Divergence points of self-similar measures and packing dimension

I. S. Baek, L. Olsen, N. Snigireva

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

Abstract

Let mu be a self-similar measure in R-d. A point x is an element of R-d for which the lim(r)SE arrow(0) log mu B(x,r)/log r does not exist is called a divergence point. Very recently there has been an enormous interest in investigating the fractal structure of various sets of divergence points. However, all previous work has focused exclusively on the study of the Hausdorff dimension of sets of divergence points and nothing is known about the packing dimension of sets of divergence points. In this paper we will give a systematic and detailed account of the problem of determining the packing dimensions of sets of divergence points of self-similar measures. An interesting and surprising consequence of our results is that, except for certain trivial cases, many natural sets of divergence points have distinct Hausdorff and packing dimensions. (c) 2007 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)267-287
Number of pages21
JournalAdvances in Mathematics
Volume214
Issue number1
DOIs
Publication statusPublished - 10 Sept 2007

Keywords

  • fractals
  • multifractals
  • Hausdorff measure
  • packing measure
  • divergence points
  • local dimension
  • normal numbers
  • BILLINGSLEY DIMENSION
  • MULTIFRACTAL ANALYSIS
  • HAUSDORFF DIMENSION
  • SETS
  • FRACTALS
  • SPACES

Fingerprint

Dive into the research topics of 'Divergence points of self-similar measures and packing dimension'. Together they form a unique fingerprint.

Cite this