Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers
In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. In this paper, we study quadratic polynomial systems with an algebraic periodic...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2018 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:221283 |
| Acesso em linha: | https://ddd.uab.cat/record/221283 https://dx.doi.org/urn:doi:10.1142/S0218127418501456 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Quadratic systems Quadratic vector fields Quadratic center Periodic orbit Limit cycle Bifurcation from center Cyclicity of the period annulus |
| Resumo: | In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree 4 surrounding a center. We show that there exists only one family of such systems satisfying that an algebraic limit cycle of degree 4 can bifurcate from the period annulus of the mentioned center under quadratic perturbations. |
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