[1]桑 波.具有一对共轭复不变直线的三次系统的中心判定问题[J].南京师大学报(自然科学版),2013,36(01):16-21.
　Sang Bo.Center Determination Problem for a Class of Cubic System with a Pair of Invariant Conjugate Imaginary Straight Lines[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):16-21.
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具有一对共轭复不变直线的三次系统的中心判定问题()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年01期
页码:
16-21
栏目:
数学
出版日期:
2013-03-31

文章信息/Info

Title:
Center Determination Problem for a Class of Cubic System with a Pair of Invariant Conjugate Imaginary Straight Lines
作者:
桑 波
聊城大学数学科学学院,山东 聊城 252059
Author(s):
Sang Bo
School of Mathematics Sciences,Liaocheng University,Liaocheng 252059,China
关键词:
三次微分系统; 中心条件; 积分因子; 对称原理
Keywords:
cubic differential systems; center conditions; integrating factor; symmetry principle
分类号:
O175.12
摘要:
对于一类具有一对共轭复不变直线和中心-焦点型奇点的三次系统,证明它以原点为中心的充要条件是其前五阶焦点量全为零.此中心条件是通过不变代数曲线构造积分因子或对称原理得以证明.
Abstract:
A class of cubic systems with a pair of invariant conjugate imaginary straight lines and a center-focus type singular point,is proved to have a center at the origin if and only if the first five focal values vanish.The presence of a center at the origin is proved by constructing integrating factor formed from invariant algebraic curves or by symmetry principle.

参考文献/References:

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[6]Cozma D.Center problem for cubic systems with a bundle of two invariant straight lines and one invariant conic[J].Buletinul Academiei de Stiinte a Republicii Moldova:Matematica,2012,68(1):32-49.
[7]刘一戎,李继彬.平面向量场的若干经典问题[M].北京:科学出版社,2010.
[8]桑波,朱思铭.焦点量算法和中心条件推导[J].数学物理学报,2008,28(1):164-173.
[9]吴文俊.数学机械化[M].北京:科学出版社,2003.

相似文献/References:

[1]桑波.两类三次微分系统的中心焦点问题[J].南京师大学报(自然科学版),2012,35(02):16.
　Sang Bo.The Center-Focus Problems for Two Classes of Cubic Systems[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(01):16.

备注/Memo

备注/Memo:
收稿日期:2012-03-01.
基金项目:数学天元基金项目(11226041).
通讯联系人:桑波,博士,副教授,研究方向:常微分方程定性理论和符号计算.E-mail:sangbopress@126.com
更新日期/Last Update: 2013-03-31