Misiurewicz polynomials for rational maps with nontrivial automorphisms
Volume 198 / 2021
Acta Arithmetica 198 (2021), 257-274
MSC: Primary 37P05; Secondary 37P45.
DOI: 10.4064/aa200413-23-9
Published online: 22 February 2021
Abstract
We consider a one-parameter family of degree $d\ge 2$ rational maps with an automorphism group containing the cyclic group of order $d$. We construct a polynomial whose roots correspond to parameter values for which the corresponding map is post-critically finite with a certain dynamical portrait. Then we prove that the polynomial is irreducible in certain cases.
