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

K J  Falconer

doi:10.1017/S0305004103006960

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

K J Falconer

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	167-174
Number of pages	8
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	136
Issue number	1
DOIs	https://doi.org/10.1017/S0305004103006960
Publication status	Published - Jan 2004

Keywords

HAUSDORFF DIMENSION
DIOPHANTINE APPROXIMATION
SETS

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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.",

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AB - 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.

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KW - DIOPHANTINE APPROXIMATION

KW - SETS

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

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Keywords

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