Induced Dynamics in Hyperspaces of Non-Autonomous Discrete Systems

Abstract

In this paper, the interrelations of some dynamical properties of the non-autonomous dynamical system (X; f1;infinity) and its induced non-autonomous dynamical system (K(X); f1;infinity) are studied, where K(X) is the hyperspace of all non-empty compact subsets of X, endowed with Vietoris topology. Various stronger forms of sensitivity and transitivity are considered. Some examples of non-autonomous systems are provided to support the results. A relation between shadowing property of the non-autonomous system (X; f1;infinity) and its induced system (K(X); f1;infinity) is studied.