Canonical Heights, Transfinite Diameters, and Polynomial Dynamics

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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.
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

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Number Theory, Dynamical Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/67448

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305181
 http://arxiv.org/abs/math/0305181

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arXiv