A REDUCTION PRINCIPLE FOR TOPOLOGICAL CLASSIFICATION OF NONAUTONOMOUSDIFFERENTIAL-EQUATIONS

The paper is concerned with equations of the form x' = A(t)x + f(t, x) , where A is a continuous matrix function defined on R, f is a continu ous vector-valued function of (t, x) with f (t, 0) = 0. It is proved t hat if x' = A(t)x has an exponential trichotomy, A is bounded and f sa tisfies the Lipschitz condition with coefficient sufficiently small, t hen these equations are topologically equivalent to the systems of equ ations of the form x1' = -x1, x2' = x2, x3' = B(t)x, + g(t, x3), where B, g satisfy the same conditions as A, f.