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Persistence of lower dimensional tori of general types in Hamiltonian systems


Authors: Yong Li and Yingfei Yi
Journal: Trans. Amer. Math. Soc. 357 (2005), 1565-1600
MSC (2000): Primary 37J40
DOI: https://doi.org/10.1090/S0002-9947-04-03564-0
Published electronically: October 5, 2004
MathSciNet review: 2115377
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Abstract: This work is a generalization to a result of J. You (1999). We study the persistence of lower dimensional tori of general type in Hamiltonian systems of general normal forms. By introducing a modified linear KAM iterative scheme to deal with small divisors, we shall prove a persistence result, under a Melnikov type of non-resonance condition, which particularly allows multiple and degenerate normal frequencies of the unperturbed lower dimensional tori.


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Additional Information

Yong Li
Affiliation: Department of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Email: ylimd@email.jlu.edu.cn

Yingfei Yi
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: yi@math.gatech.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03564-0
Keywords: Hamiltonian systems, invariant tori, KAM theory, Melnikov problem, persistence
Received by editor(s): November 14, 2001
Received by editor(s) in revised form: November 11, 2003
Published electronically: October 5, 2004
Additional Notes: The first author was partially supported by NSFC grant 19971042, National 973 Project of China: Nonlinearity, the outstanding young’s project of Ministry of Education of China, and National outstanding young’s award of China
The second author was partially supported by NSF grants DMS9803581 and DMS-0204119
Article copyright: © Copyright 2004 American Mathematical Society

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