| 复域上几个过极限环积分流形的几何结构 |
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| 引用本文： | 蒋风光,管克英. 复域上几个过极限环积分流形的几何结构[J]. 北京交通大学学报(自然科学版), 2004, 28(3): 21-26 |
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| 作者姓名： | 蒋风光 管克英 |
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| 作者单位： | 北京交通大学,理学院,北京,100044;北京交通大学,理学院,北京,100044 |
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| 摘 要： | 研究了几个多项式自治系统在复域上过其极限环积分流形的复杂的几何结构,得到了在积分流形碰到无穷远奇点后黎曼曲面的4种变化趋向,并且从李群角度上证明了这些系统具有不可积性.
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| 关 键 词： | 微分方程解析理论 复平面 极限环 积分流形 李群 |
| 文章编号： | 1000-1506(2004)03-0021-06 |
| 修稿时间： | 2003-10-09 |
Several Geometric Structure of Integral Manifold Passing Limit Cycle on Complex Domain |
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| JIANG Feng-guang,GUAN Ke-ying. Several Geometric Structure of Integral Manifold Passing Limit Cycle on Complex Domain[J]. JOURNAL OF BEIJING JIAOTONG UNIVERSITY, 2004, 28(3): 21-26 |
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| Authors: | JIANG Feng-guang GUAN Ke-ying |
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| Abstract: | Several polynomial autonomous systems, which have at least one limit cycle, are studied by using numerical evaluation and qualitative method. Their geometric structures of solveing manifold passing limit cycle on complex number plane are obtained. They are more complex than on the real number plane. We also prove that those systems are not integrable in the sense of Lie Groups. |
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| Keywords: | analytic theory of differential eqation complex number plane limit cycle integral manifold Lie Groups |
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