Density-equicontinuity and Density-sensitivity
Density-equicontinuity 和密度敏感作者机构:School of Mathematics and StatisticsJiangsu Normal UniversityXuzhou 221116P.R.China School of Mathematics(Zhuhai)Sun Yat-sen UniversityZhuhai 519082P.R.China
出 版 物:《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期:2021年第37卷第2期
页 面:345-361页
核心收录:
学科分类:0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 071101[理学-系统理论] 0701[理学-数学]
基 金:Jie Li is supported by NSF of Jiangsu Province(Grant No.BK20170225) NNSF of China(Grant Nos.11701231and 12031019) Science Foundation of Jiangsu Normal University(Grant No.17XLR011) Si Ming Tu is supported by NNSF of China(Grant Nos.11801584 and 11871228)
主 题:Density equicontinuity density sensitivity sequence entropy
摘 要:In this paper we introduce the notions of(Banach) density-equicontinuity and densitysensitivity. On the equicontinuity side, it is shown that a topological dynamical system is densityequicontinuous if and only if it is Banach density-equicontinuous. On the sensitivity side, we introduce the notion of density-sensitive tuple to characterize the multi-variant version of density-sensitivity. We further look into the relation of sequence entropy tuple and density-sensitive tuple both in measuretheoretical and topological setting, and it turns out that every sequence entropy tuple for some ergodic measure on an invertible dynamical system is density-sensitive for this measure;and every topological sequence entropy tuple in a dynamical system having an ergodic measure with full support is densitysensitive for this measure.