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• W2047805905 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 the 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." @default.
• W2047805905 created "2016-06-24" @default.
• W2047805905 creator A5085767356 @default.
• W2047805905 creator A5091905999 @default.
• W2047805905 date "2014-07-01" @default.
• W2047805905 modified "2023-10-04" @default.
• W2047805905 title "Periodic orbits from second order perturbation via rational trigonometric integrals" @default.
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• W2047805905 doi "https://doi.org/10.1016/j.physd.2014.05.002" @default.
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