A shooting approach to chaos in the Lorenz equations
type: Item
instance of: scholarly article
title: A shooting approach to chaos in the Lorenz equations
zbMATH Open document ID: 0849.34031
author: S. P. Hastings
author: W. C. Troy
published in: Journal of Differential Equations
publication date: 1996-07-09T00:00:00Z
review text: The authors prove that under certain conditions on sign changes for one variable \(x\) and its derivative \(x'\) the Lorenz equations support a form of chaos. The conditions have been verified numerically in a different paper using interval arithmetic for a particular set of parameter values. After choosing a proper line segment it is shown that for any sequence \(S = \{\sigma_j\}\) of natural numbers one can construct initial conditions on this segment, such that the number of sign changes of \(x'\) between consecutive zeros of \(x\) is in one-to-one correspondence with \(\sigma_j\).
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 881700
zbMATH Keywords: shooting
zbMATH Keywords: Lorenz equations
zbMATH Keywords: chaos
zbMATH Keywords: interval arithmetic
reviewed by: Alois Steindl
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0060
OpenAlex ID: W2032192133
DOI: 10.1006/JDEQ.1996.0060
description: scientific article; zbMATH DE number 881700