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.
- Darboux integrability
- Rational first integral