Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics

Yûsuke Okuyama. "Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics." Acta Arithmetica 161.2 (2013): 101-125. <http://eudml.org/doc/279489>.

@article{YûsukeOkuyama2013,
abstract = {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.},
author = {Yûsuke Okuyama},
journal = {Acta Arithmetica},
keywords = {characterization of equidistribution; adelic equidistribution; Diophantine approximation; equidistribution theorem; non-Archimedean dynamics; complex dynamics},
language = {eng},
number = {2},
pages = {101-125},
title = {Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics},
url = {http://eudml.org/doc/279489},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Yûsuke Okuyama
TI - Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 2
SP - 101
EP - 125
AB - 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.
LA - eng
KW - characterization of equidistribution; adelic equidistribution; Diophantine approximation; equidistribution theorem; non-Archimedean dynamics; complex dynamics
UR - http://eudml.org/doc/279489
ER -