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Mathematics > Dynamical Systems

arXiv:1805.07668 (math)
[Submitted on 19 May 2018 (v1), last revised 10 Jan 2019 (this version, v2)]

Title:An a priori bound of rational functions on the Berkovich projective line

Authors:Yûsuke Okuyama
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Abstract:We establish a locally uniform a priori bound on the dynamics of a rational function $f$ of degree $>1$ on the Berkovich projective line over an algebraically closed field of any characteristic that is complete with respect to a non-trivial and non-archimedean absolute value, and deduce an equidistribution result for moving targets towards the equilibrium (or canonical) measure $\mu_f$, under the no potentially good reductions condition. This partly answers a question posed by Favre and Rivera-Letelier.
Comments: 10 pages. (v2) The complex counterpart is separated and the title is shortened
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV); Number Theory (math.NT)
Cite as: arXiv:1805.07668 [math.DS]
  (or arXiv:1805.07668v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1805.07668

Submission history

From: Yûsuke Okuyama [view email]
[v1] Sat, 19 May 2018 22:28:08 UTC (16 KB)
[v2] Thu, 10 Jan 2019 04:24:48 UTC (11 KB)
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