Theoreme d'equidistribution de Brolin en dynamique p-adique

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We prove an analog of the famous equidistribution theorem of Brolin for rational mappings in one variable defined over the p-adic field C_p. We construct a mixing invariant probability measure which describes the asymptotic distribution of iterated preimages of a given point. This measure is supported on the Berkovich space associated to the projective line over C_p. We show that its support is precisely the Julia set as defined by Rivera-Letelier. Our results are based on the construction of a Laplace operator on real trees with arbitrary number of branching as done by Favre-Jonsson.
7 pages, accepted in the Comptes Rendus de l'Academie des Sciences

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Dynamical Systems, Number Theory, 37F10; 11S80

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http://salesiana.dossiersoluciones.com/handle/123456789/72025

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407469
 http://arxiv.org/abs/math/0407469

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arXiv