复域上几个过极限环积分流形的几何结构

Several Geometric Structure of Integral Manifold Passing Limit Cycle on Complex Domain

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.

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.