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

Symbolic dynamics for the geodesic flow on Hecke surfaces

Dieter Mayer 1, and  Fredrik Strömberg 2,

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.
Keywords: symbolic dynamics, Hecke triangle groups, continued fractions, geodesic flow.
Mathematics Subject Classification: Primary: 37D40, Secondary: 37E05, 11A55, 11K50.
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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