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arXiv · 2402.13713

$S$-integral preperiodic points for monomial semigroups over number fields

Marley Young
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Abstract

We consider semigroup dynamical systems defined by several monnomials over a number field $K$. We prove a finiteness result for preperiodic points of such systems which are $S$-integral with respect to a non-preperiodic point $\beta$, which is uniform as $\beta$ varies over number fields of bounded degree. This generalises results of Baker, Ih and Rumely, which were made uniform by Yap, and verifies a special case of a natural generalisation of a conjecture of Ih.

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Marley Young. 2024-02-21. $S$-integral preperiodic points for monomial semigroups over number fields. https://arxiv.org/abs/2402.13713

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