Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients

In this paper we consider the effective reducibility of the following linear differential equation: \ifmmode\expandafter\else\expandafter\.\fix=(A*Q(t,))x,||0, where A is a constant matrix, Q(t,) is quasiperiodic in t, and is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to \ifmmode\expandafter\else\expandafter\.\fiy=(A()*R(t,))y,||0, where R* is exponentially small in .