A new view of the Lorenz attractor
type: Item
instance of: scholarly article
title: A new view of the Lorenz attractor
zbMATH Open document ID: 1016.37016
DOI: 10.1023/A:1017964715240
author: N. A. Magnitskii
author: S. V. Sidorov
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The scenario of appearance of the Lorenz attractor is studied. The authors propose a method, which allows to reduce the problem of finding unstable periodic orbits to the one-dimensional case. Using this method they show the erroneous of some elements of ``traditional'' view on the scenario for the attractor birth. In particular, they show that at \(r=r_1=13.9266\dots\) (\(\sigma=10\), \(b=8/3\)) the separatrices \(\Gamma_1\) and \(\Gamma_2\) resulting from an origin do not form homoclinic loops. Respectively, the mechanism of the birth of unstable limit cycles in Lorenz systems is reconsidered.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C28
zbMATH DE Number: 1915966
zbMATH Keywords: Lorenz attractor
zbMATH Keywords: unstable periodic orbits
zbMATH Keywords: dimension reducing
MaRDI profile type: Publication
full work available at URL: a:1017964715240
OpenAlex ID: W117662906
description: scientific article; zbMATH DE number 1915966