Seeking Darboux Polynomials

Antoni Ferragut, Armengol Gasull

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)


© 2014, Springer Science+Business Media Dordrecht. We introduce several techniques which allow to simplify the expression of the cofactor of Darboux polynomials of polynomial differential systems in $\mathbb {R}^{n}$. We apply these techniques to some well-known systems when n=2,3,4. We also propose a general method for computing Darboux polynomials in the plane. As an application we prove that a family of potential systems, that includes the van der Pol one, has no Darboux polynomials, giving in particular a new simple proof that the van der Pol limit cycle is not algebraic.
Original languageEnglish
Pages (from-to)167-186
JournalActa Applicandae Mathematicae
Issue number1
Publication statusPublished - 29 Oct 2015


  • Birational map
  • Cofactor
  • Darboux polynomial
  • Non-algebraic limit cycle
  • Planar polynomial differential system


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