Topological dynamics for the endograph metric II: Extremely radical properties
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908605949673472 |
|---|---|
| author | López-Martínez, Antoni |
| author_facet | López-Martínez, Antoni |
| contents | Given a dynamical system $(X,f)$ we investigate several topological dynamical properties for its Zadeh extension $(\mathcal{F}(X),\hat{f})$ endowed with the endograph metric $d_{E}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological dynamics for the endograph metric II: Extremely radical properties López-Martínez, Antoni Dynamical Systems 37B02, 37B05, 37B65, 54A40, 54B20 Given a dynamical system $(X,f)$ we investigate several topological dynamical properties for its Zadeh extension $(\mathcal{F}(X),\hat{f})$ endowed with the endograph metric $d_{E}$. 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. |
| title | Topological dynamics for the endograph metric II: Extremely radical properties |
| topic | Dynamical Systems 37B02, 37B05, 37B65, 54A40, 54B20 |
| url | https://arxiv.org/abs/2510.19337 |