GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN {\tf R}$^{^{\hbox{\normal 3}}}$ |
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| Authors: | ZHANG Xin'an CHEN Lansun and LIANG Zhaojun |
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| Institution: | Institute of Mathematics, Academia Sinica, Beijing 100080,
China;Department of Mathematics, Central China Normal University,Wuhan 430079, China,Institute of Mathematics, Academia Sinica, Beijing 100080,
China and Department of Mathematics, Central China Normal University,
Wuhan 430079, 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. |
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| Keywords: | Tangent vector field Invariant cone Global topological equivalence |
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