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Finite orbits for rational functions

J. K. Canci
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Abstract

Let $K$ be a number field and $ϕ\in K(z)$ a rational function. Let $S$ be the set of all archimedean places of $K$ and all non-archimedean places associated to the prime ideals of bad reduction for $ϕ$. We prove an upper bound for length of finite orbits of $ϕ$ in $\mathbb{P}_1(K)$ depending only on the cardinality of $S$.

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J. K. Canci. 2006-07-24. Finite orbits for rational functions. https://arxiv.org/abs/math/0512338

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