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.
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Acknowledgements
The authors would like to thank Jian Li and Xiangdong Ye for bringing us the questions and for useful discussions when doing the research. We also thank Jie Li for the careful reading which help the writing of the paper. Finally the authors thank the referee for his/her careful reading. The authors were supported by NNSF of China (11431012).
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Qiu, J., Zhao, J. A Note on Mean Equicontinuity. J Dyn Diff Equat 32, 101–116 (2020). https://doi.org/10.1007/s10884-018-9716-5
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DOI: https://doi.org/10.1007/s10884-018-9716-5