Some ergodic properties of metrics on hyperbolic groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2017
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| Acceso en línea: | |
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| _version_ | 1866914594910371840 |
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| author | Bader, Uri Furman, Alex |
| author_facet | Bader, Uri Furman, Alex |
| contents | Let $Γ$ be a non-elementary Gromov-hyperbolic group, and $\partial Γ$ denote its Gromov boundary. We consider $Γ$-invariant proper $δ$-hyperbolic, quasi-convex metric $d$ on $Γ$, and the associated Patterson-Sullivan measure class $[ν]$ on $\partial^{(2)}Γ$, and its square $[ν\timesν]$ on $\partial^{(2)}Γ$ -- the space of distinct pairs of points on the boundary. We construct an analogue of a geodesic flow to study ergodicity properties of the $Γ$-actions on $(\partialΓ,ν)$ and on $(\partial^{(2)}Γ,[ν\timesν])$. We also prove some ergodic theorems for $Γ$-actions guided by the geometry of $(Γ,d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_02020 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Some ergodic properties of metrics on hyperbolic groups Bader, Uri Furman, Alex Dynamical Systems 37Axx, 37Dxx Let $Γ$ be a non-elementary Gromov-hyperbolic group, and $\partial Γ$ denote its Gromov boundary. We consider $Γ$-invariant proper $δ$-hyperbolic, quasi-convex metric $d$ on $Γ$, and the associated Patterson-Sullivan measure class $[ν]$ on $\partial^{(2)}Γ$, and its square $[ν\timesν]$ on $\partial^{(2)}Γ$ -- the space of distinct pairs of points on the boundary. We construct an analogue of a geodesic flow to study ergodicity properties of the $Γ$-actions on $(\partialΓ,ν)$ and on $(\partial^{(2)}Γ,[ν\timesν])$. We also prove some ergodic theorems for $Γ$-actions guided by the geometry of $(Γ,d)$. |
| title | Some ergodic properties of metrics on hyperbolic groups |
| topic | Dynamical Systems 37Axx, 37Dxx |
| url | https://arxiv.org/abs/1707.02020 |