2019•FilomatOpen access

Induced dynamics in hyperspaces of non-autonomous discrete systems

Radhika Vasisht, Ruchi Das

Abstract

In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical system (X, f1, ?) and its induced non-autonomous dynamical system (K(X), f1, ?) 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, ?) and its induced system (K(X), f1, ?) is studied.

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Key concepts: Hyperspace, Infinity, Mathematics, Dynamical systems theory, Transitive relation, Dynamical system (definition), Pure mathematics, Topology (electrical circuits)