Invariant Foliations and Decoupling of Non-autonomous Difference Equations

In this paper, we continue a previous study of the geometric properties of a certain prototype system of nonautonomous difference equations. In fact, we show that by means of the fundamental theorem on the existence of invariant fiber bundles two foliations of the extended state space can be found. This detailed information about the geometric structure of the underlying system is then used to construct transformations establishing the topological equivalence between a given coupled and a completely uncoupled system.