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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
##### Keywords:
arithmetic dynamics; good reduction; periodic points
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##### References:
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