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arXiv · 0910.4566

Morse coding for a Fuchsian group of a finite covolume

Arseny Egorov
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Abstract

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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Arseny Egorov. 2009-10-23. Morse coding for a Fuchsian group of a finite covolume. https://doi.org/10.3934/jmd.2009.3.637

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