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Integrodifference equations are versatile models in theoretical ecology forthe spatial dispersal of species evolving in non-overlapping generations. Thedynamics of these infinite-dimensional discrete dynamical systems is oftenillustrated using computational simulations. This paper studies the effect ofNystr\"om discretization to the local dynamics of periodic integrodifferenceequations with H\"older continuous functions over a compact domain as statespace. We prove persistence and convergence for hyperbolic periodic solutionsand their associated stable and unstable manifolds respecting the convergenceorder of the quadrature/cubature method.

Numerical dynamics of integrodifference equations: Periodic solutions and invariant manifolds in $C^\alpha(\Omega)$