The equidistribution of small point for strongly regular pairs of polynomial maps

2012/03/06 by Chong Gyu Lee, Lee, Chong Gyu
Mathematics · #11G50 #14G50 #32H50 #37P05 #37P30 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.CV #math.DS #math.NT #msc:11G50 #msc:14G50 #msc:32H50 #msc:37P05 #msc:37P30

paper · pdf · doi:10.48550/arxiv.1203.1224

arxiv created 2012/03/07 · arxiv updated 2012/03/08

Abstract

In this paper, we prove the equidistribution of periodic points of a regular polynomial automorphism f : Aⁿ -> Aⁿ defined over a number field K: let f be a regular polynomial automorphism defined over a number field K and let v be a prime place. Then, there exists an f-invariant probability measure mu_f,v on Berkovich space of Pⁿ(C_v) such that the set of periodic points of f is equidistributed with respect to mu_f,v. We will prove it by equidistribution of small points for strongly regular pair of polynomial maps.

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