Symbolic Dynamics and Hyperbolic Groups

ISBN-13: 9783540564997 / Angielski / Miękka / 1993 / 140 str.

M. Coornaert; Michel Coornaert; Athanase Papadopoulos

Opis

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.

Spis treści

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.