Topological flows for hyperbolic groups

Ryokichi Tanaka

doi:10.1017/etds.2020.101

Topological flows for hyperbolic groups

Ryokichi Tanaka

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	3474-3520
Number of pages	47
Journal	Ergodic Theory and Dynamical Systems
Volume	41
Issue number	11
DOIs	https://doi.org/10.1017/etds.2020.101
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

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10.1017/etds.2020.101

Cite this

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title = "Topological flows for hyperbolic groups",

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.",

keywords = "Cannon's automatic structure, Hausdorff dimension, Patterson-Sullivan measure, geodesic current, hyperbolic group",

author = "Ryokichi Tanaka",

note = "Publisher Copyright: {\textcopyright} 2020 The Author(s). Published by Cambridge University Press.",

year = "2021",

month = nov,

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KW - Cannon's automatic structure

KW - Hausdorff dimension

KW - Patterson-Sullivan measure

KW - geodesic current

KW - hyperbolic group

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Topological flows for hyperbolic groups

Abstract

Keywords

ASJC Scopus subject areas

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