Singular substitutions of constant length

Artemi Berlinkov, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider primitive aperiodic substitutions of constant length 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 in absolute value. The proof is based on results of Queffélec combined with estimates of the local dimension of the spectral measure at zero.

Original languageEnglish
Pages (from-to)2384-2402
Number of pages19
JournalErgodic Theory and Dynamical Systems
Issue number9
StatePublished - 1 Sep 2019

Bibliographical note

Publisher Copyright:
© Cambridge University Press, 2018.


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