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arXiv · 2011.00314

Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics

Yûsuke Okuyama
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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.

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Yûsuke Okuyama. 2020-10-31. Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics. https://arxiv.org/abs/2011.00314

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