Equidistribution of saddle periodic points for Henon-type automorphisms of C^k

TL;DR

This paper proves that saddle periodic points for Henon-type automorphisms of complex k-space distribute evenly according to the equilibrium measure, using a new approach based on densities of positive closed currents.

Contribution

It introduces a general strategy for establishing equidistribution in any dimension, advancing the understanding of dynamical currents in complex dynamics.

Findings

Saddle periodic points are equidistributed with respect to the equilibrium measure.

Development of a new method based on densities of positive closed currents.

Several properties of dynamical currents are established.

Abstract

In this paper, we prove the equidistribution of saddle periodic points for Henon-type automorphisms of C^k with respect to it equilibrium measure. A general strategy to obtain equidistribution properties in any dimension is presented. It is based on our recent theory of densities for positive closed currents. Several fine properties of dynamical currents are also proved.