Symbolic dynamics for the geodesic flow on Hecke surfaces

Dieter Mayer, Fredrik Strömberg

Published 2008-01-25Version 1

In this paper we discuss a coding and the associated symbolic dynamics for the geodesic flow on Hecke triangle surfaces. We construct an explicit cross section for which the first return map factors through a simple (explicit) map given in terms of the generating map of a particular continued fraction expansion closely related to the Hecke triangle groups. We also obtain explicit expressions for the associated first return times.