Canonical Heights, Transfinite Diameters, and Polynomial Dynamics
Number Theory
2007-05-23 v2 Dynamical Systems
Abstract
Let phi(z) be a polynomial of degree at least 2 with coefficients in a number field K. Iterating phi gives rise to a dynamical system and a corresponding canonical height function, as defined by Call and Silverman. We prove a simple product formula relating the transfinite diameters of the filled Julia sets of phi 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.
Keywords
Cite
@article{arxiv.math/0305181,
title = {Canonical Heights, Transfinite Diameters, and Polynomial Dynamics},
author = {Matthew Baker and Liang-Chung Hsia},
journal= {arXiv preprint arXiv:math/0305181},
year = {2007}
}
Comments
28 pages, revised version. Lemma 7.1 and Theorem 4.3 have been corrected, and Remark 7.3 and Corollary 8.3 have been added