The bifurcation measure is exponentially mixing

TL;DR

This paper proves that the bifurcation measure for certain rational maps on complex projective space exhibits exponential mixing, using general mixing theorems for meromorphic maps on Kähler manifolds.

Contribution

It introduces new mixing theorems for meromorphic maps and applies them to establish exponential mixing of the bifurcation measure in complex dynamics.

Findings

Bifurcation measure is exponentially mixing.

General mixing theorems for meromorphic maps are established.

Application to rational maps on complex projective space.

Abstract

We prove general mixing theorems for sequences of meromorphic maps on compact K\"ahler manifolds. We deduce that the bifurcation measure is exponentially mixing for a family of rational maps of $\mathbb{P}^q(\mathbb{C})$ endowed with suitably many marked points.