Uniform chain transitivity and uniform chain mixing properties in uniform hyperspaces

TL;DR

This paper extends the concepts of chain transitivity and mixing to dynamical systems on uniform hyperspaces, broadening their applicability beyond metric spaces.

Contribution

It introduces and analyzes uniform chain transitivity and mixing properties for dynamical systems in uniform hyperspaces, generalizing existing metric space concepts.

Findings

Established definitions of chain transitivity and mixing in uniform hyperspaces.

Proved properties and relationships of these concepts in the new setting.

Extended classical dynamical systems notions to a broader topological context.

Abstract

We introduce and study the topological concepts of chain transitivity, mixing and chain mixing property for dynamical systems induced by uniform hyperspaces. These notions generalize the relevant concepts for metric spaces.