A note on sensitivity and chaos on hyperspaces of uniform spaces

‎In this paper, we examine the dynamical characteristics of actions on the set of compact subsets within the phase space. Specifically, if $X$ is identified as a uniform space, we denote $\mathscr{K}(X)$ as the collection of non-empty closed subsets of $X$ equipped with the Hausdorff topology. If $f$ represents a continuous self-map on $X$, there exist several naturally induced continuous self-maps on $\mathscr{K}(X)$. The principal focus of our investigation is the relationship between the dynamics of $f$ and these induced mappings. For this purpose, we present topological notions of sensitivity and mixing properties pertinent to dynamical systems derived from uniform hyperspaces.