Symbolic dynamics for the geodesic flow on locally symmetric orbifolds of rank one
Abstract
Description
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 $Γ\backslash H$, 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 $\R$. 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
16 pages, 4 figures, Lemma 3.1 corrected and corresponding changes in the proof of Proposition 3.3