Numerical Dynamics of Integrodifference Equations: Hierarchies of Invariant Bundles in Lp (Ω)

Abstract

We study how the “full hierarchy” of invariant manifolds for nonautonomous integrodifference equations on the Banach spaces of p-integrable functions behaves under spatial discretization of Galerkin type. These manifolds include the classical stable, center-stable, center, center-unstable and unstable ones, and can be represented as graphs of -functions. For kernels with a smoothing property, our main result establishes closeness of these graphs in the -topology under numerical discretizations preserving the convergence order of the method. It is formulated in a quantitative fashion and technically results from a general perturbation theorem on the existence of invariant bundles (i.e. nonautonomous invariant manifolds).