Symbolic dynamics for the geodesic flow on Hecke surfaces

Dieter Mayer; Fredrik Strömberg

doi:10.3934/jmd.2008.2.581

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2008, Volume 2, Issue 4: 581-627. Doi: 10.3934/jmd.2008.2.581

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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
2.
Fachbereich Mathematik, AG AGF,, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt

Received: January 2008

Revised: June 2008

Published: September 2008

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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.

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

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