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Journal Articles Ergodic Theory and Dynamical Systems Year : 2009

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.

Dates and versions

hal-00693130 , version 1 (01-05-2012)

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Julien Barral, Stephane Seuret. The singularity spectrum of the inverse of cookie-cutters. Ergodic Theory and Dynamical Systems, 2009, 29 (4), pp.1075--1095. ⟨10.1017/S0143385708000618⟩. ⟨hal-00693130⟩
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