Patterson-Sullivan theory for coarse cocycles
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914898625167360 |
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| author | Blayac, Pierre-Louis Canary, Richard Zhu, Feng Zimmer, Andrew |
| author_facet | Blayac, Pierre-Louis Canary, Richard Zhu, Feng Zimmer, Andrew |
| contents | In this paper we develop a theory of Patterson--Sullivan measures associated to coarse cocycles of convergence groups. This framework includes Patterson-Sullivan measures associated to the Busemann cocycle on the geodesic boundary of a Gromov hyperbolic metric spaces and Patterson-Sullivan measures on flag manifolds associated to Anosov (or more general transverse) subgroups of semisimple Lie groups, as well as more examples. Under some natural geometric assumptions on the coarse cocycle, we prove existence, uniqueness, and ergodicity results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Patterson-Sullivan theory for coarse cocycles Blayac, Pierre-Louis Canary, Richard Zhu, Feng Zimmer, Andrew Dynamical Systems Differential Geometry Geometric Topology In this paper we develop a theory of Patterson--Sullivan measures associated to coarse cocycles of convergence groups. This framework includes Patterson-Sullivan measures associated to the Busemann cocycle on the geodesic boundary of a Gromov hyperbolic metric spaces and Patterson-Sullivan measures on flag manifolds associated to Anosov (or more general transverse) subgroups of semisimple Lie groups, as well as more examples. Under some natural geometric assumptions on the coarse cocycle, we prove existence, uniqueness, and ergodicity results. |
| title | Patterson-Sullivan theory for coarse cocycles |
| topic | Dynamical Systems Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2404.09713 |