# Variance continuity for Lorenz flows

## TL;DR

This paper proves that the variance in the Central Limit Theorem for Lorenz flows and nearby flows varies continuously, ensuring stability of statistical properties under small perturbations.

## Contribution

It establishes the continuity of variance in the CLT for Lorenz flows, a novel result in the statistical stability of chaotic dynamical systems.

## Key findings

- Variance in the CLT is continuous for Lorenz flows.
- Continuity holds for flows close in the $C^2$-topology.
- Supports stability of statistical properties under perturbations.

## Abstract

The classical Lorenz flow, and any flow which is close to it in the $C^2$-topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuously.