Topological dynamics for the endograph metric I: Equivalences with other metrics

Document Type : Research Paper

Author

Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València

10.22111/ijfs.2026.54067.9574

Abstract

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.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 2
March and April 2026
Pages 81-100

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