  Given two monic polynomials f and g with coefficients in a number field K,
and some a in K, we examine the action of the absolute Galois group of K on the
directed graph of iterated preimages of a under the correspondence g(y)=f(x),
assuming that deg(f)>deg(g) and that gcd(deg(f), deg(g))=1. If a prime of K
exists at which f and g have integral coefficients, and at which a is not
integral, we show that this directed graph of preimages consists of finitely
many Galois-orbits. We obtain this result by establishing a p-adic
uniformization of such correspondences, tenuously related to Bottcher's
uniformization of polynomial dynamical systems over the complex numbers.
