First-order perturbation for multi-parameter center families

Autor(es)

Itikawa, Jackson ^[1] ; Oliveira, Regilene ^[2] ; Torregrosa, Joan ^{[3, 4]}

Afiliação do(s) autor(es)

^[1] Univ Fed Rondonia, Dept Math, BR-76801059 Porto Velho, RO - Brazil

^[2] Univ Sao Paulo, Dept Matemat, ICMC, Ave Trabalhador Saocarlense 400, BR-13566590 Sao Carlos, SP - Brazil

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

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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 309, p. 291-310, FEB 5 2022.
• Citações Web of Science: 0

Resumo

In the weak 16th Hilbert problem, the Poincare-Pontryagin-Melnikov function, M1(h), is used for obtaining isolated periodic orbits bifurcating from centers up to a first-order analysis. This problem becomes more difficult when a family of centers is considered. In this work we provide a compact expression for the first-order Taylor series of the function M1(h, a) with respect to a, being a the multi-parameter in the unperturbed center family. More concretely, when the center family has an explicit first integral or inverse integrating factor depending on a. We use this new bifurcation mechanism to increase the number of limit cycles appearing up to a first-order analysis without the difficulties that higher-order studies present. We show its effectiveness by applying it to some classical examples. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). (AU)

• Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Temático