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

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/192060

Title: On the number of zeros of the Abelian integrals for a class of perturbed Lienard systems
Author(s): Zhang, Tonghua; Tian, Yu C.; Tade, Moses O.
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 Lienard systems. We proved the main result using the Picard-Fuchs equations and the algebraic structure of the integrals.
Publication type: Journal article
Source: International Journal of Bifurcation and Chaos, Vol. 17, no. 9 (Sep 2007), pp. 3281-3287
Publication year: 2007
FOR Code(s): 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics
Keyword(s): Abelia; Abelian integrals; Algebra; Algebraic structure; Bifurcation; Bifurcation (mathematics); Hilbert-Arnold problem; Integral equations; Lienard system; Limit cycle; Numerical analysis; Perturbation techniques; Problem solving
Publisher: World Scientific Publishing
ISSN: 0218-1274
Publisher URL: http://dx.doi.org/10.1142/s0218127407019032
Peer reviewed