تقرير
Recurrence in collective dynamics: From the hyperspace to fuzzy dynamical systems
| العنوان: | Recurrence in collective dynamics: From the hyperspace to fuzzy dynamical systems |
|---|---|
| المؤلفون: | Álvarez, Illych, López-Martínez, Antoni, Peris, Alfred |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, 37B02, 37B20, 54A40, 54B20 |
| الوصف: | We study for a dynamical system $f:X\longrightarrow X$ some of the principal topological recurrence-kind properties with respect to the induced maps $\overline{f}:\mathcal{K}(X)\longrightarrow\mathcal{K}(X)$, on the hyperspace of non-empty compact subsets of $X$, and $\hat{f}:\mathcal{F}(X)\longrightarrow\mathcal{F}(X)$, on the space of normal fuzzy sets consisting of the upper-semicontinuous functions $u:X\longrightarrow [0,1]$ with compact support and such that $u^{-1}(\{1\})\neq\varnothing$. In particular, we characterize the properties of topological and multiple recurrence for the extended systems $(\mathcal{K}(X),\overline{f})$ and $(\mathcal{F}(X),\hat{f})$. Special attention is given to the case where the underlying space is completely metrizable, for which we obtain some stronger point-recurrence equivalences. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.15826 |
| رقم الأكسشن: | edsarx.2406.15826 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |