Arithmetic Coding and Entropy for the Positive Geodesic Flow on the Modular Surface

  title={Arithmetic Coding and Entropy for the Positive Geodesic Flow on the Modular Surface},
  author={SVETLANA KATOK},
  • Published 2002
In this article we study geodesics on the modular surface by means of their arithmetic codes. Closed geodesics for which arithmetic and geometric codes coincide were identified in [9]. 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 turns out… CONTINUE READING
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