Symbolic Dynamics and Hyperbolic Groups (Lecture Notes in Mathematics): 1539 - Brossura

Coornaert, Michel

Brossura

ISBN 10: 3540564993 ISBN 13: 9783540564997

Casa editrice: Springer, 1993

Riassunto

Gromov's theory of hyperbolic groups has had a big impact on combinatorial group theory and has connections with such branches of mathematics as differential geometry, representation theory, ergodic theory and dynamical systems. This book elaborates on some of Gromov's ideas on hyperbolic spaces and hyperbolic groups in relation to 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 often chaotic, both as a topological space and as a dynamical system, and a description of this boundary and its 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 on symbolic dynamics.

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Contenuti

A quick review of Gromov hyperbolic spaces.- Symbolic dynamics.- The boundary of a hyperbolic group as a finitely presented dynamical system.- Another finite presentation for the action of a hyperbolic group on its boundary.- Trees and hyperbolic boundary.- Semi-Markovian spaces.- The boundary of a torsion-free hyperbolic group as a semi-Markovian space.

Product Description

Book by Coornaert Michel Papadopoulos Athanase

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 3540564993
• ISBN 13: 9783540564997
• Rilegatura: Copertina flessibile
• Numero di pagine: 148
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania