Mixing and CLT for H\'enon-Sibony maps: plurisubharmonic observables

TL;DR

This paper proves exponential mixing and the central limit theorem for plurisubharmonic observables in Hénon and Hénon-Sibony maps, extending understanding of statistical properties in complex dynamical systems.

Contribution

It establishes exponential mixing of all orders and the CLT for unbounded plurisubharmonic observables in Hénon and Hénon-Sibony maps, a significant extension in complex dynamics.

Findings

Exponential mixing of all orders for the measure of maximal entropy.

Plurisubharmonic functions satisfy the CLT under these maps.

Results apply to all Hénon-Sibony maps on c6^k.

Abstract

Let $f$ be a complex H\'enon map and $\mu$ its unique measure of maximal entropy. We prove that $\mu$ is exponentially mixing of all orders for all (not necessarily bounded) plurisubharmonic observables, and that all plurisubharmonic functions satisfy the central limit theorem with respect to $\mu$. Our results hold more generally for every H\'enon-Sibony map on $\mathbb{C}^k$.