Typical behaviour along geodesic rays in hyperbolic groups

Stephen Cantrell

Published 2019-06-02Version 1

Let $G$ be a non-elementary hyperbolic group and take a real valued function such as a group homomorphism, quasimorphism or the displacement function associated to the action of $G$ on a hyperbolic metric space. In this paper we study the limiting behaviour of such a function along typical geodesic rays in the Gromov boundary of $G$.