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World Scientific Publishing, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 09(17), p. 3281-3287

DOI: 10.1142/s0218127407019032

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On the number of zeros of the Abelian integrals for a class of perturbed Lienard systems

Journal article published in 2007 by Tonghua Zhang ORCID, Yu-Chu Tian, Moses O. Tadé
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This paper is available in a repository.

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Abstract

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 Liénard systems. We proved the main result using the Picard–Fuchs equations and the algebraic structure of the integrals.