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Exponential multiple mixing for commuting automorphisms of a nilmanifold
Ergodic Theory and Dynamical Systems ( IF 0.9 ) Pub Date : 2023-10-11 , DOI: 10.1017/etds.2023.73 TIMOTHÉE BÉNARD , PÉTER P. VARJÚ
Ergodic Theory and Dynamical Systems ( IF 0.9 ) Pub Date : 2023-10-11 , DOI: 10.1017/etds.2023.73 TIMOTHÉE BÉNARD , PÉTER P. VARJÚ
Let $l\in \mathbb {N}_{\ge 1}$ 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 the results of Gorodnik and Spatzier [Mixing properties of commuting nilmanifold automorphisms. Acta Math. 215 (2015), 127–159].
中文翻译:
尼尔流形通勤自同构的指数多重混合
让 $l\in \mathbb {N}_{\ge 1}$ 和 $\alpha : \mathbb {Z}^l\rightarrow \text {Aut}(\mathscr {N})$ 是一个动作 $\mathbb {Z}^l$ 通过紧尼尔流形上的自同构 $\mathscr{N}$ 。我们假设每个人的行动 $\阿尔法(z)$ 是遍历的 $z\in \mathbb {Z}^l\smallsetminus \{0\}$ 并表明 $\阿尔法$ 满足指数n - 任意整数的混合 $n\geq 2$ 。这扩展了 Gorodnik 和 Spatzier 的结果[通勤尼尔流形自同构的混合特性。数学学报。 215(2015),127-159]。
更新日期:2023-10-11
中文翻译:
尼尔流形通勤自同构的指数多重混合
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