具有等时中心的二次微分系统的极限环分支

Limit cycle bifurcations of a quadratic differential system with isochronous center

对于扰动等时微分系统x=√2/2 xy+εf(x,y),y=√2/2(2-2x+y^(2))+εg(x,y),其中0<ε<<1,f(x,y)和g(x,y)是关于x和y的n次多项式,应用Picard-Fuchs方程给出其Abel积分零点个数的上界,进而得到该系统极限环个数的上界.

Fora perturbed quadratic isochronous differential system x=√2/2 xy+εf(x,y),y=√2/2(2-2x+y^(2))+εg(x,y),where 0<ε<<1,f(x,y)and(x,y)are polynomials of x and y of degree n,by using Picard-Fuchs equation,the upper bound forthe number of zeros of the Abel integral is given,which imply the upper bound of the number of limit cycles of this system.