Exponential mixing for automorphisms on compact Kaehler manifolds

TL;DR

This paper proves that holomorphic automorphisms with positive entropy on compact Kähler manifolds exhibit exponential mixing in their equilibrium measures, extending results to higher dimensions under certain conditions.

Contribution

It establishes exponential mixing for automorphisms on compact Kähler manifolds, generalizing previous results to higher dimensions with specific dynamical degree conditions.

Findings

Equilibrium measure is exponentially mixing for automorphisms on compact Kähler surfaces.

The result extends to higher-dimensional Kähler manifolds under natural dynamical degree conditions.

Uses recent developments in pluripotential theory to achieve the proof.

Abstract

Let f be a holomorphic automorphism of positive entropy on a compact Kaehler surface. We show that the equilibrium measure of f is exponentially mixing. The proof uses some recent development on the pluripotential theory. The result also holds for automorphisms on compact Kaehler manifolds of higher dimension under a natural condition on their dynamical degrees.