  Given a holomorphic self-map of complex projective space of degree larger
than one, we prove that there exists a finite collection of totally invariant
algebraic sets with the following property: given any positive closed
(1,1)-current of mass 1 with no mass on any element of this family, the
sequence of normalized pull-backs of the current converges to the Green
current. Under suitable geometric conditions on the collection of totally
invariant algebraic sets, we prove a sharper equidistribution result.
