The Global Dynamics of a Class of Vector Fields in R3

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

作者机构：School of Mathematics and Statistics Central China Normal University Wuhan 430079 P. R. China Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第12期

页      面：2469-2480页

核心收录：

学科分类：1305[艺术学-设计学（可授艺术学、工学学位）] 13[艺术学] 07[理学] 08[工学] 080203[工学-机械设计及理论] 070104[理学-应用数学] 081304[工学-建筑技术科学] 0802[工学-机械工程] 0813[工学-建筑学] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

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

主　　题：Tangent vector field invariant cone heteroclinic orbit vector field 

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 *** 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.