Symbolic dynamcis [i.e. dynamics] and hyperbolic groups
By: Michel Coornaert, Athanase Papadopoulos.
Contributors: Papadopoulos, Athanase.
Series: Lecture notes in mathematics ;; 1539; Lecture notes in mathematics (Springer-Verlag) ;; 1539.
Publisher: Springer-Verlag
Published: 1993
Place of publication: Berlin; New York
Language: eng
Number of pages: 138
Subjects: Global differential geometry.; Hyperbolic groups.; Differentiable dynamical systems.; Topological dynamics.
Other titles: Symbolic dynamcis and hyperbolic groups; Symbolic dynamics and hyperbolic groups
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.
Notes: Includes bibliographical references and index.