Abstract
Abstract
We show that a rational function f of degree
$>1$
on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value has no potentially good reductions if and only if the Berkovich Julia set of f is uniformly perfect. As an application, a uniform regularity of the boundary of each Berkovich Fatou component of f is also established.
Publisher
Cambridge University Press (CUP)
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