Rational first integrals in the Darboux theory of integrability in Cn

被引：42
|
作者：
Llibre, Jaume [1 ]
Zhang, Xiang [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2010年 / 134卷 / 02期
关键词：
Darboux integrability; Rational first integral; EQUATIONS;
D O I：
10.1016/j.bulsci.2007.12.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 1979 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in R-n or C-n of degree d is at least ((d+n-1)(n)) + n, then the vector field has a rational first integral. His proof used sophisticated tools of algebraic geometry. We provide an easy and elementary proof of Jouanolou's result using linear algebra. (C) 2007 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：189 / 195
页数：7
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