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| Home > Articles > Published articles > Periodic orbits from second order perturbation via rational trigonometric integrals |
(Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Date: | 2014 |
| Abstract: | 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. |
| Grants: | Ministerio de Economía y Competitividad MTM2011-22751 Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad UNAB10-4E-378 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | 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 |
| Published in: | Physica D. Nonlinear phenomena, Vol. 280-281 (2014) , p. 59-72, ISSN 0167-2789 |
29 p, 488.3 KB |
