The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops | |
Chow, SN ; Li, CZ ; Yi, YF | |
2002 | |
关键词 | 16TH HILBERT PROBLEM LIMIT-CYCLES PERTURBATIONS NUMBER CENTERS |
英文摘要 | We study the cyclicity of period annuli (or annulus) for general degenerate quadratic Hamiltonian systems with an elliptic segment or a saddle loop, under quadratic perturbations. By using geometrical arguments and studying the respective Abelian integral based on the Picard-Fuchs equation, it is shown that the cyclicity of period annuli (or annulus) for such systems equals two. Ibis result, together with those of Gavrilov and Iliev (2000), Iliev (1996), Zhao et al (2000) and Zhao and Zhu (2001) gives a complete solution to the infinitesimal Hilbert 16th problem in the case of degenerate quadratic Hamiltonian systems under quadratic perturbations.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000175414100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Mathematics; SCI(E); 25; ARTICLE; 349-374; 22 |
语种 | 英语 |
出处 | SCI |
出版者 | ergodic theory and dynamical systems |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/388399] ![]() |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Chow, SN,Li, CZ,Yi, YF. The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops. 2002-01-01. |
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