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September  2006, 16(3): 635-655. doi: 10.3934/dcds.2006.16.635

On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition

Dongfeng Zhang 1, and  Junxiang Xu 2,

1. 

Department of Mathematics, Southeast University, Nanjing 210096, China
2. 

Department of Mathematics, Southeast University, Nanjing 211189, China

Received  January 2006 Revised  June 2006 Published  August 2006

In this paper we prove the persistence of elliptic lower dimensional invariant tori for nearly integrable Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition by an improved KAM iteration, and the persisting invariant tori are Gevrey smooth with respect to parameters in the sense of Whitney, with a Gevrey index depending on the Gevrey class of Hamiltonian systems and on the exponent in the Diophantine condition. Moreover the Gevrey index should be optimal for the Diophantine condition in the proof of our theorem.
Keywords: Hamiltonian systems, Rüssmann's non-degeneracy condition., KAM iteration, Gevrey-smooth.
Mathematics Subject Classification: 70H08, 37J40, 34C2.
Citation: Dongfeng Zhang, Junxiang Xu. On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition. Discrete & Continuous Dynamical Systems, 2006, 16 (3) : 635-655. doi: 10.3934/dcds.2006.16.635
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