Backward orbits of critical points

We examine the Galois groups of the extensions K((f' circle f(n))(-1)(0))/K where K is a number field for polynomials f (x) is an element of K[x]. We use our understanding of this group to study the proportion of primes for which f has a padic attracting periodic point for a "typical" f and apply the result to the split case of the Dynamical Mordell-Lang Conjecture. (c) 2023 Elsevier Inc. All rights reserved.