Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2)

被引：0

作者：

张祥

机构：

[1] China

[2] Department of Mathematics

[3] Shanghai Jiaotong University Shanghai 200030

来源：

Science China Mathematics | 2003年 / 02期

基金：

中国国家自然科学基金;

关键词：

holomorphic foliation; invariant algebraic curve; rational first integral; cubic limit cycle;

D O I：

暂无

中图分类号：

O187 [代数几何];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degrees of invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that any holomorphic foliation of degree 2 does not have cubic limit cycles.

引用

页码：271 / 279

页数：9