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.
Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
On the generalised transfer operators of the Farey map with complex temperature
Selberg zeta functions, cuspidal accelerations, and existence of strict transfer operator approaches
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