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On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems
Huang DB(黄德斌); Liu CR(刘曾荣)
Source PublicationNonlinearity
2000
Volume13Issue:1Pages:189-202
ISSN0951-7715
AbstractIn this paper, sufficiently smooth Hamiltonian systems with perturbations are considered. By combining a smooth version of the Kolmogorov-Arnold-Moser theorem and the theory of normally hyperbolic invariant manifolds, we show that under the conditions of nonresonance and nondegeneracy, most hyperbolic invariant tori and their stable and unstable manifolds survive smoothly under sufficiently smooth autonomous perturbation. This result can be generalized directly to the case of time-dependent quasi-periodic perturbations. Finally, an example from geometrical optics is used to illustrate our method.
DOI10.1088/0951-7715/13/1/309
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Indexed BySCI
Language英语
WOS IDWOS:000084894300010
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Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/55304
Collection力学所知识产出(1956-2008)
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GB/T 7714
Huang DB,Liu CR. On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems[J]. Nonlinearity,2000,13(1):189-202.
APA Huang DB,&Liu CR.(2000).On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems.Nonlinearity,13(1),189-202.
MLA Huang DB,et al."On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems".Nonlinearity 13.1(2000):189-202.
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