Exponential mixing property for H\'enon-Sibony maps of $\mathbb{C}^k$

TL;DR

This paper proves that the equilibrium measure of Hénon-Sibony maps in complex k-space exhibits exponential mixing for plurisubharmonic functions, advancing understanding of their dynamical properties.

Contribution

It establishes the exponential mixing property for the equilibrium measure of Hénon-Sibony maps, a significant step in complex dynamics.

Findings

Proves exponential mixing for the equilibrium measure

Applies to Hénon-Sibony maps in complex k-space

Enhances understanding of dynamical behavior

Abstract

Let $f$ be a H\'enon-Sibony map (regular polynomial automorphism) of $\mathbb{C}^k$ and let $\mu$ be the equilibrium measure of $f$. In this paper we prove that $\mu$ is exponentially mixing for plurisubharmonic test functions.