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The singularity spectrum of the inverse of cookie-cutters

Abstract : Gibbs measures mu on cookie-cutter sets are the archetype of multifractal measures on Cantor sets. We compute the singularity spectrum of the inverse measure of g. Such a measure is discrete (it is constituted only by Dirac masses), it satisfies a multifractal formalism and its L(q)-spectrum possesses one point of non-differentiability. The results rely on heterogeneous ubiquity theorems.
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Submitted on : Tuesday, May 1, 2012 - 9:40:53 PM
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Julien Barral, Stephane Seuret. The singularity spectrum of the inverse of cookie-cutters. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2009, 29 (4), pp.1075--1095. ⟨10.1017/S0143385708000618⟩. ⟨hal-00693130⟩



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