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	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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