# Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group

Document Type : Original Article

Author

Faculty of Mathematical Sciences, University of Guilan, P.O.Box 1914, Rasht, Iran.

Abstract

The Hecke group $G_\alpha$ is a family of discrete sub-groups of
$PSL(2,\,\mathbb{R})$. The quotient space of the action of
$G_\alpha$ on the upper half plane gives a Riemann surface. The
geodesic flows on this surface are ergodic. Here, by constructing
a phase space for the geodesic flows hitting an appropriate cross
section, we find the arithmetic code of these flows and show
that their code space is a topological Markov chain.

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