Equidistribution for non-pluripolar currents on compact K\"ahler manifolds

TL;DR

This paper proves that on a compact Kähler manifold, the normalized pull-backs of non-pluripolar currents under a surjective holomorphic endomorphism converge to the Green current, revealing a form of equidistribution.

Contribution

It establishes the convergence of normalized pull-backs of non-pluripolar currents to the Green current for certain holomorphic endomorphisms on compact Kähler manifolds.

Findings

Normalized pull-backs converge to the Green current

Results apply to endomorphisms with simple action on cohomology

Advances understanding of equidistribution in complex dynamics

Abstract

Let $X$ be a compact K\"ahler manifold of complex dimension $k\ge 2$ and $f:X\to X$ a surjective holomorphic endomorphism of simple action on cohomology. We prove that the sequence of normalized pull-backs of a non-pluripolar current under iterates of $f$ converges to the Green current associated with $f$.