CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES AT THE EQUATOR IN A CLASS OF SEVEN DEGREE POLYNOMIAL DIFFERENTIAL SYSTEM

Center conditions and bifurcation of limit cycles from the equator in a class of polynomial system of degree seven are studied.By converting real planar system into complex system,the recursion formula for the computation of singular point quantities of the infinity are given,and with computer algebra system Mathematica,the first 14 singular point quantities of the infinity are deduced.At the same time,the conditions for the infinity to be a center and 14 degree fine focus are derived respectively.According to the above,a system of degree seven that bifurcates 12 limit cycles from the infinity is constructed.