Dynamics of automorphisms on compact K\"ahler manifolds

TL;DR

This paper investigates the dynamics of holomorphic automorphisms on compact Kähler manifolds with simple Hodge cohomology actions, revealing laminar structures in Green currents and uniqueness of the measure of maximal entropy.

Contribution

It demonstrates that such automorphisms have Green currents with complex laminar structures and a unique invariant measure of maximal entropy, advancing understanding of their dynamical properties.

Findings

Green currents admit complex laminar structures

Green measure is the unique measure of maximal entropy

Automorphisms have simple actions on Hodge cohomology

Abstract

We study holomorphic automorphisms on compact K\"ahler manifolds having simple actions on the Hodge cohomology ring. We show for such automorphisms that the main dynamical Green currents admit complex laminar structures (woven currents) and the Green measure is the unique invariant probability measure of maximal entropy.