LAUSR

We use evolution maps to construct center-stable, center-unstable and center invariant manifolds with optimal regularity for a nonautonomous dynamics with discrete time. The proofs comprise essentially two steps: first we reformulate the original problem in terms of an autonomous problem involving evolutions maps, and then we apply an autonomous result to construct autonomous invariant manifolds that we are able to push back to the original problem. We also describe how the invariant manifolds vary with the perturbations. The main novelty of our work is the method of proof, which leads to simple proofs.