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 language | English |
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Pages (from-to) | 189-195 |
Journal | Bulletin des Sciences Mathematiques |
Volume | 134 |
DOIs | |
Publication status | Published - 1 Mar 2010 |
Keywords
- Darboux integrability
- Rational first integral