A Criterion for Potentially Good Reduction in Non-archimedean Dynamics

2013/11/26 by Benedetto, Robert L. · 2 citations
#37P05 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1311.6695

Abstract

Let K be a non-archimedean field, and let f 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 f and their preimages, that determines whether or not the dynamical system f on P¹ has potentially good reduction.

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