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arXiv · 1709.08751

Index divisibility in the orbit of 0 for integral polynomials

T. Alden Gassert·Michael T. Urbanski
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Abstract

Let $f(x) \in \bbz[x]$ and consider the index divisibility set $D = \{n \in \bbn : n \mid f^n(0)\}$. We present a number of properties of $D$ in the case that $(f^n(0))_{n=1}^\infty$ is a rigid divisibility sequence, generalizing a number of results of Chen, Stange, and the first author. We then study the polynomial $x^d + x^e + c \in \bbz[x]$, where $d > e \ge 2$ and determine all cases where this map has a finite index divisibility set.

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T. Alden Gassert, Michael T. Urbanski. 2017-09-25. Index divisibility in the orbit of 0 for integral polynomials. https://arxiv.org/abs/1709.08751

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