TY  - BOOK
AU  - Coornaert,Michel
AU  - Papadopoulos,Athanase
ED  - SpringerLink (Online service)
TI  - Symbolic Dynamics and Hyperbolic Groups
T2  - Lecture Notes in Mathematics,
SN  - 9783540475736
AV  - QA613-613.8 
U1  - 514.34 23
PY  - 1993///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Group theory
KW  - Global analysis (Mathematics)
KW  - Cell aggregation
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Analysis
KW  - Group Theory and Generalizations
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0092577
ER  -