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The Global Dynamics of a Class of Vector Fields in R3 被引量:1
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作者 xin an zhang Zhao Jun LIanG Lan Sun CHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第12期2469-2480,共12页
In this paper, .we find a bridge connecting a class of vector fields in R3 with the planar vector fields and give a criterion of the existence of closed orbits, heteroclinic orbits and.homoclinic orbits of a class of ... In this paper, .we find a bridge connecting a class of vector fields in R3 with the planar vector fields and give a criterion of the existence of closed orbits, heteroclinic orbits and.homoclinic orbits of a class of vector fields in R3. All the possible nonwandering sets of this class of vector fields fall into three classes: (i) singularities; (ii) closed orbits; (iii) graphs of unions of singularities and the trajectories connecting them. The necessary and sufficient conditions for the boundedness of the vector fields are also obtained. 展开更多
关键词 Tangent vector field invariant cone heteroclinic orbit vector field
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