  It is shown that if three distinct values of a meromorphic function f:C^n ->
P^1 of hyper-order strictly less than 2/3 have forward invariant pre-images
with respect to a translation t:C^n -> C^n, t(z)=z+c, then f is a periodic
function with period c. This result can be seen as a generalization of M.
Green's Picard-type theorem in the special case where the hyper-order of f is
less than 2/3, since the empty pre-images of the usual Picard exceptional
values are by definition always forward invariant. In addition, difference
analogues of the lemma on the logarithmic derivative and of the second main
theorem of Nevanlinna theory for meromorphic functions C^n -> P^1 are given,
and their applications to partial difference equations are discussed.
