Degenerate lower-dimensional tori in Hamiltonian systems |
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Authors: | Yuecai Han Yingfei Yi |
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Institution: | a College of Mathematics, Jilin University, Changchun 130012, PR China b School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA |
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Abstract: | We study the persistence of lower-dimensional tori in Hamiltonian systems of the form , where (x,y,z)∈Tn×Rn×R2m, ε is a small parameter, and M(ω) can be singular. We show under a weak Melnikov nonresonant condition and certain singularity-removing conditions on the perturbation that the majority of unperturbed n-tori can still survive from the small perturbation. As an application, we will consider the persistence of invariant tori on certain resonant surfaces of a nearly integrable, properly degenerate Hamiltonian system for which neither the Kolmogorov nor the g-nondegenerate condition is satisfied. |
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Keywords: | primary 58F05 58F27 58F30 |
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