Darboux theory of integrability in the sparse case |
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Authors: | Guillaume Chèze |
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Institution: | Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Paul Sabatier Toulouse 3, MIP Bât 1R3, 31 062 Toulouse cedex 9, France |
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Abstract: | 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 consider the size of a Newton polytope associated to the vector field. Furthermore, we show that in this context the bound is optimal. |
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Keywords: | 34A34 34C14 13N15 |
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