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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… Click to show full 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 $\text{Ind}_{\text{fip}}$-pairs and a non-trivial regionally proximal relation of order $\infty$ are constructed.
Keywords:
system;
systems non;
minimal case;
null systems;
non minimal
Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2020
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Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2020
Link to full text (if available)
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recommendations!