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Geodesic Flow on the Quotient Space of the ⟩ on the Upper Half Plane Action of ⟨z + 2, − 1

By Dawoud Ahmadi Dastjerdi and Sanaz Lamei


Let G be the group generated by z ↦ → z +2 and z ↦ → − 1, z ∈ C. This z group acts on the upper half plane and the associated quotient surface is topologically a sphere with two cusps. Assigning a “geometric ” code to an oriented geodesic not going to cusps, with alphabets in Z \ {0}, enables us to conjugate the geodesic flow on this surface to a special flow over the symbolic space of these geometric codes. We will show that for k ≥ 1, a subsystem with codes from Z \ {0, ±1, ±2, · · · , ±k} is a TBS: topologically Bernouli scheme. For similar codes for geodesic flow on modular surface, this was true for k ≥ 3. We also give bounds for the entropy of these subsystems

Year: 2014
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