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Symbolic Dynamics and Hyperbolic Groups : Orbis Biblicus Et Orientalis, - Michel Coornaert

Symbolic Dynamics and Hyperbolic Groups

Orbis Biblicus Et Orientalis,

Paperback Published: 8th March 1993
ISBN: 9783540564997
Number Of Pages: 140

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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.This book is an elaboration on some ideas of Gromov onhyperbolic spaces and hyperbolic groups in relation withsymbolic dynamics. Particular attention is paid to thedynamical system defined by the action of a hyperbolic groupon its boundary. The boundary is most oftenchaotic both asa topological space and as a dynamical system, and adescription of this boundary and the action is given interms of subshifts of finite type.The book is self-contained and includes two introductorychapters, one on Gromov's hyperbolic geometry and the otherone on symbolic dynamics. It is intended for students andresearchers in geometry and in dynamical systems, and can beused asthe basis for a graduate course on these subjects.

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.

ISBN: 9783540564997
ISBN-10: 3540564993
Series: Orbis Biblicus Et Orientalis,
Audience: General
Format: Paperback
Language: English
Number Of Pages: 140
Published: 8th March 1993
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.81
Weight (kg): 0.22