Entire solutions of the Allen–Cahn–Nagumo equation in a multi-dimensional space
On $ \epsilon $-escaping trajectories in homogeneous spaces
Mean equicontinuity, complexity and applications
Jie Li 1, , Xiangdong Ye 2, and Tao Yu 3,
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
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
Department of Mathematics, Shantou University, Shantou 515063, China
Received December 2019 Published March 2020
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.
Keywords: Mean equicontinuity, discrete spectrum, topo-isomorphy, bounded complexity, Möbius disjointness.
Mathematics Subject Classification: 54H20, 37A35, 37B05.
Citation: Jie Li, Xiangdong Ye, Tao Yu. Mean equicontinuity, complexity and applications. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 359-393. doi: 10.3934/dcds.2020167
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Jie Li Xiangdong Ye Tao Yu