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arXiv · 2209.01785

Numerical dynamics of integrodifference equations: Hierarchies of invariant bundles in $L^p(\Omega)$

Christian Pötzsche
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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 $C^m$-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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Christian Pötzsche. 2022-09-05. Numerical dynamics of integrodifference equations: Hierarchies of invariant bundles in $L^p(\Omega)$. https://arxiv.org/abs/2209.01785

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