Gleason-type polynomials for rational maps with nontrivial automorphisms

Minsik Han

Published 2020-02-03Version 1

In this paper, we consider a 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 are the values of parametrizing variable of the family which make the corresponding map be post-critically finite with a certain dynamical portrait. Then we prove that the polynomial is irreducible in certain cases.