| ZHANG Xin'an,CHEN Lansun,LIANG Zhaojun.[J].数学年刊A辑,1999,20(2):185~194 |
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| GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN {\tf R}$^{^{\hbox{\normal 3}}}$ |
| Received:September 08, 1997 Revised:September 29, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Tangent vector field, Invariant cone,
Global topological equivalence |
| 基金项目: |
| Author Name | Affiliation | | ZHANG Xin'an | Institute of Mathematics, Academia Sinica, Beijing 100080,
China
Department of Mathematics, Central China Normal University,Wuhan 430079, China | | CHEN Lansun | Institute of Mathematics, Academia Sinica, Beijing 100080,
China | | LIANG Zhaojun | Department of Mathematics, Central China Normal University,
Wuhan 430079, China |
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| 中文摘要: |
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| 英文摘要: |
| In this paper, the authors prove that the flows of homogeneous vector field $Q(x)$ at infinity are topologically equivalent to the flows of the tangent vector field $Q_T(u)$ $(u\in S^2)$
on the sphere $S^2$, and show the theorems for the global topological classification of $Q(x)$. They derive the necessary and sufficient conditions for the global asymptotic stability and the boundedness of vector field $Q(x),$ and obtain the
criterion for the global topological equivalence of two homogeneous vector fields. |
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