关于平面解析系统的拟齐次分解  

On the Quasi-Homogeneous Decomposition of Planar Analytic System

作　　者：陈秀红[1] 黄土森[1] 

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2014年第5期546-549,564,共5页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(10871181;11101370)

摘　　要：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.

关 键 词：拟齐次多项式 牛顿图 拟齐次多项式向量场 拟齐次分解 

分 类 号：O175.14[理学—数学]