2412_10801
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Otal-Peigné's Theorem for Gromov-hyperbolic spaces
Cavallucci, Nicola
Metric Geometry
Differential Geometry
Dynamical Systems
37D40, 53C23
We extend the classical Otal-Peigné's Theorem to the class of proper, Gromov-hyperbolic spaces that are line-convex. Namely, we prove that when a group acts discretely and virtually freely by isometries on a metric space in this class then its critical exponent equals the topological entropy of the geodesic flow of the quotient metric space. We also show examples of proper, Gromov-hyperbolic spaces that are not line-convex and for which the statement fails.
title Otal-Peigné's Theorem for Gromov-hyperbolic spaces
topic Metric Geometry
Differential Geometry
Dynamical Systems
37D40, 53C23
url https://arxiv.org/abs/2412.10801