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Misiurewicz polynomials for rational maps with nontrivial automorphisms. (English) Zbl 1469.37067

For a given integer \(d \geq 2\) the author defines a Misiurewicz polynomial \(G_m\) for \(m=1,2,\dots\). For example, for \(d=3\) we have \(G_1=-a-6\) and \[ G_2=-a^6-a^5-30a^4-144a^3-216a^2-648a-1944. \] He shows that for each prime number \(d \geq 3\) the \(m\)-th Misiurewicz polynomial \(G_m\) is irreducible over \(\mathbb Q\) for \(m=1,2,3\). The proof is based on the theory of Newton polygons.

MSC:

37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps
37P45 Families and moduli spaces in arithmetic and non-Archimedean dynamical systems
11R09 Polynomials (irreducibility, etc.)
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