# Hölder differentiability of self-conformal devil's staircases

@article{Troscheit2014HlderDO, title={H{\"o}lder differentiability of self-conformal devil's staircases}, author={Sascha Troscheit}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2014}, volume={156}, pages={295 - 311} }

Abstract 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… Expand

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