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

  • KENNETH J. FALCONER (a1)
Abstract

We examine the multifractal spectra of one-sided local dimensions of Ahlfors regular measures on ${\bf R}$. 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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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