Attractive sets of periodic integrodiff...

We consider periodic difference equations in infinite-dimensional Banach spaces possessing compact asymptotically stable set 𝒜. It is established that such 𝒜 persists under spatial discretizations by means of projection methods as nearby closed and bounded uniformly asymptotically stable sets, which moreover converge to 𝒜in the Hausdorff metric for increasingly more accurate schemes. The proof is based on a Lyapunov function guaranteed by an ambient converse theorem and a pullback construction. As application serves integrodifference equations on spaces of continuous and p-integrable functions over a compact habitat.