Mixing and CLT for Hénon–Sibony maps: Plurisubharmonic observables

Abstract

Let $f$ be a complex Hénon 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 Hénon–Sibony map on ${\mathbb{C}}^k$.