一类多项式微分系统无穷远点的中心-焦点判定  

THE DETERMINATION OF CENTER-FOCUS AT THE INFINITY FOR A CLASS OF POLYNOMIAL DIFFERENTIAL SYSTEM

作　　者：张齐[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075

出　　处：《经济数学》2007年第1期98-102,共5页Journal of Quantitative Economics

摘　　要：本文研究了一类七次系统无穷远点的中心-焦点判定问题.通过将实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十二个奇点量,进一步导出了无穷远点成为中心的条件和分别成为七阶、九阶、十二阶细焦点的条件.In this paper, the determination of center - focus at the infinity for a class of seven degree differential system was studied. By converting real planar system into complex system, the recursion formula for the computation of singular point quantities of the infinity was given, and , with computer algebraic system Mathematica, the first 12 singular point quantities of the infinity were deduced. At the same time, the conditions for the infinity to be a center and 7,9 or 12 degree fine focus were derived respectively.

关 键 词：七次多项式系统 无穷远点 焦点量 奇点量 中心-焦点判定 

分 类 号：O175.12[理学—数学]