Pullback attractors in nonautonomous difference equations

Nonautonomous difference equations are formulated as cocycles which general ize semigroups corresponding to autonomous difference equations. Pullback a ttractors are the appropriate generalization of autonomous attractors to co cycles. The existence of a pullback attractor follows when the difference e quation cocycle has a pullback absorbing set. Results from the literature a re outlined, including the construction of a Lyapunov function characterizi ng pullback attraction, and illustrated with several examples.