Special Session 106: 

General KAM theorems and their applications to invariant tori with prescribed frequencies

Xu Junxiang
Southeast University
Peoples Rep of China
Co-Author(s):    Xuezhu Lu
Abstract:
In this paper we develop some new KAM technique to prove two general KAM theorems for nearly integrable Hamiltonian systems without assuming any non-degeneracy condition. Many of KAM-type results (including the classical KAM theorem) are special cases of our theorems under some non-degeneracy condition and some smoothness condition. Moreover, we can obtain some interesting results about KAM tori with prescribed frequencies.