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  • Book
  • © 1993

Symbolic Dynamics and Hyperbolic Groups

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
  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

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.

Keywords

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

Bibliographic Information

  • Book Title: Symbolic Dynamics and Hyperbolic Groups

  • Authors: Michel Coornaert, Athanase Papadopoulos

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0092577

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-56499-7Published: 08 March 1993

  • eBook ISBN: 978-3-540-47573-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 140

  • Topics: Manifolds and Cell Complexes, Analysis, Group Theory and Generalizations

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions