Invariant manifolds for difference equations with generalized trichotomies.

On an arbitrary Banach space, assuming that a linear nonautonomous difference equation xm+1 = Amxm admits a very general type of trichotomy, we establish conditions for the existence of global Lipschitz invariant center manifolds of the perturbed equation xm+1 = Amxm + fm(xm). Our results not only improve results already existing in the literature, but also include new cases. [ABSTRACT FROM AUTHOR]