From invariant manifolds to fiber bundles: Numerical dynamics of integrodifference equations

Integrodifference equations are successful models to describe spatial dispersal and temporary evolution. For this reason they can be understood as a discrete-time counterpart to reaction-diffusion equations and form an interesting class of infinite-dimensional dynamical systems. Nevertheless, for the sake of numerical simulations integrodifference equations require a spatial discretization.
In this talk, we investigate how their full hierarchy of invariant manifolds (stable, center-stable, center, center-unstable, unstable) behaves under the commonly used discretizations methods. We begin with the classical situation near periodic solutions and proceed to a general nonautonomous framework.
\begin{thebibliography}{9} \bibitem{Poetzsche:1} \textsc{F. Lutscher}, \textit{Integrodifference Equations in Spatial Ecology}, Interdisciplinary Applied Mathematics, Springer, Cham, 2019.
\bibitem{Poetzsche:2} \textsc{C. Pötzsche}, Numerical dynamics of integrodifference equations: Periodic solutions and invariant manifolds in $C^\alpha(\Omega)$, submitted (2021)
\bibitem{Poetzsche:3} \textsc{C. Pötzsche}, Numerical dynamics of integrodifference equations: Hierarchies of invariant bundles of $L^p(\Omega)$, Numer. Funct. Anal. Optimization, accepted (2023) \end{thebibliography}