  We present numerical simulations of a Kerr black hole perturbed by a pulse of
ingoing gravitational radiation. For strong perturbations we find up to five
concentric marginally outer trapped surfaces. These trapped surfaces appear and
disappear in pairs, so that the total number of such surfaces at any given time
is odd. The world tubes traced out by the marginally outer trapped surfaces are
found to be spacelike during the highly dynamical regime, approaching a null
hypersurface at early and late times. We analyze the structure of these
marginally trapped tubes in the context of the dynamical horizon formalism,
computing the expansion of outgoing and incoming null geodesics, as well as
evaluating the dynamical horizon flux law and the angular momentum flux law.
Finally, we compute the event horizon. The event horizon is well-behaved and
approaches the apparent horizon before and after the highly dynamical regime.
No new generators enter the event horizon during the simulation.
