基于构造积分因子的中心和焦点判别方法

摘要

In this paper we consider real differential systems which at singular points have purely imaginary eigenvalues.We show that the real invariant algebraic curves of the system are not identically zero in some deleted neighborhood U°(O).A method for seeking local first integrals or integrating factors is proposed,which can be used in determining the types of the equilibrium points.%研究具有一对纯虚特征值的实系统的实不变代数曲线在原点空心邻域非零的性质,使用不变代数曲线和指数因子构造局部首次积分或积分因子,提出进行平衡点类型判别的方法.