2021/11/02 by Boris Kalinin, Victoria Sadovskaya, Kalinin, Boris +3
Mathematics · Physics and Astronomy · #37C15 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2111.01309
openalex publication_date 2021/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its smooth perturbation f We show that if H is weakly differentiable then it is C1+Hölder and, if A is also weakly irreducible, then H is C^∞. As a part of the proof, we establish results of independent interest on Hölder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C^∞ in prior local rigidity results.