## 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 ℝ. We use thermodynamic multifractal formalism to calculate the Hausdorff dimension of the sets S^{α} _{0}, S^{α} _{∞} and S^{α}, 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.

Original language | English |
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Pages (from-to) | 295-311 |

Number of pages | 17 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 156 |

Issue number | 2 |

Early online date | 9 Jan 2014 |

DOIs | |

Publication status | Published - 1 Mar 2014 |