Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces

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	Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
	Wang, Wei ; Hu, Xijun ; Long, Yiming
	2007-09-15
发表期刊	DUKE MATHEMATICAL JOURNAL
ISSN	0012-7094
卷号	139 期号:3 页码:411-462
摘要	There is a long-standing conjecture in Hamiltonian analysis which claims that there exist at least n geometrically distinct closed characteristics on every compact convex hypersurface in R-2n with n >= 2. Besides many partial results, this conjecture has been completely solved only for n = 2. In this article, we give a confirmed answer to this conjecture for n = 3. In order to prove this result, we establish first a new resonance identity for closed characteristics on every compact convex hypersurface Sigma in R-2n when the number of geometrically distinct closed characteristics on Sigma is finite. Then, using this identity and earlier techniques of the index iteration theory, we prove the mentioned multiplicity result for R-6. If there are exactly two geometrically distinct closed characteristics on a compact convex hypersurface in R-4, we prove that both of them must be irrationally elliptic.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000249292200001
出版者	DUKE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5007
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Wei
作者单位	1.Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China 3.Nankai Univ, Key Lab Pure Math & Combinator, Minist Educ, Chern Inst Math, Tianjin 300071, Peoples R China
推荐引用方式 GB/T 7714	Wang, Wei,Hu, Xijun,Long, Yiming. Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces[J]. DUKE MATHEMATICAL JOURNAL,2007,139(3):411-462.
APA	Wang, Wei,Hu, Xijun,&Long, Yiming.(2007).Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces.DUKE MATHEMATICAL JOURNAL,139(3),411-462.
MLA	Wang, Wei,et al."Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces".DUKE MATHEMATICAL JOURNAL 139.3(2007):411-462.