2003/05/13 by Matthew Baker, Baker, Matthew, Liang-Chung Hsia +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT) #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.math/0305181
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
openalex publication_date 2003/05/13 · arxiv created 2004/07/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.