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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-1,
author = {Y\^usuke Okuyama},
title = {Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {101-125},
zbl = {1302.37070},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-1}
}
Yûsuke Okuyama. Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics. Acta Arithmetica, Tome 161 (2013) pp. 101-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-1/