On the Reducibility of a Class of Linear Almost Periodic Hamiltonian Systems

• Afzal, Muhammad ^[1] ; Guo, Shuzheng ^[1] ; Piao, Daxiong ^[1]
  1. [1] Ocean University of China

     Ocean University of China

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 723-738
• Idioma: inglés
• DOI: 10.1007/s12346-018-0309-9
• Enlaces
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• Resumen

  • In this paper, we study the reducibility problem for a class of analytic almost periodic linear Hamiltonian systems dxdt=J[A+εQ(t)]xwhere A is a symmetric matrix, J is an anti-symmetric symplectic matrix, Q(t) is an analytic almost periodic symmetric matrix with respect to t, and ε is a sufficiently small parameter. It is also assumed that JA has possible multiple eigenvalues and the basic frequencies of Q satisfy the non-resonance conditions. It is shown that, under some non-resonant conditions, some non-degeneracy conditions and for most sufficiently small ε , the Hamiltonian system can be reduced to a constant coefficients Hamiltonian system by means of an almost periodic symplectic change of variables with the same basic frequencies as Q(t).

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