English

Computing geometric Lorenz attractors with arbitrary precision

Dynamical Systems 2017-02-15 v1 Computational Complexity Chaotic Dynamics

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.

Cite

@article{arxiv.1702.04059,
  title  = {Computing geometric Lorenz attractors with arbitrary precision},
  author = {Daniel Graca and Cristobal Rojas and Ning Zhong},
  journal= {arXiv preprint arXiv:1702.04059},
  year   = {2017}
}

Comments

19 pages, 4 figures

R2 v1 2026-06-22T18:17:36.731Z