Groups, Geometry, and Dynamics

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Volume 2, Issue 2, 2008, pp. 165–184

DOI: 10.4171/GGD/35

Symbolic dynamics and relatively hyperbolic groups

François Dahmani (1) and Asli Yaman (2)

(1) Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062, TOULOUSE CEDEX 9, FRANCE
(2) Centre de Recerca Matemàtica, Apartat 50, E-08193, BELLATERRA, SPAIN

We study the action of a relatively hyperbolic group on its boundary by methods of symbolic dynamics. We show that this dynamical system is expansive, and, under a condition on parabolic subgroups (satisfied in most examples), that it is finitely presented, meaning that it can be factorized through a subshift of finite type.

Keywords: Relatively hyperbolic groups, symbolic dynamics