First-order perturbation for multi-parameter center families
| Autor: | Regilene Oliveira, Jackson Itikawa, Joan Torregrosa |
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| Rok vydání: | 2022 |
| Předmět: |
Applied Mathematics
Averaging theory Inverse Function (mathematics) Limit cycle Expression (computer science) Multi-parameter perturbation Melnikov functions Integrating factor symbols.namesake Taylor series symbols Applied mathematics SISTEMAS DINÂMICOS Center (algebra and category theory) Limit (mathematics) Analysis Bifurcation Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | In the weak 16th Hilbert problem, the Poincare-Pontryagin-Melnikov function, M 1 ( 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 M 1 ( 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. |
| Databáze: | OpenAIRE |
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