On the Effective Reducibility of a Class of Quasi-Periodic Hamiltonian Systems

Jia Li ^[1] ; Junxiang Xu ^[2]
1. [1] Xuzhou Institute of Technology
  
  Xuzhou Institute of Technology
  
  China
2. [2] Southeast University
  
  Southeast University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 14, Nº 2, 2015 (Ejemplar dedicado a: Hamiltonian Systems and Celestial Mechanics, HAMSYS-2014), págs. 281-290
Idioma: inglés
DOI: 10.1007/s12346-015-0157-9
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Resumen
- In this paper, we consider the effective reducibility of the following quasi-periodic Hamiltonian system x˙=(A+εQ(t,ε))x, |ε|≤ε0, where A is a constant matrix with different eigenvalues, Q(t,ε) is analytic quasi-periodic on Dρ with respect to t. Under non-resonant conditions, by a quasi-periodic symplectic transformation, the Hamiltonian system can be reducible to a quasi-periodic Hamiltonian system y˙=(A∗(ε)+εR∗(t,ε))y, |ε|≤ε0, where R∗ is exponentially small in ε .