One-sided multifractal analysis and points of non-differentiability of devil's staircases

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Abstract

We examine the multifractal spectra of one-sided local dimensions of Ahlfors regular measures on R. This brings into a natural context a curious property that has been observed in a number of instances, namely that the Hausdorff dimension of the set of points of non-differentiability of a self-affine 'devil's staircase' function is the square of the dimension of the set of points of increase.

Original languageEnglish
Pages (from-to)167-174
Number of pages8
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume136
Issue number1
DOIs
Publication statusPublished - Jan 2004

Keywords

  • HAUSDORFF DIMENSION
  • DIOPHANTINE APPROXIMATION
  • SETS

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