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A Thermodynamic Formalism Approach to the Selberg Zeta Function for Hecke Triangle Surfaces of Infinite Area

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Abstract

We provide an explicit construction of a cross section for the geodesic flow on infinite-area Hecke triangle surfaces, which allows us to conduct a transfer operator approach to the Selberg zeta function. Further, we construct closely related cross sections for the billiard flow on the associated triangle surfaces and endow the arising discrete dynamical systems and transfer operator families with two weight functions, which presumably encode Dirichlet respectively Neumann boundary conditions. The Fredholm determinants of these transfer operator families constitute dynamical zeta functions, which provide a factorization of the Selberg zeta function of the Hecke triangle surfaces.

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

    Anke D. Pohl

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Communicated by S. Zelditch

The author acknowledges the support by the Volkswagen Foundation.

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Pohl, A.D. A Thermodynamic Formalism Approach to the Selberg Zeta Function for Hecke Triangle Surfaces of Infinite Area. Commun. Math. Phys. 337, 103–126 (2015). https://doi.org/10.1007/s00220-015-2304-1

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