Topological flows for hyperbolic groups

  title={Topological flows for hyperbolic groups},
  author={Ryokichi Tanaka},
  journal={Ergodic Theory and Dynamical Systems},
  pages={3474 - 3520}
  • Ryokichi Tanaka
  • Published 9 December 2019
  • Mathematics
  • Ergodic Theory and Dynamical Systems
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. 
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