Multiscale KAM theorem for Hamiltonian systems |
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Authors: | Weichao Qian Yong Li Xue Yang |
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Affiliation: | 1. School of Mathematics and Statistics, & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, PR China;2. School of Mathematics, Jilin University, Changchun, 130012, PR China |
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Abstract: | In this paper, we study the persistence of invariant tori in nearly integrable multiscale Hamiltonian systems with highorder degeneracy in the integrable part. Such Hamiltonian systems arise naturally in planar and spatial lunar problems of celestial mechanics for which the persistence problem connects closely to the stability of the systems. We introduce multiscale nondegenerate condition and multiscale Diophantine condition, comparable to the usual Diophantine condition. Using quasilinear KAM method, we prove a multiscale KAM theorem. |
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Keywords: | primary 37J40 70H08 Multiscale KAM theorem Hamiltonian system Multiscale nondegenerate condition |
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