Numerical dynamics of integrodifference equations: Hierarchies of invariant bundles in L^p(Ω)
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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 C^m-functions. For kernels with a smoothing property, our main result establishes closeness of these graphs in the C^m-1-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).
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