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

• Autorzy: Yûsuke Okuyama
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11S82: Non-Archimedean dynamical systems \SeeMainly{}
• 37P50: Dynamical systems on Berkovich spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 2
• Strony: 101-125

Daty

wydano

2013

Twórcy

autor

Yûsuke Okuyama

• Division of Mathematics, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan

Identyfikatory

DOI

10.4064/aa161-2-1