A global shadow lemma and logarithm law for geometrically finite Hilbert geometries
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913758017748992 |
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| author | Bray, Harrison Tiozzo, Giulio |
| author_facet | Bray, Harrison Tiozzo, Giulio |
| contents | For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-Sullivan measures, as well as a Dirichlet-type theorem and a logarithm law for excursion of geodesics into cusps. We then apply these results to geometrically finite quotients of strictly convex Hilbert geometries with C^1 boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04618 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A global shadow lemma and logarithm law for geometrically finite Hilbert geometries Bray, Harrison Tiozzo, Giulio Dynamical Systems 37D40 For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-Sullivan measures, as well as a Dirichlet-type theorem and a logarithm law for excursion of geodesics into cusps. We then apply these results to geometrically finite quotients of strictly convex Hilbert geometries with C^1 boundary. |
| title | A global shadow lemma and logarithm law for geometrically finite Hilbert geometries |
| topic | Dynamical Systems 37D40 |
| url | https://arxiv.org/abs/2111.04618 |