On chaotic sets of solutions for a class of differential inclusions on $\mathbb{R}^2$
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914014535090176 |
|---|---|
| author | Volná, Barbora |
| author_facet | Volná, Barbora |
| contents | We deal with a set of solutions of the continuous multi-valued dynamical systems on $\mathbb{R}^2$ of the form $\dot x \in F(x)$ where $F(x)$ is a set-valued function and $F=\{f_1,f_2\}$. Such dynamical systems are frequently used in mathematical economics. We rectify the sufficient conditions for a set of solutions of this system to exhibit Devaney chaos, $ω$-chaos and infinite topological entropy from: B.R. Raines, D.R. Stockman, Fixed points imply chaos for a class of differential inclusions that arise in economic models, Trans. American Math. Society 364 (5) (2012), 2479--2492. We significantly improve their results. At the end, we illustrate these problems on our own macroeconomic model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_05705 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On chaotic sets of solutions for a class of differential inclusions on $\mathbb{R}^2$ Volná, Barbora Dynamical Systems 34A60, 54H20, 37D45, 37N40 We deal with a set of solutions of the continuous multi-valued dynamical systems on $\mathbb{R}^2$ of the form $\dot x \in F(x)$ where $F(x)$ is a set-valued function and $F=\{f_1,f_2\}$. Such dynamical systems are frequently used in mathematical economics. We rectify the sufficient conditions for a set of solutions of this system to exhibit Devaney chaos, $ω$-chaos and infinite topological entropy from: B.R. Raines, D.R. Stockman, Fixed points imply chaos for a class of differential inclusions that arise in economic models, Trans. American Math. Society 364 (5) (2012), 2479--2492. We significantly improve their results. At the end, we illustrate these problems on our own macroeconomic model. |
| title | On chaotic sets of solutions for a class of differential inclusions on $\mathbb{R}^2$ |
| topic | Dynamical Systems 34A60, 54H20, 37D45, 37N40 |
| url | https://arxiv.org/abs/1903.05705 |