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arXiv · 1905.08934

$Δ$-Weakly Mixing Subset In Positive Entropy Actions Of A Nilpotent Group

Kairan Liu
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Abstract

The notion of $Δ$-weakly mixing subsets is introduced for countable torsion-free discrete group actions. It is shown that for a finitely generated torsion-free discrete nilpotent group action, positive topological entropy implies the existence of $Δ$-weakly mixing subsets, and while there exists a finitely generated torsion-free discrete solvable group action which has positive topological entropy but without any $Δ$-weakly mixing subsets.

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Kairan Liu. 2019-05-22. $Δ$-Weakly Mixing Subset In Positive Entropy Actions Of A Nilpotent Group. https://arxiv.org/abs/1905.08934

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