Generating Functions for Special Flows over the 1-Step Countable Topological Markov Chains

Details Generating Functions for Special Flows over the 1-Step Countable Topological Markov Chains Generating Functions for Special Flows over the 1-Step Countable Topological Markov Chains

2011-01-23

arxiv.org/abs/1101.4374v1

Mathematics

Dynamical Systems

19 pages

Scientific paper

Let $Y$ be a topological Markov chain with finite leading and follower sets. Special flow over $Y$ whose height function depends on the time zero of elements of $Y$ is constructed. Then a formula for computing the entropy of this flow will be given. As an application, we give a lower estimate for the entropy of a class of geodesic flows on the modular surface. We also give sufficient conditions to guarantee the existence of a measure with maximal entropy.

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