Symbolic Dynamics and Hyperbolic Groups (Paperback)

Michel Coornaert

ISBN 10: 3540564993 / ISBN 13: 9783540564997

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1993

Paperback. 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. Gromov's theory of hyperbolic groups have had a big impactin combinatorial group theory and has deep connections withmany branches of mathematics suchdifferential geometry,representation theory, ergodic theory and dynamical systems. Particular attention is paid to thedynamical system defined by the action of a hyperbolic groupon its boundary. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783540564997

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.

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.

Dati bibliografici

Titolo: Symbolic Dynamics and Hyperbolic Groups (...
Casa editrice: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
Data di pubblicazione: 1993
Legatura: Paperback
Condizione: new