| Texto completo | |
| Autor(es): |
Cunha, Matheus G. C.
;
Novaes, Douglas D.
;
Ponce, Gabriel
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Nonlinearity; v. 37, n. 12, p. 22-pg., 2024-12-02. |
| Resumo | |
The concept of sliding Shilnikov connection has been recently introduced and represents an important notion in Filippov systems, because its existence implies chaotic behavior on an invariant subset of the system. The investigation of its properties has just begun, and understanding the topology and complexity of its invariant set is of interest. In this paper, we conduct a local analysis on the first return map associated to a sliding Shilnikov connection, which reveals a conformal iterated function system (CIFS) structure. By using the theory of CIFS, we estimate the Hausdorff dimension of the local invariant set of the first return map, showing, in particular, that is a positive number smaller than 1, and with one-dimensional Lebesgue measure equal to zero. Moreover, we prove that the closure of the local invariant set is a Cantor set and retains both the Hausdorff dimension and Lebesgue measure of the local invariant set. Furthermore, this closure consists of the local invariant set along with the set of all pre-images, under the first return map, of the visible fold-regular point contained in the connection. (AU) | |
| Processo FAPESP: | 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos |
| Beneficiário: | Marco Antônio Teixeira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/07762-2 - Dinâmica, rigidez suave e propriedades ergódicas de aplicações e fluxos hiperbólicos |
| Beneficiário: | Gabriel Ponce |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| 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: | 22/09633-5 - Teoria da média no estudo de toros invariantes e comportamento periódico em equações e inclusões diferenciais |
| Beneficiário: | Douglas Duarte Novaes |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |