| Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems |
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| 引用本文： | 柳振鑫,伊贺达赉,黄庆道. Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems[J]. 东北数学, 2005, 21(4): 447-464 |
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| 作者姓名： | 柳振鑫 伊贺达赉 黄庆道 |
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| 作者单位： | School of Mathematics Jilin University，Changchun，130012，School of Mathematics，Jilin University，Changchun，130012，School of Mathematics，Jilin University，Changchun，130012 |
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| 摘 要： | In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graff and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on sub manifolds.
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| 关 键 词： | Hamiltonian系统 双曲线方程 KAM理论 持久性 |
Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems |
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| LIU Zhen-xin,YIHE Da-lai and HUANG Qing-dao. Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems[J]. Northeastern Mathematical Journal, 2005, 21(4): 447-464 |
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| Authors: | LIU Zhen-xin YIHE Da-lai HUANG Qing-dao |
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| Affiliation: | School of Mathematics, Jilin University, Changchun, 130012 |
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| Abstract: | In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graff and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on sub manifolds. |
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| Keywords: | hyperbolic invariant tori KAM theorem generalized Hamiltonian system |
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