【摘要】 本文研究了一类三次系统无穷远点的中心条件与赤道极限环分枝问题。通过将实平面系统转化为复系统研究,给出了计算无穷远点奇点量的递推公式,并在计算机上用Mathematica推导出该系统无穷远点前七个无穷远点奇点量,进一步导出了无穷远点成为中心的条件和七阶细焦点的条件,得到了三次系统无穷远点分支出七个极限环的一个实例。更多还原

【Abstract】 Studied in this paper are center conditions and bifurcation of limit cycles from the equator for a class of cubic polynomial system.By converting the real planar system into complex system,the recursion formula for the computation of singular quantities at infinity are given,and,with Mathemat- ica,the first 7 singular point quantities at infinity are deduced.At the same time,the condition for the infinity to be a center and 7 degree fine focus are derived,respectively.A cubic system that bifurcates 7 limit cycles from infinity is obtained.更多还原