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arXiv · 1301.1286

Hölder differentiability of self-conformal devil's staircases

Sascha Troscheit
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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). We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets $S^α_{0}$, $S^α_{\infty}$ and $S^α$, the set of points at which this function has, respectively, Hölder derivative 0, $\infty$ or no derivative in the general sense. This extends recent work by Darst, Dekking, Falconer, Kesseböhmer and Stratmann and Yao, Zhang and Li.

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Sascha Troscheit. 2013-01-07. Hölder differentiability of self-conformal devil's staircases. https://doi.org/10.1017/s0305004113000698

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