Topological flows for hyperbolic groups
Dynamical Systems
2023-06-22 v1 Group Theory
Abstract
We show that for every non-elementary hyperbolic group the Bowen-Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of maximal Hausdorff dimension on the boundary square. Applications include a characterization of roughly similar hyperbolic metrics via mean distortion.
Cite
@article{arxiv.1912.03808,
title = {Topological flows for hyperbolic groups},
author = {Ryokichi Tanaka},
journal= {arXiv preprint arXiv:1912.03808},
year = {2023}
}