Cyclicity versus center problem

Armengol Gasull, Jaume Giné

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)


We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed. © Springer Basel AG 2010.
Original languageEnglish
Pages (from-to)101-113
JournalQualitative Theory of Dynamical Systems
Issue number1-2
Publication statusPublished - 1 Jan 2010


  • Cyclicity
  • Focal quantities
  • Limit cycles
  • Lyapunov constants
  • Polynomial differential system


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