一类二次可逆系统的Abel积分

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积分零点个数的上界问题,得到了当n≥4时,上界为10n+[n/2]-1.

By using the method of Picard-Fuchs equation and the Riccati equation method, we give an upper bound on the number of zeros of Abelian integrals for the quadratic reversible system under polynomial perturbations of arbitrary degree n. The upper bound is10n＋[m/2]-1when n≥4.