Gibbs measures for geodesic flow on CAT(-1) spaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913761207517184 |
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| author | Dilsavor, Caleb Thompson, Daniel J. |
| author_facet | Dilsavor, Caleb Thompson, Daniel J. |
| contents | For a proper geodesically complete CAT(-1) space equipped with a discrete non-elementary action, and a bounded continuous potential with the Bowen property, we construct weighted quasi-conformal Patterson densities and use them to build a Gibbs measure on the space of geodesic lines. Our construction yields a Gibbs measure with local product structure for any potential in this class, which includes bounded Hölder continuous potentials. Furthermore, if the Gibbs measure is finite, then we prove that it is the unique equilibrium state. In contrast to previous results in this direction, we do not require any condition that the potential must take the same value on two geodesic lines which share a common segment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03297 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gibbs measures for geodesic flow on CAT(-1) spaces Dilsavor, Caleb Thompson, Daniel J. Dynamical Systems Metric Geometry 37D40, 37D35, 51F30 For a proper geodesically complete CAT(-1) space equipped with a discrete non-elementary action, and a bounded continuous potential with the Bowen property, we construct weighted quasi-conformal Patterson densities and use them to build a Gibbs measure on the space of geodesic lines. Our construction yields a Gibbs measure with local product structure for any potential in this class, which includes bounded Hölder continuous potentials. Furthermore, if the Gibbs measure is finite, then we prove that it is the unique equilibrium state. In contrast to previous results in this direction, we do not require any condition that the potential must take the same value on two geodesic lines which share a common segment. |
| title | Gibbs measures for geodesic flow on CAT(-1) spaces |
| topic | Dynamical Systems Metric Geometry 37D40, 37D35, 51F30 |
| url | https://arxiv.org/abs/2309.03297 |