一类平面三次拟齐次向量场的全局拓扑结构

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 419-425.

一类平面三次拟齐次向量场的全局拓扑结构

黄改改¹, 冯光庭², 张兴安¹

1.华中师范大学数学与统计学学院武汉 |430079|
2.湖北第二师范学院数学与统计学院武汉 |430205

收稿日期:2012-10-30 修回日期:2013-11-18 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
国家自然科学基金(11071275)、中央高校专项基金(CCNU10B01005)和湖北省自然科学基金(2013CFB013)资助.

A Global Topological Structure of a Class of Cubic Quasi-Homogeneous Vector Fields

HUANG Gai-Gai¹, FENG Guang-Ting², ZHANG Xing-An¹

1.School of Mathematics and Statistics, Central China Normal University, Wuhan 430079|
2.School of Mathematics and Statistics, Hubei University of Education, Wuhan 430205

Received:2012-10-30 Revised:2013-11-18 Online:2014-04-25 Published:2014-04-25
Supported by:
国家自然科学基金(11071275)、中央高校专项基金(CCNU10B01005)和湖北省自然科学基金(2013CFB013)资助.

摘要/Abstract

摘要：

利用中心投影变换的思想证明一类平面三次拟齐次向量场的几何性质依赖于它的切向量场和诱导向量场. 讨论了该系统的拓扑结构,并进行了分类; 证明了该系统具有25类不同类的拓扑结构相图.

关键词: 拟齐次向量场, 切向量场, 不变直线, 全局拓扑分类

Abstract:

In this paper,we use the idea of the central projection transformation to prove that the geometric properties of a class of cubic vector field depends on its tangent vector and induced vector field. We investigate its topological structures and classified, and we obtain 25 types of different topological classification of this vector field.

Key words: Quasi-homogeneous vector field, Tangent vector field, Invariant line, Global topological classification

中图分类号:

34C05

黄改改, 冯光庭, 张兴安. 一类平面三次拟齐次向量场的全局拓扑结构[J]. 数学物理学报, 2014, 34(2): 419-425.

HUANG Gai-Gai, FENG Guang-Ting, ZHANG Xing-An. A Global Topological Structure of a Class of Cubic Quasi-Homogeneous Vector Fields[J]. Acta mathematica scientia,Series A, 2014, 34(2): 419-425.

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