Darboux theory of integrability in the sparse case

Darboux's theorem and Jouanolou's theorem deal with the existence of first integrals and rational first integrals of a polynomial vector field. These results are given in terms of the degree of the polynomial vector field. Here we show that we can get the same kind of results if we conside...

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Veröffentlicht in:	Journal of Differential Equations 2014-07, Vol.257 (2), p.601-609
1. Verfasser:	Chèze, Guillaume
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical Analysis and ODEs Darboux integrability Exactly Solvable and Integrable Systems Invariant algebraic hypersurfaces Mathematics Newton polytope Nonlinear Sciences Optimal bound Rational first integral
Online-Zugang:	Volltext
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