Symbolic coding for the geodesic flow associated to a word hyperbolic group

Abstract

Let Γ be a word hyperbolic group M. Gromov has constructed a compact space \(\) equipped with a flow which is defined up to orbit-equivalence and which is called the geodesic flow of Γ. In the special case where Γ is the fundamental group of a Riemannian manifold of negative sectional curvature, \(\) is the unit tangent bundle of the manifold equipped with the usual geodesic flow. In this paper, we construct, for every hyperbolic group Γ, a subshift of finite type and a continuous map from the suspension of this subshift onto \(\), which is uniformly bounded-to-one and which sends each orbit of the suspension flow onto an orbit of the geodesic flow.