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

2025/10/20 by Antoni López-Martínez, López-Martínez, Antoni · 2 citations
Mathematics · #37B02 #37B20 #47A16 #54A40 #54B20 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2510.17990

openalex publication_date 2025/10/20 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Given a dynamical system (X,f) we investigate several topological dynamical properties for its Zadeh extension (F(X),f) endowed with the endograph metric d_E. In particular, we prove that for topological A-transitivity, topological (ℓ,A)-recurrence, Devaney chaos, and for the specification property, the endograph metric behaves similarly to the supremum metric d_∞, the Skorokhod metric d₀ 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.

Citations

• Li-Yorke chaos on fuzzy dynamical systems
• Topological dynamics for the endograph metric II: Extremely radical properties
• Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree
• Transitivity of some uniformities on fuzzy sets
• Frequently recurrence properties and block families
• Characterizations of endograph metric and Γ-convergence on fuzzy sets

Cited by

• Li-Yorke chaos on fuzzy dynamical systems
• Topological dynamics for the endograph metric II: Extremely radical properties

Related

• Topological dynamics for the endograph metric II: Extremely radical properties
• Conceptions of Topological Transitivity
• Types of mixings and transitivities in topological dynamics
• Topological Transitivity of Nonautonomous Dynamical Systems
• On hyperbolic attractors and repellers of endomorphisms