Iterates of post-critically finite polynomials of the form \boldsymbolx^d+c

2025/08/05 by Goksel, Vefa
#11R09 #37P15 #37P20 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.03308

Abstract

Fix a prime number d. The post-critically finite polynomials of the form f_d,c = x^d+c∈ ℂ[x] play a fundamental role in polynomial dynamics. While many results are known in the complex dynamical setting, much less is understood about the arithmetic properties of these polynomials. In this paper, we describe the factorization of the iterates of post-critically finite polynomials f_d,c over their fields of definition. As a consequence, we prove new cases of a conjecture of Andrews and Petsche on abelian arboreal Galois representations.

Citations

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Related

• On the orbit of a post-critically finite polynomial of the form x^d + c
• Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case
• On postcritically finite polynomials, part 1: critical portraits
• Infinitely wildly ramified arboreal representations for postcritically finite polynomials with potential good reduction
• Arboreal Galois groups of postcritically finite quadratic polynomials: The periodic case