Mixed generalized dimensions of self-similar measures

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Abstract

Classical multifractal analysis studies the local scaling behaviour of a single measure. However, recently mixed multifractal has generated interest. Mixed multifractal analysis studies the simultaneous scaling behaviour of finitely many measures and provides the basis for a significantly better understanding of the local geometry of fractal measures. The purpose of this paper is twofold. Firstly, we define and develop a general and unifying mixed multifractal theory of mixed Renyi dimensions (also sometimes called the generalized dimensions), mixed L-q-dimensions and mixed coarse multifractal spectra for arbitrary doubling measures. Secondly, as an application of the general theory developed in this paper, we provide a complete description of the mixed multifractal theory of finitely many self-similar measures. © 2004 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)516-539
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Volume306
DOIs
Publication statusPublished - 15 Jun 2005

Keywords

  • fractals
  • multifractals
  • mixed multifiractal spectrum
  • L-q-spectrum
  • Hausdorff measure
  • packing measure
  • divergence points
  • local dimension
  • self-similar measure
  • DIVERGENCE POINTS
  • FRACTALS
  • SETS

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