Automorphic forms for infinite-area hyperbolic surfaces

Since several years it is known that certain discretizations for the geodesic flow on hyperbolic surfaces of finite area allow to provide a dynamical characterizations of Maass cusp forms and a dynamical construction of their period functions. An important ingredient for these results is the characterization of Laplace eigenfunctions in parabolic cohomology by Bruggeman--Lewis--Zagier. 

We discuss an extension of these results to Hecke triangle surfaces of infinite area and automorphic forms that are more general than Maass cusp forms. This is joint work with R. Bruggeman.