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2013 | 161 | 2 | 101-125
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Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics

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We determine when the equidistribution property for possibly moving targets holds for a rational function of degree more than one on the projective line over an algebraically closed field of any characteristic and complete with respect to a non-trivial absolute value. This characterization could be useful in the positive characteristic case. Based on a variational argument, we give a purely local proof of the adelic equidistribution theorem for possibly moving targets, which is due to Favre and Rivera-Letelier, using a dynamical Diophantine approximation theorem by Silverman and by Szpiro-Tucker. We also give a proof of a general equidistribution theorem for possibly moving targets, which is due to Lyubich in the archimedean case and to Favre and Rivera-Letelier for constant targets in the non-archimedean and any characteristic case, and for moving targets in the non-archimedean and zero characteristic case.
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  • Division of Mathematics, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan
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bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-1
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