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 | |
| State | Published - 1 Sep 2019 |
Bibliographical note
Publisher Copyright:© Cambridge University Press, 2018.
Funding
Acknowledgements. We are grateful to Fabien Durand and Nir Lev for helpful discussions. Thanks also go to Michael Baake, Franz Gähler, and Mariusz Lemańczyk for their comments on the first version of the paper. Both authors were supported in part by the Israel Science Foundation (grant 396/15). A. Berlinkov was supported in part by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel. We are grateful to Fabien Durand and Nir Lev for helpful discussions. Thanks also go to Michael Baake, Franz G?hler, and Mariusz Lem?nczyk for their comments on the first version of the paper. Both authors were supported in part by the Israel Science Foundation (grant 396/15). A. Berlinkov was supported in part by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel.
| Funders | Funder number |
|---|---|
| Center for Absorption in Science | |
| Fabien Durand | |
| Ministry of Aliyah and Immigrant Absorption | |
| Israel Science Foundation | 396/15 |
| Ministry of Health, State of Israel |