Induced Dynamics in Hyperspaces of Non-Autonomous Discrete Systems

TL;DR

This paper explores how certain dynamical properties like sensitivity, transitivity, and shadowing in non-autonomous systems relate to their induced hyperspace systems, providing theoretical insights and examples.

Contribution

It establishes new connections between properties of non-autonomous systems and their hyperspace counterparts, expanding understanding of induced dynamics.

Findings

Relations between sensitivity and transitivity in systems and hyperspaces

Conditions under which shadowing property transfers to hyperspaces

Examples illustrating the theoretical results

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.