Darboux theory of integrability in the sparse case
Classical Analysis and ODEs
2012-10-31 v1 Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1210.7780,
title = {Darboux theory of integrability in the sparse case},
author = {Guillaume Chèze},
journal= {arXiv preprint arXiv:1210.7780},
year = {2012}
}