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Hölder-differentiability of Gibbs distribution functions

Published online by Cambridge University Press:  01 September 2009

MARC KESSEBÖHMER  and
BERND O. STRATMANN
MARC KESSEBÖHMER
Affiliation:
Fachbereich 3 – Mathematik und Informatik, Universität Bremen, D–28359 Bremen, Germany. e-mail: mhk@math.uni-bremen.de
BERND O. STRATMANN
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland. e-mail: bos@maths.st-and.ac.uk
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 489 - 503
Copyright
Copyright © Cambridge Philosophical Society 2009

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