On the Number of Zeros of the Abelian Intergrals for a Class of Perturbed Lienard Systems
Zhang, Tonghua , Tian, Yu-Chu, & Tade, Moses O. (2007) On the Number of Zeros of the Abelian Intergrals for a Class of Perturbed Lienard Systems. International Journal of Bifurcation and Chaos, 17(9), pp. 3281-3287.
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 Linéar systems. We proved the main result using the Picard-Fuchs equations and the algebraic structure of the integrals.
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