Periodic orbits from second order perturbation via rational trigonometric integrals
The second order Poincaré-Pontryagin-Melnikov perturbation theory is used in this paper to study the number of bifurcated periodic orbits from certain centers. This approach also allows us to give the shape and the period up to first order. We address these problems for some classes of Abel differen...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150713 |
| Acesso em linha: | https://ddd.uab.cat/record/150713 https://dx.doi.org/urn:doi:10.1016/j.physd.2014.05.002 |
| Access Level: | acceso abierto |
| Palavra-chave: | Polynomial differential equation Abel equation Bifurcation of periodic orbits Number, shape and period of periodic solutions First and second order perturbation Isochronous quadratic centers Simultaneous bifurcation |
| Resumo: | The second order Poincaré-Pontryagin-Melnikov perturbation theory is used in this paper to study the number of bifurcated periodic orbits from certain centers. This approach also allows us to give the shape and the period up to first order. We address these problems for some classes of Abel differential equations and quadratic isochronous vector fields in the plane. We prove that two is the maximum number of hyperbolic periodic orbits bifurcating from the isochronous quadratic centers with a birational linearization under quadratic perturbations of second order. In particular the configurations (2, 0) and (1, 1) are realizable when two centers are perturbed simultaneously. The required computations show that all the considered families share the same iterated rational trigonometric integrals. |
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