On the Number of zeros of the Abelian integrals for a Class of perturbed LiÉnard Systems

Addressing the weakened Hilbert's 16th problem or the Hilbert–Arnold problem, this paper gives an upper bound B(n) ≤ 7n + 5 for the number of zeros of the Abelian integrals for a class of Lienard systems. We proved the main result using the Picard–Fuchs equations and the algebraic structure of the integrals.

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