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.
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 |
| Deposited On: | 25 Jan 2008 |
| Last Modified: | 02 Mar 2012 09:36 |
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