Melnikov-Type Theorem for Time Reversible System

• He, Xiaolong ^[1] ; Qiu, Huanhuan ^[2] ; Shen, Jianhua ^[1]
  1. [1] Hangzhou Normal University

     Hangzhou Normal University

     China

     
  2. [2] Chongqing Jiaotong University

     Chongqing Jiaotong University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
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• Resumen

  • 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.