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The singularity spectrum of the inverse of cookie-cutters

Published online by Cambridge University Press:  01 August 2009

JULIEN BARRAL  and
STÉPHANE SEURET
JULIEN BARRAL
Affiliation:
INRIA Rocquencourt, 78153 Le Chesnay Cedex, France (email: julien.barral@inria.fr)
STÉPHANE SEURET
Affiliation:
Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, CNRS UMR 8050-61, avenue du Général de Gaulle, 94010 Créteil Cedex, France (email: seuret@univ-paris12.fr)
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Abstract

Gibbs measures μ on cookie-cutter sets are the archetype of multifractal measures on Cantor sets. We compute the singularity spectrum of the inverse measure of μ. Such a measure is discrete (it is constituted only by Dirac masses), it satisfies a multifractal formalism and its Lq-spectrum possesses one point of non-differentiability. The results rely on heterogeneous ubiquity theorems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1075 - 1095
Copyright
Copyright © Cambridge University Press 2009

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