| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 309, p. 291-310, FEB 5 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 19/21181-0 - New frontiers in Singularity Theory |
| Grantee: | Regilene Delazari dos Santos Oliveira |
| Support Opportunities: | Research Projects - Thematic Grants |