Divergence points of deformed empirical measures.
type: Item
instance of: scholarly article
title: Divergence points of deformed empirical measures.
zbMATH Open document ID: 1041.28005
author: L. Olsen
published in: Mathematical Research Letters
publication date: 2002-01-01T00:00:00Z
review text: The author proposes a multi-fractal framework based on deformations of empirical measures. By considering particular deformations, essentially all multi-fractal spectra are obtained. Upper and lower bounds for the multi-fractal spectrum for an arbitrary continuous deformation are given. A variational principle for the general multi-fractal spectrum is provided. It is proved that for a large class of deformations the set of divergence points has full dimension. As an application the author states a variational principle for a very general type of mixed multi-fractal spectrum of ergodic averages.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 1930991
zbMATH Keywords: multi-fractal
zbMATH Keywords: empirical measure
zbMATH Keywords: multi-fractal spectrum
zbMATH Keywords: variational principle
zbMATH Keywords: divergence points
zbMATH Keywords: ergodic averages
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
DOI: 10.4310/MRL.2002.V9.N6.A1
description: scientific article; zbMATH DE number 1930991