Analytic nilpotent centers as limits of nondegenerate centers revisited

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• 作者：Isaac A. Garcí ; a^a ; ^{garcia@matematica.udl.cat" class="auth_mail" title="E-mail the corresponding author} ; Hé ; ctor Giacomini^b ; ^{Hector.Giacomini@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author} ; Jaume Giné ; ^a ; ^{gine@matematica.udl.cat" class="auth_mail" title="E-mail the corresponding author} ; Jaume Llibre^c ; ^{jllibre@mat.uab.cat" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nilpotent center ; Poincaré ; &ndash ; Liapunov constants
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：441
• 期：2
• 页码：893-899
• 全文大小：293 K

文摘

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.