Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics
Y\^usuke Okuyama
TL;DR
This paper investigates the density of repelling periodic points in the Julia set of non-archimedean rational functions, providing partial results through logarithmic equidistribution on the Berkovich projective line.
Contribution
It offers a partial positive answer to the open problem by analyzing logarithmic equidistribution in non-archimedean dynamics.
Findings
Partial positive answer to the density of repelling periodic points
Establishment of logarithmic equidistribution on the Berkovich line
Insights into non-archimedean Julia sets
Abstract
It is an open problem whether repelling periodic points are dense in the classical Julia set of a non-archimedean rational function of degree more than one. We give a partial positive answer to this question based on a study of a logarithmic equidistribution on the Berkovich projective line over non-archimedean fields.
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