Title: Hölder-differentiability of Gibbs distribution functions

Abstract: In this paper we give non-trivial applications of the  
thermodynamic formalism to the theory of distribution functions of  
Gibbs measures (devil's staircases) supported on limit sets of  
finitely generated conformal iterated function systems in $\mathbb{R} 
$. For a large class of these Gibbs states we determine the Hausdorff  
dimension of the set of points at which the distribution function of  
these measures is not $\alpha$-Hölder-differentiable. (This is joint  
work with B.O. Stratmann)