Reducibility for a Class of Nonlinear Quasi-Periodic Systems under Brjuno-Russmann’s Non-resonance Conditions

• Chunpeng Zhu ^[1] ; Jia Li
  1. [1] Xuzhou Institute of Technology

     Xuzhou Institute of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • This paper studies the following analytic quasi-periodic nonlinear system x˙ = (A + εQ(t, ε))x + εg(t, ε) + h(x, t, ε), where A is a constant matrix and h = O(x2). We prove that under Brjuno-Russmann’s non-resonance conditions and non-degeneracy conditions, for most small enough parameter ε, this nonlinear system is reducible by a quasi-periodic mapping.