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

Weshow 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
Journal	Ergodic Theory and Dynamical Systems
DOIs	https://doi.org/10.1017/etds.2020.101
Publication status	Accepted/In press - 2020

Keywords

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

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1017/etds.2020.101

Fingerprint Dive into the research topics of 'Topological flows for hyperbolic groups'. Together they form a unique fingerprint.

Cite this

@article{7dc26ff2abb14ddf8db1dd5f385902d7,

title = "Topological flows for hyperbolic groups",

abstract = "Weshow 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",

year = "2020",

doi = "10.1017/etds.2020.101",

language = "English",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Topological flows for hyperbolic groups

AU - Tanaka, Ryokichi

PY - 2020

Y1 - 2020

N2 - Weshow 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.

AB - Weshow 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.

KW - Cannon's automatic structure

KW - Hausdorff dimension

KW - Patterson-Sullivan measure

KW - geodesic current

KW - hyperbolic group

UR - http://www.scopus.com/inward/record.url?scp=85095806556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85095806556&partnerID=8YFLogxK

U2 - 10.1017/etds.2020.101

DO - 10.1017/etds.2020.101

M3 - Article

AN - SCOPUS:85095806556

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

ER -

Topological flows for hyperbolic groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this