The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space.

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...

This book presents a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric group theory and other branches of mathematics and theoretical computer science.

Topological Dimension and Dynamical Systems

This book complements the authors’ monographCellular Automata and Groups[CAG] (Springer Monographs in Mathematics). It consists of more than 500 solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of...