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arXiv · 2111.01309

Smooth local rigidity for hyperbolic toral automorphisms

Boris Kalinin·Victoria Sadovskaya·Zhenqi Jenny Wang
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Abstract

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 $C^{1+H\"older}$ 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 H\"older 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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Boris Kalinin, Victoria Sadovskaya, Zhenqi Jenny Wang. 2021-11-02. Smooth local rigidity for hyperbolic toral automorphisms. https://arxiv.org/abs/2111.01309

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