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

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 $\mathbb{C}^k$.