Canonical heights, transfinite diameters, and polynomial dynamics

By Matthew Baker, Liang-Chung Hsia. 2003

68 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f2db37e7d4a7a5b88969a5ce2cefcea203b8e6a6

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A finiteness theorem for canonical heights attached to rational maps over function fields (2006, background): “This would provide a better value of ε but worse upper bound on N than is given by the argument above.”
Preperiodic points of polynomials over global fields (2005, background): “In general, however, knowing nothing about the polynomial other than its degree and the radius rv, we cannot substantially improve on Lemma 4.1.”
Distribution of rational maps with a preperiodic critical point (2006, background): “It is a consequence of [A], and it was explicitely stated (when d = 2) in [ BaH , Theorem 8.13].”