Symbolic dynamics for the geodesic flow on locally symmetric orbifolds of rank one

Abstract

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 $Γ=\PGamma_0(p)$, $p$ prime. Its associated discrete dynamical system naturally induces a symbolic dynamics on $\mathbb{R}$. The transfer operator produced from this symbolic dynamics has a particularly simple structure.

16 pages, 4 figures, Lemma 3.1 corrected and corresponding changes in the proof of Proposition 3.3