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Analytic nilpotent centers as limits of nondegenerate centers revisited

Isaac A. Garcia Hector Giacomini 1, 2 Jaume Giné Jaume Llibre 3
1 FDP - Fédération de recherche Denis Poisson
2 LMPT - Laboratoire de Mathématiques et Physique Théorique
3 Departament de Matemàtiques [Barcelona]
Abstract : We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré– Liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers.
Keywords : planar systems-nilpotent center-Poincaré-Lyapunov method
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https://hal.archives-ouvertes.fr/hal-01309525
Contributor : Hector Giacomini <>
Submitted on : Friday, April 29, 2016 - 4:34:08 PM
Last modification on : Thursday, February 7, 2019 - 4:18:44 PM

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Isaac A. Garcia, Hector Giacomini, Jaume Giné, Jaume Llibre. Analytic nilpotent centers as limits of nondegenerate centers revisited. Journal of Mathematical Analysis and Applications, Elsevier, 2016, 441, pp.893-899. ⟨10.1016/j.jmaa.2016.04.046⟩. ⟨hal-01309525⟩

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