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In this paper we develop some new KAM-technique to prove two general KAMtheorems for nearly integrable hamiltonian systems without assuming anynon-degeneracy condition. Many of KAM-type results (including the classical KAMtheorem) are special cases of our theorems under some non-degeneracy conditionand some smoothness condition.  Moreover, we can obtain some interesting results about KAM tori withprescribed frequencies.

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