摘要
本文讨论了ｎ维欧氏空间Ｒｎ（ｎ＞２）上的多项式向量场集合的系数拓扑不变量，可分为具有不同全局拓扑性质的两类不交的子集合；证明了Ｒｎ上的多项式向量场可连续地延拓成ｎ维射影空间ＲＰｎ上的连续多项式向量场的充要条件，反应了其次数与系数相关的拓扑性质；还证明了平面上的多项式向量场的赤道是闭轨线和不变集的充要条件．
This paper has discussed the topological coefficient invariance of the set of the polynomial vector fields in n-dimensional Euclidean space R n (n>2). The set can be divided into two types of disjoint subsets. We prove the necessary and sufficient conditions that the polynomial vector fields in R n can becontinuously extended to the continuous polynomial vector fields inn-dimensional projective space RP n, which indicates the topological property between the coefficients and degrees. We also prove the necessary and sufficient conditions that the equator(or the points of R 2 at infinity)of planar polynomial vector fields is a closed orbit or an invariant set.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1998年第5期955-964,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金
湖北省自然科学基金
关键词
射影空间
多项式向量场
拓扑等价
多项式系统
Projective space, Continuous polynomial rector fields, Topological equivalence
