The Global Dynamics of a Class of Vector Fields in R3  

作　　者：Xin An ZHANG Zhao Jun LIANG Lan Sun CHEN 

机构地区：[1]School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China [2]Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第12期2469-2480,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10771081）

摘　　要：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.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.

关 键 词：Tangent vector field invariant cone heteroclinic orbit vector field 

分 类 号：O175.1[理学—数学] TP391.72[理学—基础数学]