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

Abstract

In this paper, we prove the equidistribution of periodic points of a regular polynomial automorphism f : A^n -> A^n 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 P^n(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.