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
Ξ. 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).Comment: 11 pages, 4 figure