Configurations of limit cycles and planar polynomial vector fields

被引：53

作者：

Llibre, J ^{[1
]}

Rodríguez, G

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Univ Santiago, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15782, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 198卷 / 02期

关键词：

limit cycles; quadratic vector fields;

D O I：

10.1016/j.jde.2003.10.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：374 / 380

页数：7

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