Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems

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October 2010, 14(3): 1237-1249. doi: 10.3934/dcdsb.2010.14.1237

Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems

Xiaocai Wang ^1, , Junxiang Xu ^2, and Dongfeng Zhang ^2,

1.	Faculty of mathematics and physics, Huaiyin Institute of Technology, Huaian, Jiangsu 223003, China
2.	Department of Mathematics, Southeast University, Nanjing 210096

Received June 2009 Revised December 2009 Published July 2010

Abstract
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In this paper we consider the persistence of lower dimensional elliptic invariant tori with prescribed frequencies in reversible systems, and prove that if the frequency mapping has non-zero Brouwer's degree at a certain point that satisfies Melnikov's non-resonance conditions, then the invariant torus with given frequency persists under small perturbations.

Keywords: invariant tori., reversible systems, KAM iteration.

Mathematics Subject Classification: Primary: 37J40; Secondary: 37E99, 47A55, 37F5.

Citation: Xiaocai Wang, Junxiang Xu, Dongfeng Zhang. Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1237-1249. doi: 10.3934/dcdsb.2010.14.1237

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