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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.

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

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ID Code: 12236
Item Type: Journal Article
Additional Information: For more information, please refer to the journal's website (see hypertext link) or contact the author.
Keywords: Abelian integrals, Liénard systems, bifurcation, limit cycle
DOI: 10.1142/S0218127407019032
ISSN: 0218-1274
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2007 World Scientific Publishing
Copyright Statement: Electronic version of an article published as International Journal of Bifurcation and Chaos, September 2007, Vol. 17, No. 09 : pp. 3281-3287, DOI: 10.1142/S0218127407019032 © [copyright World Scientific Publishing Company] http://www.worldscientific.com/doi/abs/10.1142/S0218127407019032
Deposited On: 25 Jan 2008
Last Modified: 19 Dec 2014 00:48

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