一类二次可逆系统Abel积分零点个数的上界

Upper Bound on the Number of Zeros of Abelian Integrals for a Class of Quadratic Reversible System

利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的线性估计,得到了当n≥3时,上界为4[2n/3]+2[2n+1/3]+[2n+2/3]+16.

By using the method of Picard-Fuchs equation and the Riccati equation method, we give a linear estimate of the number of zeros of Abelian integrals for the quadratic reversible systems under polynomial perturbations of arbitrary degree n.The upper bound is 4[2n/3]＋2[2n＋1/3]＋[2n＋2/3]＋ 16 when n≥3.