  Let K be a number field or a function field, let F:P^1 --> P^1 be a rational
map of degree at least two defined over K, let P be a point in P^1(K) having
infinite F-orbit, and let Z be a finite subset of Z. We prove a local-global
criterion for the intersection of the F-orbit of P and the finite set Z. This
is a special case of a dynamical Brauer-Manin criterion suggested by Hsia and
Silverman.
