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arXiv · 1901.02356

Null systems in the non-minimal case

Jiahao Qiu·Jianjie Zhao
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Abstract

In this paper, it is shown that if a dynamical system is null and distal, then it is equicontinuous. It turns out that a null system with closed proximal relation is mean equicontinuous. As a direct application, it follows that a null dynamical system with dense minimal points is also mean equicontinuous. Meanwhile, a distal system with trivial $\text{Ind}_{fip}$-pairs, and a non-trivial regionally proximal relation of order $\infty$ is constructed.

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Jiahao Qiu, Jianjie Zhao. 2019-01-05. Null systems in the non-minimal case. https://arxiv.org/abs/1901.02356

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