Lower bounds for the local cyclicity for families of centers

Autor(es)

Gine, Jaume ^[1] ; Gouveia, Luiz F. S. ^{[2, 3]} ; Torregrosa, Joan ^{[3, 4]}

Afiliação do(s) autor(es)

^[1] Univ Lleida, Dept Matemat, Avda Jaume II 69, Lleida 6925001, Catalonia - Spain

^[2] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto - Brazil

^[3] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia - Spain

^[4] Ctr Recerca Matemat, Campus Bellaterra, Barcelona 08193, Catalonia - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 275, p. 309-331, FEB 25 2021.
• Citações Web of Science: 0

Resumo

In this paper, we are interested in how the local cyclicity of a family of centers depends on the parameters. This fact was pointed out in {[}21], to prove that there exists a family of cubic centers, labeled by C D-31(12) in {[}25], with more local cyclicity than expected. In this family, there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some crucial missing points in the arguments that we correct here. We take advantage of a better understanding of the bifurcation phenomenon in nongeneric cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorphic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 20/04717-0 - Sistemas dinâmicos com simetrias e equações diferenciais implícitas
• Beneficiário: Luiz Fernando da Silva Gouveia
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado