Canonical heights, transfinite diameters, and polynomial dynamics

Matthew H. Baker*, Liang Chung Hsia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


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
Publication statusPublished - 2005 Aug
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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