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Topological dynamics for the endograph metric I: Equivalences with other metrics | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 2، خرداد و تیر 2026، صفحه 81-100 اصل مقاله (556.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.54067.9574 | ||
| نویسنده | ||
| Antoni López-Martínez* | ||
| Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València | ||
| چکیده | ||
| Given a dynamical system $(X,f)$ we investigate several dynamical properties for its Zadeh extension $(F(X),\hat{f})$ endowed with the endograph metric $d_E$. In particular, we prove that for topological A-transitivity, topological (ℓ,A)-recurrence, Devaney chaos, and the specification property, the endograph metric behaves similarly to the supremum metric $d_∞$, the Skorokhod metric $d_0$ and the sendograph metric $d_S$. Our results not only resolve certain open questions in the existing literature, but also yield completely new outcomes in terms of point-A-transitivity. | ||
| کلیدواژهها | ||
| Fuzzy dynamical systems؛ Transitivity؛ Recurrence؛ Chaos | ||
| مراجع | ||
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