A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems

We present a numerical method to prove certain statements about the global dynamics of infinite-dimensional maps. The method combines set-oriented numerical tools for the computation of invariant sets and isolating neighborhoods, the Conley index theory, and analytic considerations. It not only allows for the detection of a certain dynamical behavior, but also for a precise computation of the corresponding invariant sets in phase space. As an example computation we show the existence of period points, connecting orbits, and chaotic dynamics in the Kot--Schaffer growth-dispersal model for plants.