TY - JOUR ID - 41250 TI - Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Lamei, Sanaz AD - Faculty of Mathematical Sciences, University of Guilan, P.O.Box 1914, Rasht, Iran. Y1 - 2016 PY - 2016 VL - 2 IS - 2 SP - 168 EP - 176 KW - Hecke group KW - geodesic flow KW - arithmetic coding DO - 10.22034/kjm.2016.41250 N2 - 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. Thegeodesic flows on this surface are ergodic. Here, by constructinga phase space for the geodesic flows hitting an appropriate crosssection, we find the arithmetic code of these flows and showthat their code space is a topological Markov chain. UR - https://www.kjm-math.org/article_41250.html L1 - https://www.kjm-math.org/article_41250_9154e7145e6560769c7f4f7801c2fa99.pdf ER -