In this paper we introduce the notions of (Banach) density-equicontinuity and density-sensitivity. On the equicontinuity side, it is shown that a topological dynamical system is density-equicontinuous 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 measure-theoretical 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 density-sensitive for this measure.

在本文中，我们介绍了（Banach）密度等连续性和密度敏感性的概念。在等连续性方面，证明了当且仅当拓扑动力学系统是Banach密度等连续时，它才是密度等连续的。在敏感度方面，我们引入了密度敏感元组的概念来表征密度敏感度的多变量版本。我们进一步研究了测度理论和拓扑设置中序列熵元组和密度敏感元组的关系，结果表明，在可逆动力学系统上，某遍历测度的每个序列熵元组都对该密度敏感。具有遍历测度并具有全力支持的动力学系统中的每个拓扑序列熵元组都对该密度敏感。