چکیده (انگلیسی):

In this paper, we described the number of zeros of Abelian integrals for four cases of quadratic reversible centers of genus one. With the results of W. Li et al. [24], we proved that the upper bound of the associated number of zeros of Abelian integrals, whose orbits are formed by quartics, quintics, sextic and eight-degree curve, under polynomial perturbations of arbitrary degree n, is linear depending on n.