The Problem of the Centre for Cubic Systems with Two Parallel Invariant Straight Lines and One Invariant Conic

被引：4

作者：

Cozma, Dumitru ^{[1
]}

机构：

[1] Tiraspol State Univ, Dept Math, MD-2069 Kishinev, Moldova

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2009年 / 16卷 / 02期

关键词：

Cubic differential systems; center-focus problem; invariant algebraic curves; integrability; DARBOUX INTEGRABILITY;

D O I：

10.1007/s00030-008-7044-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For cubic differential systems with two parallel invariant straight lines and at least one invariant conic it is proved that a singular point with pure imaginary eigenvalues (a weak focus) is a centre if and only if the first three Liapunov quantities L (j) , j = 1, 2, 3 vanish.

引用

页码：213 / 234

页数：22

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