Regular and Chaotic Dynamics

, Volume 21, Issue 1, pp 107–125 | Cite as

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

  • Junxiang Xu
  • Xuezhu Lu


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.


Hamiltonian system KAM iteration invariant tori nondegeneracy condition 

MSC2010 numbers

34C27 37J40 70H08 


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingChina

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