I will explain how the perforative phenomena shown to occur among simple amenable C*-algebras by Villadsen and Toms can be realized within a dynamical framework. More specifically, I will show how to construct a minimal homeomorphism for which the K0 group of the crossed product fails to be weakly unperforated, and a minimal homeomorphism for which the crossed product has the same Elliott invariant as an AT-algebra but has Cuntz semigroup which fails to be almost unperforated. This is joint work with Julien Giol.