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A note on sensitivity and chaos on hyperspaces of uniform spaces | ||
| Journal of Mahani Mathematical Research | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 مرداد 1404 اصل مقاله (495.07 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24576.1740 | ||
| نویسندگان | ||
| Nooshin Darban Maghami؛ Seyyed Alireza Ahmadi* ؛ Zahra Shabani | ||
| Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, Zahedan, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| sensitivity؛ transitivity؛ distal؛ hyperspaces؛ uniform space | ||
| مراجع | ||
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[4] Darban Maghami, N., Ahmadi, S.A. & Shabani, Z. (2025). Strong chain transitivity in hyperspaces of uniform spaces, Appl. Gen. Topol. doi:10.4995/agt.2025.21100.
[5] Das, T., Lee,K., Richeson, D. & Wiseman, J. (2013). Spectral decomposition for topologically anosov homeomorphisms on noncompact and non-metrizable spaces. Topology Appl., 160, no. 1, 149{158.
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[8] Pirfalak,F., Ahmadi,S. A., Wu, X., & Kouhestani, N. (2021). Topological Average Shadowing Property on Uniform Spaces. Qual. Theory Dyn. Syst., 20(2), no. 31 (15 pages).
[9] Salman, M., Wu, X., & Das, R. (2021). Sensitivity of nonautonomous dynamical systems on uniform spaces. International Journal of Bifurcation and Chaos, 31, no. 1, 2150017 (11 pages).
[10] Wang, Y., Wei, G. & Campbell, William H. (2009). Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems. Topology Appl. 156, no. 4, 803{811.
[11] Wu,X., Liang, S., Ma, X., Lu, T. & Ahmadi, S. A. (2020). The mean sensitivity and mean equicontinuity in uniform spaces. Int. J. Bifurcation and Chaos, 2050122 (11 pages). | ||
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آمار تعداد مشاهده مقاله: 5 تعداد دریافت فایل اصل مقاله: 4 |
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