  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.
