  We present a strategy for a geometric construction of cross sections for the
geodesic flow on locally symmetric orbifolds of rank one. We work it out in
detail for $\Gamma\backslash H$, where $H$ is the upper half plane and
$\Gamma=\PGamma_0(p)$, $p$ prime. Its associated discrete dynamical system
naturally induces a symbolic dynamics on $\R$. The transfer operator produced
from this symbolic dynamics has a particularly simple structure.
