Transactions of the American Mathematical Society

Author(s): Yong Li; Yingfei Yi
Journal: Trans. Amer. Math. Soc. 357 (2005), 1565-1600.
MSC (2000): Primary 37J40
Posted: October 5, 2004
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37J40

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: 10.1090/S0002-9947-04-03564-0
PII: S 0002-9947(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
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society

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