| 桑波.一类三次系统的中心判定问题[J].数学年刊A辑,2014,35(3):361~372 |
| 一类三次系统的中心判定问题 |
| Center Determination Problem for a Class of Cubic System |
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| DOI： |
| 中文关键词: 三次微分系统, 中心条件, 积分因子, 逆积分因子, 极限环 |
| 英文关键词:Cubic differential systems, Center conditions, Integrating factor, Inverse integrating factor, Limit cycle |
| 基金项目:国家自然科学基金 (No.10871214) |
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| 中文摘要: |
| 对于一类具有三次曲线解$x^{{2}} (x-1)-y^2-1=0$, 通过点$(1, 0)$的直线解和中心-焦点型奇点的三次系统,
证明了它以原点为中心的充要条件是它的前五阶焦点量全为零. 这些中心条件是
通过构造积分因子得以验证的. |
| 英文摘要: |
| A class of cubic system with a cubic curve solution $x^{{2}} (x-1)-y^2-1=0$,
a straight line solution passing through $(1, 0)$ 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.
All these center conditions are verified by constructing integrating factors. |
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