Canonical heights, transfinite diameters, and polynomial dynamics

Matthew H. Baker, Liang-Chung Hsia

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Let φ(z) be a polynomial of degree at least 2 with coefficients in a number field K. Iterating φ gives rise to a dynamical system and a corresponding canonical height function ĥφ, as defined by Call and Silverman. We prove a simple product formula relating the transfinite diameters of the filled Julia sets of φ over various completions of K, and we apply this formula to give a generalization of Bilu's equidistribution theorem for sequences of points whose canonical heights tend to zero.

Original languageEnglish
Pages (from-to)61-92
Number of pages32
JournalJournal fur die Reine und Angewandte Mathematik
Issue number585
DOIs
Publication statusPublished - 2005 Jan 1

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Canonical Height
Dynamical systems
Polynomials
Equidistribution
Product formula
Order of a polynomial
Polynomial
Julia set
Number field
Completion
Dynamical system
Tend
Zero
Coefficient
Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Canonical heights, transfinite diameters, and polynomial dynamics. / Baker, Matthew H.; Hsia, Liang-Chung.

In: Journal fur die Reine und Angewandte Mathematik, No. 585, 01.01.2005, p. 61-92.

Research output: Contribution to journalArticle

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