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October 2021 Equidistribution in non-archimedean parameter curves towards the activity measures
Reimi Irokawa, Yûsuke Okuyama
Proc. Japan Acad. Ser. A Math. Sci. 97(8): 57-60 (October 2021). DOI: 10.3792/pjaa.97.011

Abstract

For every pair of an analytic family $f=f_{t}$ of endomorphisms of degree $>1$ of the Berkovich projective line $\mathbb{P}^{1,\mathrm{an}}$ over an algebraically closed and complete non-trivially valued field $K$ and an analytically marked point $a=a(t)$ in $\mathbb{P}^{1,\mathrm{an}}$ both parametrized by a domain $V$ in the Berkovich analytification of a smooth projective algebraic curve $C/K$, we establish the equidistribution of the averaged pullbacks of any value in $\mathbb{P}^{1,\mathrm{an}}$ but a subset of logarithmic capacity 0 under the sequence of the morphisms $a_{n}=a_{n}(t)=f_{t}^{n}(a(t)):V\to\mathbb{P}^{1,\mathrm{an}}$, towards the activity measure $\mu_{(f,a)}$ on $V$ associated with $f$ and $a$.

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Reimi Irokawa. Yûsuke Okuyama. "Equidistribution in non-archimedean parameter curves towards the activity measures." Proc. Japan Acad. Ser. A Math. Sci. 97 (8) 57 - 60, October 2021. https://doi.org/10.3792/pjaa.97.011

Information

Published: October 2021
First available in Project Euclid: 1 October 2021

Digital Object Identifier: 10.3792/pjaa.97.011

Subjects:
Primary: 37P50
Secondary: 37P45

Keywords: activity measure , analitically marked point , Analytic family of morphisms , equidistribution , potential theory on Berkovich curves , Varilon exceptional set

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 8 • October 2021
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