TY - JOUR
T1 - Rational first integrals in the Darboux theory of integrability in Cn
AU - Llibre, Jaume
AU - Zhang, Xiang
PY - 2010/3/1
Y1 - 2010/3/1
N2 - 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.
AB - 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.
KW - Darboux integrability
KW - Rational first integral
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=3149139
UR - https://www.scopus.com/pages/publications/76349096041
U2 - 10.1016/j.bulsci.2007.12.001
DO - 10.1016/j.bulsci.2007.12.001
M3 - Article
SN - 0007-4497
VL - 134
SP - 189
EP - 195
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
ER -