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Full Description
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.
Contents
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.
