Symbolic dynamics and hyperbolic groups
type: Item
instance of: scholarly article
title: Symbolic dynamics and hyperbolic groups
zbMATH Open document ID: 0783.58017
author: Michel Coornaert
author: Athanase Papadopoulos
published in: Lecture Notes in Mathematics
publication date: 1993-03-31T00:00:00Z
review text: The book explains aspects of Gromov's theory of hyperbolic spaces and hyperbolic groups from the point of view of symbolic dynamics. Symbolic dynamics is a way of topologically describing a dynamical system by semi- conjugating it to a subshift of finite type. Depending on the properties of this semi-conjugacy one can classify the dynamical system as being of finite type, or finitely presented, etc. In any case a combinatorial model of the dynamics is provided. The dynamical system studied in the book is a hyperbolic group acting on its own hyperbolic boundary. Two direct constructions of symbolic dynamics are provided which make this a finitely presented dynamical system. This description is later used to obtain a combinatorial model of the hyperbolic boundary (of a torsion- free hyperbolic group) as a so-called semi-Markovian space. The book provides a careful and complete account of a part of a vigorously developing subject. A summary of Gromov's theory of hyperbolic spaces is provided, as well as a summary of facts about symbolic dynamics. This way, the book should be accessible to a geometer eager to learn how the formalism of symbolic dynamics works, as well as to a dynamicist interested in hyperbolic groups.
reviewed by: Grzegorz Świątek
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 58-02
zbMATH DE Number: 146166
zbMATH Keywords: finitely presented system
zbMATH Keywords: hyperbolic spaces
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: subshift of finite type
zbMATH Keywords: Gromov's theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0092577
OpenAlex ID: W4205459534
DOI: 10.1007/BFB0092577
description: scientific article; zbMATH DE number 146166