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null systems

Ergodic Theory and Dynamical Systems (1)

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1 results

Null systems in the non-minimal case
Part of
- Topological dynamics
- Connections with other structures, applications
JIAHAO QIU, JIANJIE ZHAO
Journal:

Ergodic Theory and Dynamical Systems / Volume 40 / Issue 12 / December 2020

Published online by Cambridge University Press:

17 June 2019, pp. 3420-3437

Print publication:

December 2020
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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 $\text{Ind}_{\text{fip}}$-pairs and a non-trivial regionally proximal relation of order $\infty$ are constructed.