A Class of Seven Degree Polynomial System With Eleven Limit Cycles at the Equator

In this paper,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 algebraic system Mathematica,the first 13 singular point quantities of the infinity are deduced.At the same time,the conditions for the infinity to be a center and 13 degree fine focus are derived respectively.A system of degree seven that bifurcates 11 limit cycles from the infinity is constructed at the first time.