Analytic nilpotent centers as limits of nondegenerate centers revisited

Isaac A. García, Héctor Giacomini, Jaume Giné, Jaume Llibre

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13 Citations (Scopus)


© 2016 Elsevier Inc. 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.
Original languageEnglish
Pages (from-to)893-899
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Sep 2016


  • Nilpotent center
  • Poincaré-Liapunov constants


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