Darboux polynomials, balances and Painlevé property

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


© 2017, Pleiades Publishing, Ltd. For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya exponents. The relation of these last two notions to the general integrability has been intensively studied over these last years.
Original languageEnglish
Pages (from-to)543-550
JournalRegular and Chaotic Dynamics
Issue number5
Publication statusPublished - 1 Sep 2017


  • Darboux polynomial
  • Kovalevskaya exponents
  • Painlevé property


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