| 一类三次系统的中心判定问题 |
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| 引用本文： | 桑波.一类三次系统的中心判定问题[J].数学年刊A辑(中文版),2014,35(3):361-372. |
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| 作者姓名： | 桑波 |
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| 作者单位： | 聊城大学数学科学学院, 山东~ 聊城 252059. |
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| 基金项目： | 国家自然科学基金 (No.10871214) |
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| 摘 要： | 对于一类具有三次衄线解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.
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| 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 |
Center Determination Problem for a Class of Cubic System |
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| SANG Bo.Center Determination Problem for a Class of Cubic System[J].Chinese Annals of Mathematics,2014,35(3):361-372. |
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| Authors: | SANG Bo |
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| Institution: | School of Mathematics Sciences, Liaocheng University,
Liaocheng 252059, Shandong, China. |
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| Abstract: | 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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| Keywords: | Cubic differential systems Center conditions Integrating factor Inverse integrating factor Limit cycle |
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