一类扰动的二次可逆系统的Abel 积分的上界估计

Upper Bound Estimation of AbelianIntegral for a Class of PerturbedQuadratic Reversible Systems

利用Riccati方程法,研究了一类亏格1形式的二次可逆系统(r9)在任意3, 2, 1次多项式扰动下的Abel积分孤立零点个数的上界。 得到的结果为: 在3, 2, 1次多项式扰动下上界是13。 这些结果是 对之前结果的改进。

By using Riccati equation method, the upper bound estimation of the number of zeros of Abelian integral for a class of quadratic reversible system (r9) of genus one under any polynomial perturbation of degree 3;2;1 is studied. The result is that the upper bound is 13 under polynomial perturbation of degree 3;2;1. These results are animprovement of the previous results.