论文标题
指数多重混合，用于通勤Nilmanifold的自动形态
Exponential multiple mixing for commuting automorphisms of a nilmanifold
论文作者
论文摘要
令$ l \ in \ Mathbb {n} _ {\ geq 1} $和$α：\ Mathbb {Z}^l \ rightArrow \ rightArrow \ text {aut}（\ m m缩{n}）$是$ \ \ m nilbb {z}^l $ comcrccress nilman of nilman on nilfis nilfis nilfiss $ \ s $ \ ccrccrianf我们假设每个$α（z）$的动作对于$ z \ in \ mathbb {z}^l \ smallSetMinus \ {0 \} $都是eRgodic，并显示$α$满足任何整数$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n \ n \ geq 2 $。这扩展了Gorodnik和Spatzier的结果[Acta Math。，215（2015）]。
Let $l\in \mathbb{N}_{\geq 1}$ and $α: \mathbb{Z}^l\rightarrow \text{Aut}(\mathscr{N})$ be an action of $\mathbb{Z}^l$ by automorphisms on a compact nilmanifold $\mathscr{N}$. We assume the action of every $α(z)$ is ergodic for $z\in \mathbb{Z}^l\smallsetminus\{0\}$ and show that $α$ satisfies exponential $n$-mixing for any integer $n\geq 2$. This extends results of Gorodnik and Spatzier [Acta Math., 215 (2015)].
