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Misiurewicz polynomials for rational maps with nontrivial automorphisms

Volume 198 / 2021

Minsik Han Acta Arithmetica 198 (2021), 257-274 MSC: Primary 37P05; Secondary 37P45. DOI: 10.4064/aa200413-23-9 Published online: 22 February 2021


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.


  • Minsik HanDepartment of Mathematics
    Box 1917
    Brown University
    Providence, RI 02912, U.S.A.

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