| Normal Form for Families of Hamiltonian Systems |
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| 作者姓名： | Zhi Guo WANG |
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| 作者单位： | [1]Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China [2]School of Mathematical Sciences, Suzhou University, Suzhou 215006, P. R. China |
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| 基金项目： | The work is supported by the National Natural Science Foundation of China （19925107） and the Special Funds for Major State Basic Research Projects of China （973 Projects）;Acknowledgements I would like to thank You Jiangong, my supervisor, for his many suggestions and constant support during this research. I am also grateful to Wang Yiqian, Geng Jiansheng, He Hailong, Liang Zhenguo and Lu Hui for valuable communication. |
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| 摘 要： | We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d ＋ 1. And some dynamical consequences are obtained.
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| 关 键 词： | 哈密顿系统 三维流形 规格化形式 KAM理论 偏微分方程 |
| 收稿时间： | 24 November 2004 |
| 修稿时间： | 2004-11-242005-03-07 |
Normal Form for Families of Hamiltonian Systems |
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| Zhi Guo WANG.Normal Form for Families of Hamiltonian Systems[J].Acta Mathematica Sinica,2007,23(7):1199-1216. |
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| Authors: | Zhi Guo Wang |
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| Institution: | (1) Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China;(2) School of Mathematical Sciences, Suzhou University, Suzhou 215006, P. R. China |
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| Abstract: | We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using
the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form
up to a remainder of weighted order 2d + 1. And some dynamical consequences are obtained.
The work is supported by the National Natural Science Foundation of China (19925107) and the Special Funds for Major State
Basic Research Projects of China (973 Projects) |
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| Keywords: | KAM lower dimensional tori normal form resonant torus |
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