Morse coding for a Fuchsian group of a finite covolume

Details Morse coding for a Fuchsian group of a finite covolume Morse coding for a Fuchsian group of a finite covolume

2009-10-23

arxiv.org/abs/0910.4566v1

Journal of Modern Dynamics, vol. 3 (2009), no.4, 637-646

Mathematics

Dynamical Systems

11 pages, 4 figures

Scientific paper

10.3934/jmd.2009.3.637

We consider the Morse coding of the geodesic flow on the hyperbolic plane $H$
with respect to a Dirichlet fundamental domain $D$ of a Fuchsian group
$\Gamma$. The main theorem states that the codes of all the generic geodesics
constitute a $k$-step topological Markov chain, if and only if the fundamental
domain $D$ is an ideal polygon (i.e. has all of its vertices on the absolute).

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