Distributional chaos of time-varying discrete dynamical systems
This paper is concerned with distributional chaos of time-varying discrete systems in metric spaces. Some basic concepts are introduced for general time-varying systems, including sequentially distributive chaos, weak mixing, and mixing. We give an example of sequentially distributive chaos of finite-dimensional linear time-varying dynamical systems, which is not distributively chaotic of type $i$ ($DCi$ for short, $i=1, 2$). We also prove that two uniformly topological equiconjugate time-varying systems have simultaneously sequentially distributive chaos and weak topological mixing.