Topological dynamics for the endograph metric II: extremely radical properties
Abstract
Abstract Given a dynamical system $(X,f)$ ( X , f ) we investigate several topological dynamical properties for its Zadeh extension $(\mathcal{F}(X),\hat{f})$ ( F ( X ) , f ˆ ) endowed with the endograph metric $d_{E}$ d E . In particular, we prove that for some contractive and expansive properties, for chain recurrence, chain transitivity and chain mixing, and for the shadowing property, the endograph metric behaves in an extremely radical way. Our results not only resolve certain open questions in the existing literature, but also yield completely new outcomes concerning the chain-type notions considered and the shadowing property.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Holomorphic and Operator Theory
Geometry and complex manifolds
Publication details
- Journal / source
- Journal of Inequalities and Applications
- Volume
- 2026
- Issue
- 1
- Publication date
- 15 May 2026
- Language
- EN