Smooth local rigidity for hyperbolic toral automorphisms

Communications of the American Mathematical Society Pub Date : 2021-11-02 DOI:10.1090/cams/22

B. Kalinin, V. Sadovskaya, Zhenqi Wang

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引用次数: 1

Abstract

We study the regularity of a conjugacy H H between a hyperbolic toral automorphism A A and its smooth perturbation f f . We show that if H H is weakly differentiable then it is C 1 + H\"older C^{1+\text {H\"older}} and, if A A is also weakly irreducible, then H H is C ∞ C^\infty . 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 ∞ C^\infty in prior local rigidity results.

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双曲型全自同构的光滑局部刚性

研究了双曲总自同构a a与其光滑摄动f之间共轭H H的正则性。我们证明了如果H H是弱可微的，那么它是c1 + Hölder C^{1+\text Hölder{，如果A A也是弱不可约的，那么H H是C∞C^ }}\infty。作为证明的一部分，我们建立了关于双曲系统上线性环间可测共轭的Hölder连续性的独立有趣的结果。作为一个推论，我们改进了先前局部刚度结果中C∞C^ \infty共轭的正则性。

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Communications of the American Mathematical Society

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