Shadowing for Infinite Dimensional Dynamical Systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912494244593664 |
|---|---|
| author | Arrieta, José M. Carvalho, Alexandre N. Takaessu Jr, Carlos R. |
| author_facet | Arrieta, José M. Carvalho, Alexandre N. Takaessu Jr, Carlos R. |
| contents | In this paper we extend to an infinite dimensional setting some results on the shadowing property that are known on finite dimensional compact manifolds without border and in $\mathbb{R}^n$. In fact, we show that if $\{\T(t):t\ge 0\}$ is a Morse-Smale semigroup defined in a Hilbert space with a global attractor $\mathcal{A}$ and non-wandering set given only by its equilibria, then $\T(1)|_{\mathcal{A}}:\mathcal{A}\to \mathcal{A} $ admits the Lipschitz Shadowing property. Moreover, for any positively invariant bounded neighborhood $\U\supset\mathcal{A}$ of the global attractor, the map $\T(1)|_{\U}:\U\to \U$ has the Hölder-Shadowing property. We obtain results related to the structural stability of Morse-Smale semigroups, that were only known on finite dimension and continuity of global attractors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shadowing for Infinite Dimensional Dynamical Systems Arrieta, José M. Carvalho, Alexandre N. Takaessu Jr, Carlos R. Dynamical Systems Analysis of PDEs In this paper we extend to an infinite dimensional setting some results on the shadowing property that are known on finite dimensional compact manifolds without border and in $\mathbb{R}^n$. In fact, we show that if $\{\T(t):t\ge 0\}$ is a Morse-Smale semigroup defined in a Hilbert space with a global attractor $\mathcal{A}$ and non-wandering set given only by its equilibria, then $\T(1)|_{\mathcal{A}}:\mathcal{A}\to \mathcal{A} $ admits the Lipschitz Shadowing property. Moreover, for any positively invariant bounded neighborhood $\U\supset\mathcal{A}$ of the global attractor, the map $\T(1)|_{\U}:\U\to \U$ has the Hölder-Shadowing property. We obtain results related to the structural stability of Morse-Smale semigroups, that were only known on finite dimension and continuity of global attractors. |
| title | Shadowing for Infinite Dimensional Dynamical Systems |
| topic | Dynamical Systems Analysis of PDEs |
| url | https://arxiv.org/abs/2502.08315 |