Realization of Anosov Diffeomorphisms on the Torus

2024/07/03 by Tamara Kucherenko, Kucherenko, Tamara, Anthony Quas +1
Mathematics · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2407.03184

Abstract

We study area preserving Anosov maps on the two-dimensional torus within a fixed homotopy class. We show that the set of pressure functions for Anosov diffeomorphisms with respect to the geometric potential is equal to the set of pressure functions for the linear Anosov automorphism with respect to Hölder potentials. We use this result to provide a negative answer to the C^1+α version of the question posed by Rodriguez Hertz on whether two homotopic area preserving C^∞ Anosov difeomorphisms whose geometric potentials have identical pressure functions must be C^∞ conjugate.

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• Accessibility of derived-from-Anosov systems
• Notes on regularity of Anosov splitting
• Conservative Anosov diffeomorphisms of the two torus without an absolutely continuous invariant measure
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