Characterization of Non-Deterministic Chaos in Two-Dimensional Non-Smooth Vector Fields
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929380497817600 |
|---|---|
| author | Euzébio, Rodrigo D. Mattos, Pedro G. Varão, Régis |
| author_facet | Euzébio, Rodrigo D. Mattos, Pedro G. Varão, Régis |
| contents | Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos when the Filippov system has non-empty sliding or escaping regions. A fundamental result for continuous flows is the equivalence of topological transitivity and existence of a dense orbit. We prove in our setting that topological transitivity for Filippov systems is indeed equivalent to the existence of a dense Filippov orbit, although, in contrast to the continuous case, we are not able to garantee that the dense orbit implies the existence of a residual set of dense orbits. Finally we prove that, in this context, topological transitivity implies strictly positive topological entropy for the Filippov system. This calculation is made using techniques similar to those from symbolic dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_12025 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Characterization of Non-Deterministic Chaos in Two-Dimensional Non-Smooth Vector Fields Euzébio, Rodrigo D. Mattos, Pedro G. Varão, Régis Dynamical Systems 34A36, 34A60, 37G15, 37B40 Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos when the Filippov system has non-empty sliding or escaping regions. A fundamental result for continuous flows is the equivalence of topological transitivity and existence of a dense orbit. We prove in our setting that topological transitivity for Filippov systems is indeed equivalent to the existence of a dense Filippov orbit, although, in contrast to the continuous case, we are not able to garantee that the dense orbit implies the existence of a residual set of dense orbits. Finally we prove that, in this context, topological transitivity implies strictly positive topological entropy for the Filippov system. This calculation is made using techniques similar to those from symbolic dynamics. |
| title | Characterization of Non-Deterministic Chaos in Two-Dimensional Non-Smooth Vector Fields |
| topic | Dynamical Systems 34A36, 34A60, 37G15, 37B40 |
| url | https://arxiv.org/abs/2101.12025 |