Density-equicontinuity and Density-sensitivity  

作　　者：Jie LI Si Ming TU 

机构地区：[1]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,P.R.China [2]School of Mathematics(Zhuhai),Sun Yat-sen University,Zhuhai 519082,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第2期345-361,共17页数学学报（英文版）

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)。

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.

关 键 词：Density equicontinuity density sensitivity sequence entropy 

分 类 号：O19[理学—数学]