Department of Mathematics, Jilin University, Changchun 130012, People's Republic of China ; School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
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.