一类平面拟齐次向量场的全局性质  

The Global Property of a Class of Planar Quasi-Homogeneous Vector Fields

作　　者：黄莉[1] 冯光庭[2] 张金慧[3] 张兴安[1] 

机构地区：[1]华中师范大学数学与统计学学院,湖北武汉430079 [2]湖北第二师范学院数学与经济学院,湖北武汉430205 [3]中原工学院理学院,河南郑州450007

出　　处：《生物数学学报》2016年第2期171-184,共14页Journal of Biomathematics

基　　金：湖北省自然科学基金(2013CFB013);国家自然科学基金(11371161);中央高校专项基金(CCNU10B01005)

摘　　要：本文利用中心投影思想证明了一类拟齐次平面向量场的几何性质仅依赖于它的诱导向量场.并根据其诱导向量场的性质证明了该向量场有10种不同拓扑结构的扇形不变区域,进而讨论了其全局拓扑结构,得到了这类向量场当n为偶数时,有17种不同的全局拓扑分类,当n为奇数时,有32种不同的全局拓扑分类.In this paper,by using the idea of the central projection it is shown that the geometric property of a class of planar quasi-homogeneous vector fields depends on their induced vector fields.By virtue of its induced vector field jr is proven that this vector field has 10 types of sector invariant fields with different topological classification.~rthermore,its global topological structure is discussed and it is shown that there are 17 types of different topological classification when n is even number and 32 types of different topological classification when n is odd number

关 键 词：拟齐次向量场 切向量场 不变直线 全局拓扑分类 

分 类 号：O175.12[理学—数学]