The Closed Orbits of a Class of Cubic Vector Fields in R^(3)  

作　　者：Hong Yan YIN Da ZHOU Xing An ZHANG 

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,P.R.China [2]School of Mathematics and Statistics,South-Central University for Nationalities,Wuhan 430074,P.R.China [3]School of Mathematical Sciences,Xiamen University,Xiamen 361005,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第12期1429-1440,共12页数学学报（英文版）

基　　金：Supported by the National Nature Science Foundation of China(Grant Nos.11871238,11971405);selfdetermined research funds of CCNU from the collegesbasic research and operation of MOE(Grant No.CCNU16JCZX10);the Natural Science Foundation of Fujian Province of China(Grant No.2015J05016);the Fundamental Research Funds of the South-Central University for Nationalities(Grant No.CZQ13016)。

摘　　要：In this paper,we investigate the isolated closed orbits of two types of cubic vector fields in R^3 by using the idea of central projection transformation,which sets up a bridge connecting the vector field X(x)in R^3 with the planar vector fields.We have proved that the cubic vector field in R^3 can have two isolated closed orbits or one closed orbit on the invariant cone.As an application of this result,we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones,and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.

关 键 词：Closed orbit central projection transformation tangent vector field invariant cone 

分 类 号：O18[理学—数学]