Sub-shadowing and specification through pointwise dynamics
[EN]In this paper, the notion of $\overline{d}$-shadowable points for continuous maps on compact metric spaces is introduced and it is proved that an equicontinuous map (not necessarily surjective) cannot have the $\overline{d}$-shadowing property. Consequently, it is shown that a minimal continuous...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/227666 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/227666 |
| Access Level: | acceso abierto |
| Palabra clave: | Shadowing Shadowable point Sub-shadowing Specification Pseudo orbital specification |
| Sumario: | [EN]In this paper, the notion of $\overline{d}$-shadowable points for continuous maps on compact metric spaces is introduced and it is proved that an equicontinuous map (not necessarily surjective) cannot have the $\overline{d}$-shadowing property. Consequently, it is shown that a minimal continuous map with the $\overline{d}$-shadowing property is chaotic in the sense of Auslander-Yorke. Then, it is proved that the existence of a pseudo-orbital specification point, the existence of an ergodic shadowable point, the pseudo-orbital specification property and the ergodic shadowing property are equivalent. Consequently, it is shown that existence of a pseudo-orbital specification point implies the specification property. Next, it is proved that the existence of a point which is both shadowable and specification point implies the pseudo-orbital specification property, the ergodic shadowing property, the shadowing property and the $\overline{d}$-shadowing property. Consequently, it is shown that the existence of a shadowable point in a topologically mixing system implies |
|---|