Analytic nilpotent centers as limits of nondegenerate centers revisited

Isaac A. Garcia; Hector Giacomini; Jaume Giné; Jaume Llibre

doi:10.1016/j.jmaa.2016.04.046

Journal articles

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 UAB - 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

Document type :

Journal articles

Domain :

Mathematics [math] / Dynamical Systems [math.DS]

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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 : Monday, March 29, 2021 - 11:50:04 AM

Analytic nilpotent centers as limits of nondegenerate centers revisited

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Analytic nilpotent centers as limits of nondegenerate centers revisited

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