On the center conditions for analytic monodromic degenerate singularities

Jaume Giné, Jaume Llibre

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9 Citations (Scopus)


In this paper, we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields and can be applied independently so that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allow to study monodromic degenerate singularities with characteristic directions. © 2012 World Scientific Publishing Company.
Original languageEnglish
Article number1250303
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number12
Publication statusPublished - 1 Jan 2012


  • Bautin method
  • Degenerate center
  • algebraically solvable
  • first integral


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