| Texto completo | |
| Autor(es): |
Garcia, Isaac A.
;
Gine, Jaume
;
Rodero, Ana Livia
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Mathematical Analysis and Applications; v. 547, n. 2, p. 14-pg., 2025-07-15. |
| Resumo | |
We are interested in bound the maximum number of small amplitude limit cycles that an analytic planar vector field can have bifurcating from any monodromic singularity as well as its stability and hyperbolic nature. We do not use the Poincar & eacute; map approach to this problem. Instead, we propose an algorithmic procedure to construct, under some assumptions, a Dulac function in a neighborhood (may be punctured) of the singularity. This approach is based on the existence of a real analytic invariant curve passing through the singularity which allows us to overcome the usual difficulty seeking for the candidates to be a Dulac function. We finally apply our results to a degenerate polynomial monodromic family. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| Processo FAPESP: | 21/12630-5 - Ciclicidade e estabilidade estrutural local de campos de vetores suaves por partes |
| Beneficiário: | Ana Livia Rodero |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 23/05686-0 - Problemas de integrabilidade, centro e ciclicidade para campos de vetores planares analíticos |
| Beneficiário: | Ana Livia Rodero |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado |