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

TL;DR

This paper proves that the periodic points of certain polynomial automorphisms over number fields are evenly distributed with respect to a specific invariant measure, using the concept of small points for strongly regular pairs.

Contribution

It establishes the equidistribution of periodic points for strongly regular pairs of polynomial maps over number fields, extending previous results to a broader class of automorphisms.

Findings

Periodic points are equidistributed with respect to an invariant measure.

The proof uses equidistribution of small points for strongly regular pairs.

Results apply to regular polynomial automorphisms over number fields.

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.