Otal-Peigné's Theorem for Gromov-hyperbolic spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912156432203776 |
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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 |