  The aim of this paper is to describe the structure of global attractors for
non-autonomous difference systems of equations with recurrent (in particular,
almost periodic) coefficients. We consider a special class of this type of
systems (the so--called weak convergent systems). We study this problem in the
framework of general non-autonomous dynamical systems (cocycles). We apply the
general results obtained in our early papers to study the almost periodic
(almost automorphic, recurrent) and asymptotically almost periodic
(asymptotically almost automorphic, asymptotically recurrent) solutions of
difference equations.
