On the Reducibility of a Class of Quasi-Periodic Hamiltonian Systems with Small Perturbation Parameter Near the Equilibrium

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

     Xuzhou Institute of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 1, 2017, págs. 127-147
• Idioma: inglés
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• Resumen

  • In this paper, we consider the following nonlinear analytic quasi-periodic Hamiltonian system x˙ = (A + εQ(t))x + εg(t) + h(x, t), x ∈ R2n, where A is a constant matrix with multiple eigenvalues, h = O(x2)(x → 0), and h(x, t), Q(t) and g(t) are analytic quasi-periodic on Dρ with respect to t. Under suitable hypothesis of analyticity, non-resonant conditions and non-degeneracy conditions, by a quasi-periodic symplectic transformation, Hamiltonian system can be reducible to a quasi-periodic Hamiltonian system with an equilibrium.