Equidistribution of the crucial measures in non-Archimedean dynamics

Kenneth Jacobs

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Text Let K be a complete, algebraically closed, non-Archimedean valued field, and let ϕ∈K(z) with deg⁡(ϕ)≥2. In this paper we consider the family of functions ordResϕn(x) which measure the resultant of ϕn at points x in PK 1 the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov–Green's function gμϕ(x,x) attached to the canonical measure of ϕ. Following this, we are able to prove an equidistribution result for Rumely's crucial measures νϕn each of which is a probability measure supported at finitely many points whose weights are determined by dynamical properties of ϕ. Video For a video summary of this paper, please visit https://youtu.be/YCCZD1iwe00.

Original languageEnglish (US)
Pages (from-to)86-138
Number of pages53
JournalJournal of Number Theory
Volume180
DOIs
StatePublished - Nov 2017

Keywords

  • Barycenter
  • Berkovich space
  • Crucial measures
  • Equidistribution
  • Non-Archimedean dynamics
  • Resultant

ASJC Scopus subject areas

  • Algebra and Number Theory

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