Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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F. Bianchi - T. C. Dinh

Every complex H{é}non map satisfies the Central Limit Theorem

created by bianchi on 10 Feb 2023

[BibTeX]

preprint

Inserted: 10 feb 2023
Last Updated: 10 feb 2023

Year: 2023

ArXiv: 2301.13535 PDF

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.

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