Symbolic coding for the geodesic flow associated to a word hyperbolic group.
type: Item
instance of: scholarly article
title: Symbolic coding for the geodesic flow associated to a word hyperbolic group.
zbMATH Open document ID: 1045.20036
author: Michel Coornaert
author: Athanase Papadopoulos
published in: Manuscripta Mathematica
publication date: 2003-03-27T00:00:00Z
full work available at URL: http://cds.cern.ch/record/428423
review text: The article continues studies of codings of geodesic flows of Riemannian manifolds. Relations with dynamical systems are outlined. On a space of geodesic flows (local) a structure of a word hyperbolic group is used. Definitions and proofs are given in details. It is shown that a word hyperbolic group acts properly discontinuously on a dynamical system. The main result of the paper is the following Theorem 0.1. Let \(\Gamma\) be a word hyperbolic group. Then there exists a two-sided subshift of finite type \((\Sigma,T)\) and a continuous mapping from the suspension \(\text{Susp}(\Sigma,T)\) of this subshift onto \(\overline G(\Gamma)\), which is uniformly bounded-to-one and which sends each orbit of the suspension flow onto an orbit of the geodesic flow. It is necessary to note that the word hyperbolic group has embedding into the group of isometries.
Mathematics Subject Classification ID: 20F67
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F69
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1889171
zbMATH Keywords: geodesic flows
zbMATH Keywords: word hyperbolic groups
zbMATH Keywords: codings
reviewed by: Sergey V. Ludkovsky
MaRDI profile type: Publication
OpenAlex ID: W2045057737
DOI: 10.1007/S00229-002-0321-9
description: scientific article; zbMATH DE number 1889171