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

In this paper, we study the reducibility problem for a class of analytic almost periodic linear Hamiltonian systems dx dt = J [ A + ε Q (t) ] x where 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). [ABSTRACT FROM AUTHOR]