Smooth zero entropy flows satisfying the classical central limit theorem

TL;DR

This paper constructs specific conservative analytic flows with zero metric entropy that still satisfy the classical central limit theorem, bridging a gap between entropy and statistical behavior.

Contribution

It introduces a novel class of zero entropy flows that adhere to the classical CLT, expanding understanding of entropy's role in statistical properties.

Findings

Flows have zero metric entropy

Flows satisfy the classical CLT

Analytic construction of such flows

Abstract

We construct conservative analytic flows of zero metric entropy which satisfy the classical central limit theorem.