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Pàgina inicial > Articles > Articles publicats > Rational first integrals for polynomial vector fields on algebraic hypersurfaces of R^N 1 |
Data: | 2012 |
Resum: | 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. |
Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Publicat a: | International journal of bifurcation and chaos in applied sciences and engineering, Vol. 22 Núm. 11 (2012) , p. 1250270 (11 pages), ISSN 1793-6551 |
Postprint 11 p, 467.1 KB |