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Symbolic Dynamics and Hyperbolic Groups

  • Book
  • © 1993

Overview

Authors:
  1. Michel Coornaert
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  2. Athanase Papadopoulos
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1539)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Michel Coornaert, Athanase Papadopoulos
    Pages 1-4

  3. A quick review of Gromov hyperbolic spaces

    • Michel Coornaert, Athanase Papadopoulos
    Pages 5-18

  4. Symbolic dynamics

    • Michel Coornaert, Athanase Papadopoulos
    Pages 19-42

  5. The boundary of a hyperbolic group as a finitely presented dynamical system

    • Michel Coornaert, Athanase Papadopoulos
    Pages 43-68

  6. Another finite presentation for the action of a hyperbolic group on its boundary

    • Michel Coornaert, Athanase Papadopoulos
    Pages 69-90

  7. Trees and hyperbolic boundary

    • Michel Coornaert, Athanase Papadopoulos
    Pages 91-106

  8. Semi-Markovian spaces

    • Michel Coornaert, Athanase Papadopoulos
    Pages 107-117

  9. The boundary of a torsion-free hyperbolic group as a semi-Markovian space

    • Michel Coornaert, Athanase Papadopoulos
    Pages 118-134

  10. Back Matter

    Pages 135-138
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Keywords

About this book

Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.

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