A method for characterizing nilpotent centers

Jaume Giné, Jaume Llibre

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15 Citations (Scopus)


To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and second for studying the bifurcation of limit cycles from it or from its period annulus. We provide necessary conditions for detecting nilpotent centers based on recent developments. Moreover we survey the last results on this problem and illustrate our approach by means of examples. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)537-545
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 May 2014


  • Bautin method
  • Degenerate center
  • Liapunov constants
  • Nilpotent center


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