Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
文献类型：期刊论文
| 作者 | Wang, Wei; Hu, Xijun; Long, Yiming |
| 刊名 | DUKE MATHEMATICAL JOURNAL
 |
| 出版日期 | 2007-09-15 |
| 卷号 | 139期号:3页码:411-462 |
| ISSN号 | 0012-7094 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000249292200001 |
| 出版者 | DUKE UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5006]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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