(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree n. We obtain that the upper bound is 7[(n − 3)/2] + 5 when n ≥ 5, 8 when n = 4, 5 when n = 3, 4 when n = 2, and 0 when n = 1 or n = 0, which linearly depends on n.