# Boris Kalinin: Smooth local rigidity for hyperbolic toral automorphisms

Time: Thu 2021-10-14 15.00 - 16.00

Lecturer: Boris Kalinin (Penn State)

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.

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Belongs to: Department of Mathematics
Last changed: Oct 06, 2021