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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 geodesicsconstitute a $k$-step topological Markov chain, if and only if the fundamentaldomain $D$ is an ideal polygon i.e. has all of its vertices on the absolute.



Author: Arseny Egorov

Source: https://arxiv.org/



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