[Papers]
[Alex Furman]

Some ergodic properties for metrics on hyperbolic groups

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 $\partial\Gamma$, 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 $(\partial^{(2)}\Gamma,[\nu\times\nu])$.

Authors:
U. Bader,
A. Furman,

Bibliographical:

Download: pdf |
arXiv:1707.02020

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[Papers]
[Alex Furman]