| Texto completo | |
| Autor(es): |
Carmona, Victoriano
;
Fernandez-Sanchez, Fernando
;
Novaes, Douglas D.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Applied Mathematics Letters; v. 137, p. 8-pg., 2023-03-01. |
| Resumo | |
The existence of a uniform upper bound for the maximum number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line has been subject of interest of hundreds of papers. After more than 30 years of investigation since Lum-Chua's work, it has remained an open question whether this uniform upper bound exists or not. Here, we give a positive answer for this question by establishing the existence of a natural number L* <= 8 for which any planar piecewise linear differential system with two zones separated by a straight line has no more than L* limit cycles. The proof is obtained by combining a newly developed integral characterization of Poincare half-maps for linear differential systems with an extension of Khovanskii's theory for investigating the number of intersection points between smooth curves and a particular kind of orbits of vector fields. (c) 2022 Elsevier Ltd. All rights reserved. (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: | 21/10606-0 - Sobre ciclos limites em espaços vetoriais lineares por partes com variedade de descontinuidade algébrica |
| Beneficiário: | Douglas Duarte Novaes |
| Modalidade de apoio: | Bolsas no Exterior - Pesquisa |
| 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: | 22/09633-5 - 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 |