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Melnikov-Type Theorem for Time Reversible System

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Abstract

We employ the Craig–Wayne–Bourgain method to study the persistence of quasi-periodic solutions under nonlinear perturbation for a class of finitely dimensional reversible system. Our results provide an alternative and detailed proof for the existence of lower dimensional invariant torus for the reversible system without using the second Melnikov condition.

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Funding

This work is supported by National Natural Science Foundation of China (12001148, 12071105, 11971143), Zhejiang Provincial Natural Science Foundation of China (LQ21A010013, LY19A010010), Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJQN202000730), and Hangzhou Normal University (2020QDJ017).

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, People’s Republic of China

    Xiaolong He & Jianhua Shen

  2. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, People’s Republic of China

    Huanhuan Qiu

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  1. Xiaolong He
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  2. Huanhuan Qiu
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  3. Jianhua Shen
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Correspondence to Huanhuan Qiu.

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He, X., Qiu, H. & Shen, J. Melnikov-Type Theorem for Time Reversible System. Qual. Theory Dyn. Syst. 21, 33 (2022). https://doi.org/10.1007/s12346-021-00553-y

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