Topological flows for hyperbolic groups

Topological flows for hyperbolic groups

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 hyperbol...

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Veröffentlicht in:Ergodic theory and dynamical systems 2021-11, Vol.41 (11), p.3474-3520
1. Verfasser: TANAKA, RYOKICHI
Format: Artikel
Sprache:eng
Schlagworte:
Entropy
Original Article
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Beschreibung
Zusammenfassung: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2020.101