A note on mean equicontinuity
Dynamical Systems
2018-11-16 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1806.09987,
title = {A note on mean equicontinuity},
author = {Jiahao Qiu and Jianjie Zhao},
journal= {arXiv preprint arXiv:1806.09987},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1312.7663 by other authors