(H,K)-TRICHOTOMIES AND ASYMPTOTICS OF NONAUTONOMOUS DIFFERENCE-SYSTEMS

Discrete nonautonomous nonlinear systems possessing (h, k)-trichotomie s are considered. We specialize to the case of solutions moving inside -and in a neighborhood of-an invariant manifold of a special kind, whi ch we call (h, k)-hyperbolic. The Aulbach-Coppel-Knobloch transformati on is then developed and used to state conditions for granting asympto tic equivalence of solutions. Our results generalize some of Aulbach's results in which the manifold considered was made of stationary point s, and the system taken was autonomous.