A generalised Skolem-Mahler-Lech theorem for affine varieties

The Skolem-Mahler-Lech theorem states that if f (n) is a sequence given by a linear recurrence over a field of characteristic 0, then the set of m, such that f (m) is equal to 0 is the union of a finite number of arithmetic progressions in m >= 0 and a finite set. We prove that if X is a subvariety of an affine variety Y over a field of characteristic 0 and q is a point in Y, and a is an automorphism of Y, then the set of m such that sigma(m) (q) lies in X is a union of a finite number of complete doubly-infinite arithmetic progressions and a finite set. We show that this is a generalisation of the Skolem-Mahler-Lech theorem.