Topological flows for hyperbolic groups

Ryokichi Tanaka

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)3474-3520
Number of pages47
JournalErgodic Theory and Dynamical Systems
Issue number11
Publication statusPublished - 2021 Nov 30


  • Cannon's automatic structure
  • Hausdorff dimension
  • Patterson-Sullivan measure
  • geodesic current
  • hyperbolic group

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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