Effective Reducibility for a Class of Linear Almost Periodic Systems

This paper studies the effective reducibility of the linear almost periodic equation x = (A + epsilon Q(t, epsilon))x, |epsilon| <= epsilon(0), where Q(t) is analytic and almost periodic on D-rho and A is a constant matrix. By an almost periodic transformation, without any nondegeneracy condition, under nonresonance conditions, the system is reduced to an almost periodic system y = (A* (epsilon) + epsilon R* (t, epsilon))y, |epsilon| <= epsilon(0), where R* is small with respect to epsilon (i.e., lim (epsilon -> 0) R*(t, epsilon) = 0).