Author : Michel Coornaert
Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 737/5 ( reviews)

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Book Synopsis Symbolic Dynamics and Hyperbolic Groups by : Michel Coornaert

Download or read book Symbolic Dynamics and Hyperbolic Groups written by Michel Coornaert. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.