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

Published online by Cambridge University Press:  15 January 2004

KENNETH J. FALCONER
KENNETH J. FALCONER
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland. e-mail: [email protected]
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 1 , January 2004 , pp. 167 - 174
Copyright
2004 Cambridge Philosophical Society

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