We present a method to prove certain statements about the global dynamics of an infinite dimensional map, namely the Kot-Schaffer growth-dispersal model for plants. The method combines (rigorous) set-oriented numerical tools, the Conley index theory and certain analytic considerations. It not only allows for the detection of a certain dynamical behaviour but also for a precise computation of the corresponding invariant sets in phase space. We will give an outline of the method and exemplarily show how to prove the existence of a heteroclinic orbit as well as of a horseshoe. This is joint work with M. Allili, S. Day and K. Mischaikow.