On the reducibility of a class of almost periodic Hamiltonian systems

Abstract

In this paper we consider the following linear almost periodic hamiltonian systemẋ = (A + εQ(t, ε))x, x ∈ R 2 , where A is a constant matrix with different eigenvalues, and Q(t, ε) is analytic almost periodic with respect to t and analytic with respect to ε. Without any non-degeneracy condition, we prove that the linear hamiltonian system is reducible for most of sufficiently small parameter ε by an almost periodic symplectic mapping. 2020 Mathematics Subject Classification. 37J40.