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A criterion for potentially good reduction in nonarchimedean dynamics. (English) Zbl 1379.37147
Summary: Let \(K\) be a nonarchimedean field, and let \(\phi \in K(z)\) be a polynomial or rational function of degree at least \(2\). We present a necessary and sufficient condition, involving only the fixed points of \(\phi \) and their preimages, that determines whether or not the dynamical system \(\phi :\mathbb {P}^1\to \mathbb {P}^1\) has potentially good reduction.

MSC:
37P50 Dynamical systems on Berkovich spaces
37P20 Dynamical systems over non-Archimedean local ground fields
11S82 Non-Archimedean dynamical systems
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