2018/06/24 by Jiahao Qiu, Jianjie Zhao, Qiu, Jiahao +1 · 2 citations
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1806.09987
In this note, it is shown that several results concerning mean equicontinuity proved before for minimal systems are actually held for general topological dynamical systems. Particularly, it turns out that a dynamical system is mean equicontinuous if and only if it is equicontinuous in the mean if and only if it is Banach (or Weyl) mean equicontinuous if and only if its regionally proximal relation is equal to the Banach proximal relation. Meanwhile, a relation is introduced such that the smallest closed invariant equivalence relation containing this relation induces the maximal mean equicontinuous factor for any system.