| Autor: |
Kasjan, Stanisław, Keller, Gerhard, Lemańczyk, Mariusz |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1093/imrn/rnx196 |
| Popis: |
Let $\mathcal B$ be an infinite subset of $\{1,2,\dots\}$. We characterize arithmetic and dynamical properties of the $\mathcal B$-free set $\mathcal F_{\mathcal B}$ through group theoretical, topological and measure theoretic properties of a set $W$ (called the window) associated with $\mathcal B$. This point of view stems from the interpretation of the set $\mathcal F_{\mathcal B}$ as a weak model set. Our main results are: $\mathcal B$ is taut if and only if the window is Haar regular; the dynamical system associated to $\mathcal F_{\mathcal B}$ is a Toeplitz system if and only if the window is topologically regular; the dynamical system associated to $\mathcal F_{\mathcal B}$ is proximal if and only if the window has empty interior; and the dynamical system associated to $\mathcal F_{\mathcal B}$ has the "na\"ively expected" maximal equicontinuous factor if and only if the interior of the window is aperiodic. |
| Databáze: |
arXiv |
| Externí odkaz: |
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