Morse Coding of the Geodesic Flow on the Quotient of the Upper Half Plane on Modular Group

The dynamical properties of the geodesic flow on surfaces with negative curvature can be read from a special flow constructed over countable Markov chain which is conjugate to the geodesic flow. The Markov chain obtains from the coding of the geodesic flow. We introduse an algorithm based on Morse method to code the geodesic flow.