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Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics
Published online by Cambridge University Press: 21 December 2021
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.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 3 , November 2022 , pp. 573 - 590
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society