Darboux theory of integrability in the sparse case

详细信息    查看全文

• 作者：Guillaume Chè ; ze ^{guillaume.cheze@math.univ-toulouse.fr" class="auth_mail}
• 关键词：34A34 ; 34C14 ; 13N15
• 刊名：Journal of Differential Equations
• 出版年：15 July 2014
• 年：2014
• 卷：257
• 期：2
• 页码：601-609
• 全文大小：222 K

文摘

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.