Invariant Manifolds as Pullback Attractors of Nonautonomous Difference Equations

Abstract We consider nonautonomous difference equations that give rise to a hierarchy of invariant fiber bundles, the so-called nonautonomous manifolds. It is our aim to point out the relationship between nonautonomous manifolds and pullback attractors, which is also important for the numerical approximation of these manifolds. In a first step we show that the unstable manifold is the pullback attractor of the system. Under the assumption of invertibility, the stable manifold is then related to the pullback attractor of inverted systems. Finally, using spectral transformations, our main result yields that every nonhyperbolic manifold is a pullback attractor of a related system.