Singular substitutions of constant length

Artemi Berlinkov; Boris Solomyak

doi:10.1017/etds.2017.133

Singular substitutions of constant length

Artemi Berlinkov
, Boris Solomyak

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	2384-2402
Number of pages	19
Journal	Ergodic Theory and Dynamical Systems
Volume	39
Issue number	9
DOIs	https://doi.org/10.1017/etds.2017.133
State	Published - 1 Sep 2019

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2017.133

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title = "Singular substitutions of constant length",

abstract = "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 Queff{\'e}lec combined with estimates of the local dimension of the spectral measure at zero.",

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year = "2019",

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AU - Solomyak, Boris

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AB - 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.

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U2 - 10.1017/etds.2017.133

DO - 10.1017/etds.2017.133

M3 - مقالة

SN - 0143-3857

VL - 39

SP - 2384

EP - 2402

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 9

ER -

Singular substitutions of constant length

Abstract

ASJC Scopus subject areas

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