Mean equicontinuity, complexity and applications

Jie Li; Xiangdong Ye; Tao Yu

doi:10.3934/dcds.2020167

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2021, Volume 41, Issue 1: 359-393. Doi: 10.3934/dcds.2020167

This issue Previous Article On $ \epsilon $-escaping trajectories in homogeneous spaces Next Article Entire solutions of the Allen–Cahn–Nagumo equation in a multi-dimensional space

Mean equicontinuity, complexity and applications

1.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
2.
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
3.
Department of Mathematics, Shantou University, Shantou 515063, China

Received: December 2019

Early access: March 2020

Published: January 2021

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Abstract

We will review the recent development of the research related to mean equicontinuity, focusing on its characterizations, its relationship with discrete spectrum, topo-isomorphy, and bounded complexity. Particularly, the application of the complexity function in the mean metric to the Sarnak and the logarithmic Sarnak Möbius disjointness conjecture will be addressed.

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Mathematics Subject Classification: 54H20, 37A35, 37B05.

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