2022/07/05 by Boris Kalinin, Victoria Sadovskaya, Kalinin, Boris +3
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2207.02321
We consider a hyperbolic toral automorphism L and its C1-small perturbation f. It is well-known that f is Anosov and topologically conjugate to L, but a conjugacy H is only Hölder continuous in general. We discuss conditions for smoothness of H, such as conjugacy of the periodic data of f and L, coincidence of their Lyapunov exponents, and weaker regularity of H, and we summarize questions, results, and techniques in this area. Then we introduce our new results: if H is weakly differentiable then it is C1+Hölder and, if L is also weakly irreducible, then H is C^∞.