Exploiting geometric signatures to accurately determine properties of attractors
type: Item
instance of: scholarly article
title: Exploiting geometric signatures to accurately determine properties of attractors
zbMATH Open document ID: 0817.58024
DOI: 10.1016/0893-9659(94)90087-6
author: V. Pereyra
published in: Applied Mathematics Letters
publication date: 1995-08-13T00:00:00Z
review text: Motivated by the standard notion of the fractal or Hausdorff-Besicovitch dimension, as connected with the number of cubes of size \(L\) needed to cover the attractor, in the \(L \to 0\) limit, the authors introduce the related geometric signature concept. For a chosen covering cube size \(L\), the derivative \(d \log N(L) / d\log L\) with \(N(L)\) the number of cubes, has \(-D\) (\(D\) is the Hausdorff dimension) as a leading contribution. The so introduced function of \(L\) is shown to be useful while estimating dimensions, characterizing lacunarity and type of attractor (self- similar, nonself-similar), and determining the length of transients for attractors.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 713788
zbMATH Keywords: attractors
zbMATH Keywords: geometric signatures
zbMATH Keywords: transients
zbMATH Keywords: fractal dimension
zbMATH Keywords: chaos
MaRDI profile type: Publication
full work available at URL: 0893-9659(94)90087-6
OpenAlex ID: W2061550451
cites work: Generalized Zeckendorf expansions
cites work: Q4881124
description: scientific article; zbMATH DE number 713788