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arXiv · 2201.02556

Exponential multiple mixing for commuting automorphisms of a nilmanifold

Timothée Bénard·Péter P. Varjú
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Abstract

Let $l\in \mathbb{N}_{\geq 1}$ and $\alpha : \mathbb{Z}^l\rightarrow \text{Aut}(\mathscr{N})$ be an action of $\mathbb{Z}^l$ by automorphisms on a compact nilmanifold $\mathscr{N}$. We assume the action of every $\alpha(z)$ is ergodic for $z\in \mathbb{Z}^l\smallsetminus\{0\}$ and show that $\alpha$ satisfies exponential $n$-mixing for any integer $n\geq 2$. This extends results of Gorodnik and Spatzier [Acta Math., 215 (2015)].

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Timothée Bénard, Péter P. Varjú. 2022-01-07. Exponential multiple mixing for commuting automorphisms of a nilmanifold. https://arxiv.org/abs/2201.02556

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