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Article Contents

# Symbolic dynamics for the geodesic flow on Hecke surfaces

• 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.
Mathematics Subject Classification: Primary: 37D40, Secondary: 37E05, 11A55, 11K50.

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