Symbolic dynamics for the geodesic flow on Hecke surfaces

Abstract

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