Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds

Anke D. Pohl

doi:10.3934/dcds.2014.34.2173

Article Contents

2014, Volume 34, Issue 5: 2173-2241. Doi: 10.3934/dcds.2014.34.2173

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Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds

Anke D. Pohl^1,

1.
Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3–5, 37073 Göttingen

Received: May 2013

Revised: August 2013

Published: May 2014

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Abstract

We construct cross sections for the geodesic flow on the orbifolds $\Gamma $\$ \mathbb{H}$ which are tailor-made for the requirements of transfer operator approaches to Maass cusp forms and Selberg zeta functions. Here, $\mathbb{H}$ denotes the hyperbolic plane and $\Gamma$ is a nonuniform geometrically finite Fuchsian group (not necessarily a lattice, not necessarily arithmetic) which satisfies an additional condition of geometric nature. The construction of the cross sections is uniform, geometric, explicit and algorithmic.

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Mathematics Subject Classification: Primary: 37D40; Secondary: 37B10, 37C30.

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