| Texto completo | |
| Autor(es): |
Carvalho, Tiago
;
Antunes, Andre do Amaral
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Differential Equations; v. 419, p. 25-pg., 2024-11-29. |
| Resumo | |
It is well known that many results obtained for piecewise smooth vector fields do not have an analogous for smooth vector fields and vice-versa. These differences are generated by the non-uniqueness of trajectory passing through a point. Inspired by the classical fact that one-dimensional discrete dynamic systems can produce chaotic behavior, we construct a conjugation between shift maps and piecewise smooth vector fields presenting homoclinic loops which are associated to symbols in such a way that the flow restricted to a homoclinic loop is codified with a symbol. The construction of the topological conjugation between the quoted piecewise smooth vector fields and the respective shift spaces needs several technicality which were solved considering a specific family of piecewise smooth vector fields (Theorem A) and then generalizing the result for an entire class of piecewise smooth vector fields (Theorem B). By means of the results obtained and the techniques employed, a new perspective on the study of piecewise smooth vector fields is brought to light and, through already established results for discrete dynamic systems, we will be able to obtain results regarding piecewise smooth vector fields. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| Processo FAPESP: | 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II |
| Beneficiário: | Claudio Aguinaldo Buzzi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 19/10450-0 - Campos vetoriais suaves por partes: Closing Lemmas, shifts e dinâmicas do tipo ferradura. |
| Beneficiário: | Tiago de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 21/12395-6 - Campos vetoriais suaves por partes: aspectos teóricos e aplicações |
| Beneficiário: | Tiago de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 17/18255-6 - Closing lemmas e shifts para campos de vetores suaves por partes |
| Beneficiário: | Andre do Amaral Antunes |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado Direto |
| Processo FAPESP: | 22/02819-6 - Sistemas dinâmicos via campos vetoriais intermitentes: aspectos teóricos e aplicações |
| Beneficiário: | Tiago de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Projeto Inicial |
| Processo FAPESP: | 17/00883-0 - Campos vetoriais suaves por partes com aplicações em problemas biológicos |
| Beneficiário: | Tiago de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |