A chaotic mapping that displays its own homoclinic structure
type: Item
instance of: scholarly article
title: A chaotic mapping that displays its own homoclinic structure
zbMATH Open document ID: 0583.76063
DOI: 10.1016/0167-2789(84)90141-6
author: R. R. Whitehead
author: N. MacDonald
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: We describe some properties of a two-dimensional non-linear mapping which has been derived from a differential equation model of turbulence. For certain parameter values the mapping displays chaotic behaviour. Owing to the peculiar way in which the phase space expands and contracts, parts of the attractor follow the oscillatory invariant curves associated with homoclinic points in non-integrable systems.
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 37C55
zbMATH DE Number: 3934628
zbMATH Keywords: transition from laminar to turbulent flow
zbMATH Keywords: Burgers' equations
zbMATH Keywords: finite difference approximation
zbMATH Keywords: two-dimensional non-linear mapping
zbMATH Keywords: differential equation model of turbulence
zbMATH Keywords: chaotic behaviour
zbMATH Keywords: oscillatory invariant curves
zbMATH Keywords: homoclinic points
zbMATH Keywords: non-integrable systems
MaRDI profile type: Publication
full work available at URL: 0167-2789(84)90141-6
OpenAlex ID: W2075125793
cites work: Deterministic Nonperiodic Flow
cites work: Regular and stochastic motion
cites work: Discrete time models for two-species competition
cites work: Snap-back repellers imply chaos in \(\mathbb{R}^n\)
description: scientific article; zbMATH DE number 3934628