关于平面解析系统的拟齐次分解

On the Quasi-Homogeneous Decomposition of Planar Analytic System

通过解析函数的拟齐次分解与牛顿图,研究了平面解析系统的拟齐次分解问题。给出了拟齐次向量场空间的维数及平面解析系统的拟齐次分解定理,并用实例给出平面多项式系统拟齐次分解的具体算法。这些结果推广了平面解析系统的拟齐次分解中的有关结论,对研究平面高次奇点性态具有参考价值。

In this paper, the quasi-homogeneous decomposition of planar analytic system is studied through the quasi-homogeneous decomposition of the analytic function and Newton diagram. The dimension of the quasi-homogeneous vector field space and quasi-homogeneous decomposition theorem of the planar analytic system are given. Besides, the specific algorithm of quasi-homogeneous decomposition of planar polynomial system is given with examples. These results generalize relevant conclusions in associating references, and are helpful to study the qualitative properties of quasi-homogeneous decomposition of pla- nar polynomial system and have reference value for studying higher-order singular point.