# 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 language English 61-92 32 Journal fur die Reine und Angewandte Mathematik 585 https://doi.org/10.1515/crll.2005.2005.585.61 Published - 2005 Jan 1

### Fingerprint

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

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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