Analytic integrability of some examples of degenerate planar vector fields

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Issue date
2016Suggested citation
Algaba, Antonio;
García, Cristóbal;
Giné, Jaume;
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(2016)
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Analytic integrability of some examples of degenerate planar vector fields.
Acta Applicandae Mathematicae, 2016, vol. 141, p. 1-15.
https://doi.org/10.1007/s10440-014-0001-2.
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This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate center problem. This classification can be done using the formal normal form theory and knowing a suitable normal form of any differential systems associated to each family.