Rational first integrals in the Darboux theory of integrability in Cn

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

32 Citations (Scopus)

Abstract

In 1979 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in Rn or Cn of degree d is at least ((d + n - 1; n)) + n, then the vector field has a rational first integral. His proof used sophisticated tools of algebraic geometry. We provide an easy and elementary proof of Jouanolou's result using linear algebra. © 2007 Elsevier Masson SAS. All rights reserved.
Original languageEnglish
Pages (from-to)189-195
JournalBulletin des Sciences Mathematiques
Volume134
DOIs
Publication statusPublished - 1 Mar 2010

Keywords

  • Darboux integrability
  • Rational first integral

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