(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, using the method of Picard-Fuchs equation and Riccati equation, for a class of quadratic reversible centers of genus one, we research the upper bound of the number of zeros of Abelian integrals for the system (r10) under arbitrary polynomial perturbations of degree n. Our main result is that the upper bound is 21n − 24 (n ≥ 3), and the upper bound depends linearly on n.