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Singular substitutions of constant length
Published online by Cambridge University Press: 18 January 2018
Abstract
We consider primitive aperiodic substitutions of constant length $q$ and prove that, in order to have a Lebesgue component in the spectrum of the associated dynamical system, it is necessary that one of the eigenvalues of the substitution matrix equals
$\sqrt{q}$ in absolute value. The proof is based on results of Queffélec combined with estimates of the local dimension of the spectral measure at zero.
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