Journal of Modern Dynamics (JMD)

Symbolic dynamics for the geodesic flow on Hecke surfaces

Pages: 581 - 627, Issue 4, October 2008      doi:10.3934/jmd.2008.2.581

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Dieter Mayer - Institut für Theoretische Physik, Technische Universität Clausthal, Abteilung Statistische Physik und Nichtlineare Dynamik, Arnold Sommerfeld Straße 6, 38678 Clausthal–Zellerfeld, Germany (email)
Fredrik Strömberg - Fachbereich Mathematik, AG AGF,, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany (email)

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

Received: January 2008;      Revised: June 2008;      Available Online: October 2008.