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.
Original language | English |
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Pages (from-to) | 3474-3520 |
Number of pages | 47 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 41 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2021 Nov 30 |
Keywords
- Cannon's automatic structure
- Hausdorff dimension
- Patterson-Sullivan measure
- geodesic current
- hyperbolic group
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics