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arXiv · 2407.13877

Global smooth rigidity for toral automorphisms

Boris Kalinin·Victoria Sadovskaya·Zhenqi Wang
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Abstract

We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism $L$ and a $C^\infty$ diffeomorphism $f$ of the torus. For a very weakly irreducible hyperbolic automorphism $L$ we show that any $C^1$ conjugacy is $C^\infty$. For a very weakly irreducible ergodic partially hyperbolic automorphism $L$ we show that any $C^{1+\text{H\"older}}$ conjugacy is $C^\infty$. As a corollary, we improve regularity of the conjugacy to $C^\infty$ in prior local and global rigidity results.

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Boris Kalinin, Victoria Sadovskaya, Zhenqi Wang. 2024-07-18. Global smooth rigidity for toral automorphisms. https://arxiv.org/abs/2407.13877

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