一类n+1次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：冯光庭[1] 殷秀芝[2] 凌中华[2] 张兴安[2] 

机构地区：[1]湖北第二师范学院数学与统计学院,武汉430205 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《系统科学与数学》2014年第4期475-487,共13页Journal of Systems Science and Mathematical Sciences

基　　金：湖北省自然科学基金(2013CFB013);国家自然科学基金(11071275;11371161);中央高校专项基金(CCNU10B01005)资助课题

摘　　要：利用中心投影的思想证明了一类n+1次平面拟齐次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,得到了该向量场当n为偶数时有13种不同的全局拓扑等价类,当n为奇数时有12种不同的全局拓扑等价类.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 of degree n ＋ 1 depends on their induced vector fields.By virtue of its induced vector field,it is proven that this vector field has 10 types of sector invariant fields with different topological classification.Furthermore,its global topological structure is discussed and it is shown that there are 13 types of different topological classification when n is even number and 12 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：O183.1[理学—数学]