ABSTRACT
In this work we analize existence and uniqueness of bounded solutions for a class of difference systems with dichotomies. Results dealing with this problem are key for other types of results, not only in the realm of difference systems, but also for O.D.E’s, and systems with impulse effect, most of which rely on fixed point arguments for showing, say, existence of summable manifolds with bounded projections [6], manifolds with asymptotic phase [2], or even linearization theorems [3], [4], and many others (see for example the references cited in [5]).
