Abstract

In this talk we will provide an easy and elementary proof of Jouanolou′s result on the existence of rational fisrt integrals. Recall that in 1979 Jouanolou used sophisticated tools of algebraic geometry to prove that the number of invariant algebraic hypersurfaces of a polynomial vector field in $Rn$ or $Cn$ of degree $d$ is sufficient larger if and only if the system has a rational first integral.