The reducibility of quasi-periodic linear Hamiltonian systems and its application to Hill's equation

2017/06/18 by Nina Xue, Xiong Li, Xue, Nina +1
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.DS

paper · pdf · doi:10.48550/arxiv.1706.05617

19 pages

arxiv created 2017/06/18 · arxiv updated 2017/06/20

Abstract

In this paper, we consider the reducibility of the quasi-periodic linear Hamiltonian system x=(A+ε Q(t))x, where A is a constant matrix with possible multiple eigenvalues, Q(t) is analytic quasi-periodic with respect to t, and ε is a sufficiently small parameter. Under some non-resonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasi-periodic symplectic change of variables with the same basic frequencies as Q(t). Application to quasi-periodic Hill's equation is also given.

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