论文标题
一组2次旋转，其完美的正方形不会形成一组可测量的复发
A set of 2-recurrence whose perfect squares do not form a set of measurable recurrence
论文作者
论文摘要
我们说$ s \ subset \ mathbb z $是一组$ k $ -RECURRENCE，如果对于每个措施保存转换$ t $ t $ t $ a概率量$（x，μ）$的$ t $，以及每种$ a \ subseteq x $带有$μ（a）> 0 $的$ n \ in s $ n \ in s $ n \ in a $ n \ n \ n \ n \ n \ n \ n \ n \ cap t^a \ cap t^^ - - cap t^^ - - cap t^^ - - - t^{ - 2n} \ cap \ dots \ cap t^{ - kn} a）> 0 $。一组$ 1 $ - 重新出现称为一组可测量的复发。 回答Frantzikinakis，Lesigne和Wierdl的问题，我们将$ \ {n^2：N \ in S \} $的属性构建一组$ 2 $ -Recurrence $ s $，不是一组可衡量的重新恢复。
We say that $S\subset\mathbb Z$ is a set of $k$-recurrence if for every measure preserving transformation $T$ of a probability measure space $(X,μ)$ and every $A\subseteq X$ with $μ(A)>0$, there is an $n\in S$ such that $μ(A\cap T^{-n} A\cap T^{-2n}\cap \dots \cap T^{-kn}A)>0$. A set of $1$-recurrence is called a set of measurable recurrence. Answering a question of Frantzikinakis, Lesigne, and Wierdl, we construct a set of $2$-recurrence $S$ with the property that $\{n^2:n\in S\}$ is not a set of measurable recurrence.
