Symbolic dynamics for the geodesic flow on Hecke surfaces

Details Symbolic dynamics for the geodesic flow on Hecke surfaces Symbolic dynamics for the geodesic flow on Hecke surfaces

2008-01-25

arxiv.org/abs/0801.3951v1

Mathematics

Dynamical Systems

42 pages, 10 figures

Scientific paper

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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