Sparsity of stable primes for dynamical sequences
Sparsity of stable primes for dynamical sequences
We show that a dynamical sequence $(f_n)_{n\in \mathbb{N}}$ of polynomials over a number field whose set of stable primes is of positive density must necessarily have a very restricted, and in particular ``near-solvable" dynamical Galois group. Together with existing heuristics, our results suggest moreover that a polynomial $f$ all of …