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.
Lamei, S. (2016). Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group. Khayyam Journal of Mathematics, 2(2), 168-176. doi: 10.22034/kjm.2016.41250
MLA
Sanaz Lamei. "Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group". Khayyam Journal of Mathematics, 2, 2, 2016, 168-176. doi: 10.22034/kjm.2016.41250
HARVARD
Lamei, S. (2016). 'Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group', Khayyam Journal of Mathematics, 2(2), pp. 168-176. doi: 10.22034/kjm.2016.41250
VANCOUVER
Lamei, S. Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group. Khayyam Journal of Mathematics, 2016; 2(2): 168-176. doi: 10.22034/kjm.2016.41250
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