Primitive divisors in arithmetic dynamics

Let phi(z) is an element of Q(z) be a rational function of degree d >= 2 with phi(0) = 0 and such that phi does not vanish to order d at 0. Let alpha is an element of Q have infinite orbit under iteration of phi and write phi(n)(alpha)=A(n)/B-n as a fracfion in lowest terms. We prove that for all but finitely many n >= 0, the numerator A(n) has a primitive divisor, i.e., there is a prime p such that p vertical bar A(n) and p inverted iota A(i) for all i < n. More generally, we prove an analogous result when phi is defined over a number field and 0 is a preperiodic point for phi.