A note on sensitivity and chaos on hyperspaces of uniform spaces

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, Zahedan, Iran.

Abstract

‎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.

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References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 239-250

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History

  • Receive Date: 24 December 2024
  • Revise Date: 04 June 2025
  • Accept Date: 15 August 2025

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