Collective Sensitivity and Collective Accessibility of Non-Autonomous Discrete Dynamical Systems

Abstract

The concepts of collectively accessible, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive are defined in non-autonomous discrete systems. It is proved that, if the mapping sequence h1,∞=(h1,h2,…) is W-chaotic, then hn,∞=(hn,hn+1,…)(∀n∈N={1,2,…}) would also be W-chaotic. W-chaos represents one of the following five properties: collectively accessible, sensitive, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive. Then, the relationship of chaotic properties between the product system (H1×H2,f1,∞×g1,∞) and factor systems (H1,f1,∞) and (H2,g1,∞) was presented. Furthermore, in this paper, it is also proved that, if the autonomous discrete system (X,h^) induced by the p-periodic discrete system (H,h1,∞) is W-chaotic, then the p-periodic discrete system (H,f1,∞) would also be W-chaotic.