Asymptotic chaos
type: Item
instance of: scholarly article
title: Asymptotic chaos
zbMATH Open document ID: 0595.58030
DOI: 10.1016/0167-2789(85)90093-4
author: P. Coullet
author: Charles Tresser
author: Alain Arneodo
author: Edward A. Spiegel
published in: Physica D
publication date: 1985-01-01T00:00:00Z
review text: The aim of the present work is to illustrate how, in a physical system with a triple instability, chaos occurs when the parameters are chosen to be arbitrarily close to the simultaneous onset of the three instabilities. The article provides a list of normal forms of ordinary differential equations describing the dynamics of systems in conditions near to three instabilities. A proof is sketched using normal form theory [\textit{V. I. Arnol'd}, Usp. Mat. Nauk 27, No.5(167), 119-184 (1972; Zbl 0248.58001)]. The numerical investigation of this asymptotic normal form strongly suggests that chaotic behavior occurs as close as possible to the onset of the triple instability.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 3958293
zbMATH Keywords: dynamic system
zbMATH Keywords: normal form
zbMATH Keywords: numerical investigation
zbMATH Keywords: instability
zbMATH Keywords: chaos
MaRDI profile type: Publication
full work available at URL: 0167-2789(85)90093-4
OpenAlex ID: W4231871155
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description: scientific article; zbMATH DE number 3958293