Let K be a nonarchimedean field, and let ϕ ∈ 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 ϕ and their preimages, that determines whether or not the dynamical system ϕ: ℙ¹ → ℙ¹ has potentially good reduction.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-3-4,
author = {Robert L. Benedetto},
title = {A criterion for potentially good reduction in nonarchimedean dynamics},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {251-256},
zbl = {06345777},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-3-4}
}
Robert L. Benedetto. A criterion for potentially good reduction in nonarchimedean dynamics. Acta Arithmetica, Tome 166 (2014) pp. 251-256. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-3-4/