Spectra of scaling indices for fractal measures: Theory and experiment
type: Item
instance of: scholarly article
title: Spectra of scaling indices for fractal measures: Theory and experiment
zbMATH Open document ID: 0614.58029
DOI: 10.1016/0167-2789(86)90117-X
author: Thomas C. Halsey
author: Mogens H. Jensen
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: Let \(\mu\) be a measure on the line, and let f(\(\alpha)\) be the fractal dimension of the set of points x such that the \(\mu\)-measures of small \(\ell\)-neighborhoods of x behave like \(\ell^{\alpha}\). The paper discusses the role of the spectrum of f in describing the structure of fractal measures on some strange attractors.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 3994610
zbMATH Keywords: transitions to chaos
zbMATH Keywords: period-doubling
zbMATH Keywords: Rayleigh-Bénard system
zbMATH Keywords: strange attractors
zbMATH Keywords: fractal dimension
zbMATH Keywords: fractal measures
reviewed by: Pertti Mattila
MaRDI profile type: Publication
cites work: The infinite number of generalized dimensions of fractals and strange attractors
cites work: The universal metric properties of nonlinear transformations
cites work: Generalizations of the Hausdorff dimension of fractal measures.
cites work: Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
full work available at URL: 0167-2789(86)90117-x
OpenAlex ID: W2070023106
description: scientific article; zbMATH DE number 3994610