平面齐次多项式系统的局部相图

Local phase portraits of plane homogeneous polynomial systems

平面系统在动力系统研究中起着极重要和基础的作用。利用奇点指数和牛顿多边形方法，讨论了一类平面齐次多项式系统在其孤立奇点附近的相图。给出了一些奇点稳定的必要和充分条件。

By using Newton polyhedra method, local phase portraits of some homogenerous polynomial vector field is discussed, some necessary and sufficient conditions forthe local stability of the origin are obtained.