Debin Huang and Zengrong Liu 2000 Nonlinearity 13 189 doi:10.1088/0951-7715/13/1/309
On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems
Debin Huang and Zengrong Liu
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In 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.
- PACS
- MSC
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37D10 Invariant manifold theory
70H08 Nearly integrable Hamiltonian systems, KAM theory
- Subjects
- Dates
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Issue 1 (January 2000)
Received 4 January 1999, in final form 29 September 1999
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On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems
Debin Huang and Zengrong Liu 2000 Nonlinearity 13 189
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