Year: 2009
Type: article
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 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 α-Hölder-differentiable. The obtained results give significant extensions of recent work by Darst, Dekking, Falconer, Li, Morris and Xiao. In particular, our results clearly show that the results of these authors have their natural home within the thermodynamic formalism.
Authors: MARC KESSEBÖHMER, BERND O. STRATMANN
Institutions: University of Bremen, University of St Andrews
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2019932687