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The singularity spectrum of the inverse of cookie-cutters
Published online by Cambridge University Press: 01 August 2009
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.
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- Copyright © Cambridge University Press 2009
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