一类二次可逆系统Abel积分零点个数的线性估计

Linear Estimate of the Number of Zeros of Abelian Integrals for a Kind 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≥4时,上界为14n-11.

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 system under polynomial perturbations of arbitrary degree n.The upper bound is 14n -11 when n≥4.