Dynamical systems of an infinite-dimensional non-linear operator
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910342046547968 |
|---|---|
| author | Olimov, U. R. Rozikov, U. A. |
| author_facet | Olimov, U. R. Rozikov, U. A. |
| contents | We investigate discrete-time dynamical systems generated by an infinite-dimensional non-linear operator that maps the Banach space $l_1$ to itself. It is demonstrated that this operator possesses up to seven fixed points. By leveraging the specific form of our operator, we illustrate that analyzing the operator can be simplified to a two-dimensional approach. Subsequently, we provide a detailed description of all fixed points, invariant sets for the two-dimensional operator and determine the set of limit points for its trajectories. These results are then applied to find the set of limit points for trajectories generated by the infinite-dimensional operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical systems of an infinite-dimensional non-linear operator Olimov, U. R. Rozikov, U. A. Dynamical Systems 37L05, 37N05 We investigate discrete-time dynamical systems generated by an infinite-dimensional non-linear operator that maps the Banach space $l_1$ to itself. It is demonstrated that this operator possesses up to seven fixed points. By leveraging the specific form of our operator, we illustrate that analyzing the operator can be simplified to a two-dimensional approach. Subsequently, we provide a detailed description of all fixed points, invariant sets for the two-dimensional operator and determine the set of limit points for its trajectories. These results are then applied to find the set of limit points for trajectories generated by the infinite-dimensional operator. |
| title | Dynamical systems of an infinite-dimensional non-linear operator |
| topic | Dynamical Systems 37L05, 37N05 |
| url | https://arxiv.org/abs/2402.15479 |