Published Paper
Inserted: 10 feb 2023
Last Updated: 29 mar 2024
Journal: Forum of Mathematics, Sigma
Volume: 12
Pages: e4
Year: 2024
Doi: https://doi.org/10.1017/fms.2023.110
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.