Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds
Anke D. Pohl
Discrete & Continuous Dynamical Systems - A 2014, 34(5): 2173-2241 doi: 10.3934/dcds.2014.34.2173
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.
keywords: cross section orbifolds. transfer operator geodesic flow Symbolic dynamics
A dynamical approach to Maass cusp forms
Anke D. Pohl
Journal of Modern Dynamics 2012, 6(4): 563-596 doi: 10.3934/jmd.2012.6.563
For nonuniform cofinite Fuchsian groups $\Gamma$ that satisfy a certain additional geometric condition, we show that the Maass cusp forms for $\Gamma$ are isomorphic to $1$-eigenfunctions of a finite-term transfer operator. The isomorphism is constructive.
keywords: geodesic flow. symbolic dynamics Maass cusp forms period functions transfer operator

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