## Journals

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JMD

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.

DCDS

In this paper we extend the transfer operator approach to Selberg's zeta function for cofinite
Fuchsian groups to the Hecke triangle groups $G_q,\, q=3,4,\ldots$, which are non-arithmetic for
$q\not= 3,4,6$. For this we make use of a Poincar\'e map for the geodesic flow on the corresponding
Hecke surfaces, which has been constructed in [13], and which is closely related to the natural extension of the generating map for the
so-called Hurwitz-Nakada continued fractions.
We also derive functional equations for the eigenfunctions of the transfer operator which for
eigenvalues $\rho =1$ are expected to be closely related to the period functions of Lewis and Zagier
for these Hecke triangle groups.

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