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| GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN R^3 |
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Citation： |
ZHANG Xin'an,CHEN Lansun,LIANG Zhaojun.GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN R^3[J].Chinese Annals of Mathematics B,1999,20(2):185~194 |
| Page view： 1054
Net amount： 752 |
Authors： |
ZHANG Xin'an; CHEN Lansun;LIANG Zhaojun |
Foundation： |
the National Natural Science
Foundation of China |
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| Abstract： |
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. |
Keywords： |
Tangent vector field, Invariant cone,
Global topological equivalence |
Classification： |
34C37, 58F09 |
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