Boris Kalinin: Smooth local rigidity for hyperbolic toral automorphisms

Abstract: This is a joint work with Victoria Sadovskaya and Zhenqi Jenny Wang. We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its perturbation f. We show that if H is weakly differentiable (for example Lipschitz) then it is C^{1+Holder} and, if A is also weakly irreducible, then H is C^\infty. As a part of the proof we establish results of independent interest on Holder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C^\infty in prior local rigidity results.