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Hölder differentiability of self-conformal devil's staircases

Published online by Cambridge University Press:  09 January 2014

SASCHA TROSCHEIT
SASCHA TROSCHEIT*
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, KY16 9SS, Scotland. e-mail: [email protected]
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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) 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 2 , March 2014 , pp. 295 - 311
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

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