Rational first integrals for polynomial vector fields on algebraic hypersurfaces of R^N 1
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Bolaños Rivera, Yudy Marcela (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2012
Abstract:	Using sophisticated techniques of Algebraic Geometry Jouanolou in 1979 showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in Rn of degree m is at least n+m−1 n+ n, then the vector field has a rational first integral. Llibre and Zhang used only Linear Algebra provided a shorter and easier proof of the result given by Jouanolou. We use ideas of Llibre and Zhang to extend the Jouanolou result to polynomial vector fields defined on algebraic regular hypersurfaces of Rn+1, this extended result completes the standard results of the Darboux theory of integrability for polynomial vector fields on regular algebraic hypersurfaces of Rn+1.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 22 Núm. 11 (2012) , p. 1250270 (11 pages), ISSN 1793-6551

DOI: 10.1142/S0218127412502707

Postprint 11 p, 467.1 KB

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