Thermodynamics of smooth models of pseudo-Anosov diffeomorphisms
Dominic Veconi (Coventry)
We discuss the thermodynamic and ergodic properties of a smooth realization of pseudo-Anosov surface homeomorphisms. In this realization, the pseudo-Anosov map is uniformly hyperbolic outside of a neighbourhood of a set of singularities, and the trajectories are slowed down so the differential is the identity at the singularities. Using Young towers, we prove existence and uniqueness of equilibrium measures for the family of observables known as the geometric t-potentials. This set of equilibrium measures includes a unique smooth Sinai-Ruelle-Bowen physical measure and a measure of maximal entropy, the latter of which has exponential decay of correlations and the Central Limit Theorem.
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