Essential perturbations of polynomial vector fields with a period annulus
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Chicone-Jacobs and Iliev found the essential perturbations of quadratic systems when considering the problem of finding the cyclicity of a period annulus. Given a perturbation of a particular family of centers of polynomial diferential systems of arbitrary degree for which the expressions of its Poincaré-Liapunov constants are known, we give the structure of its k-th Melnikov function. This allows to find the essential perturbations in concrete cases. We study here in detail the essential perturbations for all the centers of the diferential systems.
Is part ofCommunications on Pure and Applied Analysis, 2015, vol. 14, num. 3, p. 1073-1095
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