Backward orbits of critical points

Abstract

We examine the Galois groups of the extensions K((f′∘fn)−1(0))/K where K is a number field for polynomials f(x)∈K[x]. We use our understanding of this group to study the proportion of primes for which f has a p-adic attracting periodic point for a “typical” f and apply the result to the split case of the Dynamical Mordell-Lang Conjecture.