  We study the problem of persistence of minimal invariant sets with smooth
boundary for a certain class of discrete-time set-valued dynamical systems,
naturally arising in the context of random dynamical systems with bounded
noise. In particular, we introduce a single-valued map, the so-called boundary
map, which has the property that a certain class of invariant submanifolds for
this map is in one-to-one correspondence with invariant sets for the
corresponding set-valued map. We show that minimal invariant sets with smooth
boundary persist under small perturbations of the set-valued map, provided that
the associated boundary map is normally hyperbolic at the unit normal bundle of
the boundary.
