论文标题
$δ$ - 沿整数序列集合的子集混合子集
$Δ$-weakly mixing subsets along a collection of sequences of integers
论文作者
论文摘要
在本文中，我们提出了一种温和的条件，称为条件$（**）$，用于整数序列，并表明，对于任何度量保存系统，Pinsker $σ$ -Algebra是一个特征性的$σ$ -SALGEBRA，沿着集合条件$（**）$（**）$（****）$。我们介绍了$δ$ - 伴有整数序列的混合子集的概念，并表明积极的拓扑熵意味着存在$δ$ - 伴随“良好”序列的集合。结果，我们表明阳性拓扑熵意味着沿移位质数的多项式时代的多变体Li-Yorke混乱。
In this paper, we propose a mild condition, named Condition $(**)$, for collections of sequence of integers and show that for any measure preserving system the Pinsker $σ$-algebra is a characteristic $σ$-algebra for the averages along a collection satisfying Condition $(**)$. We introduce the notion of $Δ$-weakly mixing subsets along a collection of sequences of integers and show that positive topological entropy implies the existence of $Δ$-weakly mixing subsets along a collection of "good" sequences. As a consequence, we show that positive topological entropy implies multi-variant Li-Yorke chaos along polynomial times of the shift prime numbers.
