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Some ergodic properties of metrics on hyperbolic groups
- Publication Year :
- 2017
-
Abstract
- Let $\Gamma$ be a non-elementary Gromov-hyperbolic group, and $\partial \Gamma$ denote its Gromov boundary. We consider $\Gamma$-invariant proper $\delta$-hyperbolic, quasi-convex metric $d$ on $\Gamma$, and the associated Patterson-Sullivan measure class $[\nu]$ on $\partial^{(2)}\Gamma$, and its square $[\nu\times\nu]$ on $\partial^{(2)}\Gamma$ -- the space of distinct pairs of points on the boundary. We construct an analogue of a geodesic flow to study ergodicity properties of the $\Gamma$-actions on $(\partial\Gamma,\nu)$ and on $(\partial^{(2)}\Gamma,[\nu\times\nu])$.<br />Comment: minor corrections in the introduction, typos
- Subjects :
- Mathematics - Dynamical Systems
37Axx, 37Dxx
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1707.02020
- Document Type :
- Working Paper