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Rational first integrals in the Darboux theory of integrability in [formula omitted]

Authors
Journal
Bulletin des Sciences Mathématiques
0007-4497
Publisher
Elsevier
Publication Date
Volume
134
Issue
2
Identifiers
DOI: 10.1016/j.bulsci.2007.12.001
Keywords
  • Darboux Integrability
  • Rational First Integral
Disciplines
  • Mathematics

Abstract

Abstract In 1979 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in R n or C n 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.

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