Symbolic Dynamics and Hyperbolic Groups

  • Authors
  • Michel¬†Coornaert
  • Athanase¬†Papadopoulos

Part of the Lecture Notes in Mathematics book series (LNM, volume 1539)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Michel Coornaert, Athanase Papadopoulos
    Pages 1-4
  3. Michel Coornaert, Athanase Papadopoulos
    Pages 5-18
  4. Michel Coornaert, Athanase Papadopoulos
    Pages 19-42
  5. Michel Coornaert, Athanase Papadopoulos
    Pages 43-68
  6. Michel Coornaert, Athanase Papadopoulos
    Pages 69-90
  7. Michel Coornaert, Athanase Papadopoulos
    Pages 91-106
  8. Michel Coornaert, Athanase Papadopoulos
    Pages 107-117
  9. Michel Coornaert, Athanase Papadopoulos
    Pages 118-134
  10. Back Matter
    Pages 135-138

About this book

Introduction

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.

Keywords

Dynamical system Fundamental theorem of calculus Gromov hyperbolic space Group theory Representation theory combinatorial groups hyperbolic group symbolic dynamics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092577
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56499-7
  • Online ISBN 978-3-540-47573-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book