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Essential perturbations of polynomial vector fields with a period annulus

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Issue date
2015
Author
Buica, Adriana
Giné, Jaume
Grau Montaña, Maite
Suggested citation
Buica, Adriana; Giné, Jaume; Grau Montaña, Maite; . (2015) . 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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Abstract
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.
URI
http://hdl.handle.net/10459.1/49432
DOI
https://doi.org/10.3934/cpaa.2015.14.1073
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Communications on Pure and Applied Analysis, 2015, vol. 14, num. 3, p. 1073-1095
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