%0 Journal Article
%T Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)
%Z 2423-4788
%A Lamei, Sanaz
%D 2016
%\ 08/01/2016
%V 2
%N 2
%P 168-176
%! Geodesic Flows on the Quotient of the Upper Half Plane over the Hecke Group
%K Hecke group
%K geodesic flow
%K arithmetic coding
%R 10.22034/kjm.2016.41250
%X 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.
%U https://www.kjm-math.org/article_41250_9154e7145e6560769c7f4f7801c2fa99.pdf