# Computing geometric Lorenz attractors with arbitrary precision

## TL;DR

This paper demonstrates that geometric Lorenz attractors and their physical measures can be computed with arbitrary precision, bridging the gap between numerical simulations and rigorous mathematical proofs.

## Contribution

It proves the computability of geometric Lorenz attractors and their physical measures, providing a rigorous foundation for numerical analysis of these chaotic systems.

## Key findings

- Geometric Lorenz attractors are computable.
- Physical measures of Lorenz attractors are computable.
- Supports rigorous numerical analysis of chaotic systems.

## Abstract

The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models have a strange attractor. In 2002 it was shown that the original Lorenz model behaves like a geometric Lorenz model and thus has a strange attractor. In this paper we show that geometric Lorenz attractors are computable, as well as their physical measures.