Persistence of lower dimensional tori of general types in Hamiltonian systems

Li, Yong; Yi, Yingfei

doi:10.1090/S0002-9947-04-03564-0

Persistence of lower dimensional tori of general types in Hamiltonian systems
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by Yong Li and Yingfei Yi PDF

Trans. Amer. Math. Soc. 357 (2005), 1565-1600 Request permission

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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