Hölder differentiability of self-conformal devil's staircases

  title={H{\"o}lder differentiability of self-conformal devil's staircases},
  author={Sascha Troscheit},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  pages={295 - 311}
  • Sascha Troscheit
  • Published 2014
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
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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  • 2004
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