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Обзоры
Self-similarity and spectral theory: on the spectrum of substitutions
A. I. Bufetovabc, B. Solomyakd a Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373 39 rue F. Joliot Curie Marseille France
b Steklov Mathematical Institute of RAS, Moscow
c Institute for Information Transmission Problems, Moscow
d Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
Аннотация:
This survey of the spectral properties of substitution dynamical systems is devoted to primitive aperiodic substitutions and associated dynamical systems: $\mathbb{Z}$-actions and $\mathbb{R}$-actions, the latter viewed as tiling flows. The focus is on the continuous part of the spectrum. For $\mathbb{Z}$-actions the maximal spectral type can be represented in terms of matrix Riesz products, whereas for tiling flows, the local dimension of the spectral measure is governed by the spectral cocycle. References are given to complete proofs and emphasize ideas and various links.
Ключевые слова:
substitutions, entropy, complexity, dynamical system, coding.
Поступила в редакцию: 20.10.2021
Образец цитирования:
A. I. Bufetov, B. Solomyak, “Self-similarity and spectral theory: on the spectrum of substitutions”, Алгебра и анализ, 34:3 (2022), 5–50; St. Petersburg Math. J., 34:3 (2023), 313–346
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1808 https://www.mathnet.ru/rus/aa/v34/i3/p5
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