On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems

Xiaocai  Wang; Junxiang Xu; Dongfeng Zhang

doi:10.3934/dcds.2016.36.1677

Article Contents

2016, Volume 36, Issue 3: 1677-1692. Doi: 10.3934/dcds.2016.36.1677

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On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems

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

Received: September 30, 2014

Revised: May 31, 2015

Published: May 2017

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Abstract

This work focuses on the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems. By KAM method and the special structure of unperturbed nonlinear terms, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of [22].

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Mathematics Subject Classification: Primary: 37J40; Secondary: 37E99, 47A55, 37F50.

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