Nanjing 210096, China
Department of Mathematics, Southeast University
Xu J., Lu X.
General KAM Theorems and their Applications to Invariant Tori with Prescribed Frequencies
2016, vol. 21, no. 1, pp. 107-125
In this paper we develop a new KAM technique to prove two general KAM theorems for nearly integrable Hamiltonian systems without assuming any nondegeneracy condition. Many of KAM-type results (including the classical KAM theorem) are special cases of our theorems under some nondegeneracy condition and some smoothness condition. Moreover, we can obtain some interesting results about KAM tori with prescribed frequencies.