A symplectic map and its application to the persistence of lower dimensional invariant tori |
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Authors: | Junxiang Xu and Jiangong You |
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Institution: | 1. Department of Applied Mathematics, Southeast University, Nanjing 210018, China 2. Department of Mathematics, Nanjing University, Nanjing 210093, China |
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Abstract: | We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional
torus up to (k,w) where ω is the frequency vector of the torus. That means the normal frequencies with a difference (k,w)
may be regarded as the same. As an application, we derive a persistence result on lower dimensional tori of nearly integrable
Hamiltonian systems when the second Melnikov’s condition is partially violated. |
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Keywords: | sympletic map persistence invariant tori |
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