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