Polynomial decay of correlations of pseudo-Anosov diffeomorphisms

2025/04/10 by Dominic Veconi, Veconi, Dominic
Mathematics · Physics and Astronomy · #37D25 #37D35 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2504.08162

openalex publication_date 2025/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a construction of a smooth realization of a pseudo-Anosov diffeomorphism of a Riemannian surface, and show that it admits a unique SRB measure with polynomial decay of correlations, large deviations, and the central limit theorem. The construction begins with a linear pseudo-Anosov diffeomorphism whose singularities are fixed points. Near the singularities, the trajectories are slowed down, and then the map is conjugated with a homeomorphism that pushes mass away from the origin. The resulting map is a C^2+ε diffeomorphism topologically conjugate to the original pseudo-Anosov map. To prove that this map has polynomial decay of correlations, our main technique is to use the fact that this map has a Young tower, and study the decay of the tail of the first return time to the base of the tower.

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