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arXiv · 2106.01585

Exponential mixing, KAM and smooth local rigidity

Ralf Spatzier·Lei Yang
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Abstract

Consider actions of $\Z ^r$ by ergodic automorphisms on a compact nilmanifolds for $r \geq 2$. We show that small $C^k$ perturbations of such higher rank partially hyperbolic actions are smoothly conjugate to the original action, using a KAM scheme. The driving force for convergence of this iteration is the exponential mixing of the original action.

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Ralf Spatzier, Lei Yang. 2021-06-03. Exponential mixing, KAM and smooth local rigidity. https://arxiv.org/abs/2106.01585

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