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

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

2008-06-17

arxiv.org/abs/0806.2729v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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