# American Institute of Mathematical Sciences

October  2008, 2(4): 581-627. doi: 10.3934/jmd.2008.2.581

## Symbolic dynamics for the geodesic flow on Hecke surfaces

 1 Institut für Theoretische Physik, Technische Universität Clausthal, Abteilung Statistische Physik und Nichtlineare Dynamik, Arnold Sommerfeld Straße 6, 38678 Clausthal–Zellerfeld, Germany 2 Fachbereich Mathematik, AG AGF,, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany

Received  January 2008 Revised  June 2008 Published  October 2008

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.
Citation: Dieter Mayer, Fredrik Strömberg. Symbolic dynamics for the geodesic flow on Hecke surfaces. Journal of Modern Dynamics, 2008, 2 (4) : 581-627. doi: 10.3934/jmd.2008.2.581
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