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On the persistence of degenerate lower-dimensional tori in reversible systems

Published online by Cambridge University Press:  07 August 2014

XIAOCAI WANG
Affiliation:
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, Jiangsu 223003, PR China email wangxiaocai325@163.com, jianxia6690@sina.com.cn
JUNXIANG XU
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, PR China email xujun@seu.edu.cn, zhdf@seu.edu.cn
DONGFENG ZHANG
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, PR China email xujun@seu.edu.cn, zhdf@seu.edu.cn

Abstract

This work focuses on the persistence of lower-dimensional tori with prescribed frequencies and singular normal matrices in reversible systems. By the Kolmogorov–Arnold–Moser theory and the special structure of unperturbed nonlinear terms in the differential equation, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [Degenerate lower dimensional tori in reversible systems. J. Math. Anal. Appl.387 (2012), 776–790].

Type
Research Article
Copyright
© Cambridge University Press, 2014 

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