Essential perturbations of polynomial vector fields with a period annulus
Issue date
2015Suggested citation
Buica, Adriana;
Giné, Jaume;
Grau Montaña, Maite;
.
(2015)
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Essential perturbations of polynomial vector fields with a period annulus.
Communications on Pure and Applied Analysis, 2015, vol. 14, num. 3, p. 1073-1095.
https://doi.org/10.3934/cpaa.2015.14.1073.
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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.