Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

摘要

In this study, we determine the associated number of zeros for Abelian integrals in four classes of quadratic reversible centers of genus one. Based on the results of [Li et al., 2002b], we prove that the upper bounds of the associated number of zeros for Abelian integrals with orbits formed by conics, cubics, quartics, and sextics, under polynomial perturbations of arbitrary degree n, depend linearly on n.