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arXiv · 2009.07677

$\Delta$-weakly mixing subsets along a collection of sequences of integers

Jian Li·Kairan Liu
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Abstract

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 $\sigma$-algebra is a characteristic $\sigma$-algebra for the averages along a collection satisfying Condition $(**)$. We introduce the notion of $\Delta$-weakly mixing subsets along a collection of sequences of integers and show that positive topological entropy implies the existence of $\Delta$-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.

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Jian Li, Kairan Liu. 2020-09-16. $\Delta$-weakly mixing subsets along a collection of sequences of integers. https://doi.org/10.1007/s10884-020-09898-5

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