Svetlana Katok (Penn State) Topological entropy estimates for the positive geodesic flow on the modular surface
In a joint work with Boris Gurevich we study geodesics on the modular surface by means of their arithmetic codes. The closed geodesics for which arithmetic and geometric codes coincide were identified by S. Katok in 1996. Here they are described as periodic orbits of a special flow over a topological Markov chain with countable alphabet which we call the positive geodesic flow. We obtain an explicit formula for the ceiling function and two-sided estimates for the topological entropy of the positive geodesic flow which is separated from one, the topological entropy of the geodesic flow on the modular surface.
