Symbolic coding for the geodesic flow associated to a word hyperbolic group.
The article continues studies of codings of geodesic flows of Riemannian manifolds. Relations with dynamical systems are outlined. On a space of geodesic flows (local) a structure of a word hyperbolic group is used. Definitions and proofs are given in details. It is shown that a word hyperbolic group acts properly discontinuously on a dynamical system. The main result of the paper is the following Theorem 0.1. Let \(\Gamma\) be a word hyperbolic group. Then there exists a two-sided subshift of finite type \((\Sigma,T)\) and a continuous mapping from the suspension \(\text{Susp}(\Sigma,T)\) of this subshift onto \(\overline G(\Gamma)\), which is uniformly bounded-to-one and which sends each orbit of the suspension flow onto an orbit of the geodesic flow. It is necessary to note that the word hyperbolic group has embedding into the group of isometries.
scientific article; zbMATH DE number 1889171