Abstract
This survey of the spectral properties of substitution dynamical systems is devoted to primitive aperiodic substitutions and associated dynamical systems: Zactions and ℝ-actions, the latter viewed as tiling flows. The focus is on the continuous part of the spectrum. For 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.
| Original language | English |
|---|---|
| Pages (from-to) | 313-346 |
| Number of pages | 34 |
| Journal | St. Petersburg Mathematical Journal |
| Volume | 34 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2023 |
Bibliographical note
Publisher Copyright:© 2023 American Mathematical Society
Funding
2020 Mathematics Subject Classification. Primary 37A15; Secondary 37A35, 37B52. Key words and phrases. Substitutions, entropy, complexity, dynamical system, coding. A. B.’s research received support from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme, grant 647133 (ICHAOS) and from the Agence Nationale de la Recherche, project ANR-18-CE40-0035. The research of B.S. was supported by the Israel Science Foundation (grant 911/19).
| Funders | Funder number |
|---|---|
| European Commission | |
| Agence Nationale de la Recherche | ANR-18-CE40-0035 |
| Israel Science Foundation | 911/19 |
| Horizon 2020 | 647133 |
Keywords
- Substitutions
- coding
- complexity
- dynamical system
- entropy
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