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Hölder differentiability of self-conformal devil's staircases

Published online by Cambridge University Press:  09 January 2014

Mathematical Institute, University of St Andrews, North Haugh, St Andrews, KY16 9SS, Scotland. e-mail:


In this paper we consider the probability distribution function of a Gibbs measure supported on a self-conformal set given by an iterated function system (devil's staircase) applied to a compact subset of ${\mathbb R}$. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets Sα0, Sα and Sα, the set of points at which this function has, respectively, Hölder derivative 0, ∞ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann, and Yao, Zhang and Li by considering arbitrary such Gibbs measures given by a potential function independent of the geometric potential.

Research Article
Copyright © Cambridge Philosophical Society 2014 

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