2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146630In 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.42 pages, 10 figuresDynamical Systems37D40 (Primary); 37E05,11A55,11K50 (Secondary)text