Study of a high-dimensional chaotic attractor
type: Item
instance of: scholarly article
title: Study of a high-dimensional chaotic attractor
zbMATH Open document ID: 0659.58036
DOI: 10.1007/BF01011917
author: S. H. Smith
published in: Journal of Statistical Physics
publication date: 1986-01-01T00:00:00Z
review text: The nature of a very high-dimensional chaotic attractor in an infinite- dimensional phase space is examined for the purpose of studying the relationships between the physical process occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the other the Fourier basis composed of the Fourier modes. We introduce the ``exterior'' subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace ``goes out'' of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 4078321
zbMATH Keywords: chaos
zbMATH Keywords: attractor interior
zbMATH Keywords: Lyapunov component
zbMATH Keywords: Lyapunov spectrum
zbMATH Keywords: Fourier component
zbMATH Keywords: high-pass filter
zbMATH Keywords: intermittency
zbMATH Keywords: chaotic attractor
zbMATH Keywords: phase space
zbMATH Keywords: Lyapunov basis
zbMATH Keywords: Fourier basis
MaRDI profile type: Publication
cites work: Deterministic Nonperiodic Flow
cites work: Nonassociative, real algebras and quadratic differential equations
full work available at URL: https://doi.org/10.1007/bf01011917
OpenAlex ID: W1990238082
description: scientific article; zbMATH DE number 4078321