关键词: 不变代数曲线, 首次积分, 积分因子, 平衡点

Abstract: 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.

Key words: invariant algebraic curve, first integral, integrating factor, equilibrium point