*preprint*

**Inserted:** 10 feb 2023

**Last Updated:** 10 feb 2023

**Year:** 2023

**Abstract:**

We consider a measurable dynamical system preserving a probability measure $\nu$. If the system is exponentially mixing of all orders for suitable observables, we prove that these observables satisfy the Central Limit Theorem (CLT) with respect to $\nu$. We show that the measure of maximal entropy of every complex H{\'e}non map is exponentially mixing of all orders for H{\"o}lder observables. It follows that the CLT holds for all complex H{\'e}non maps and H{\"o}lder observables.