Dynamics of $\mathscr{B}$-free systems generated by Behrend sets. I
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916255757238272 |
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| author | Kasjan, Stanisław Lemańczyk, Mariusz Alterman, Sebastian Zuniga |
| author_facet | Kasjan, Stanisław Lemańczyk, Mariusz Alterman, Sebastian Zuniga |
| contents | We study the complexity of $\mathscr{B}$-free subshifts which are proximal and of zero entropy. Such subshifts are generated by Behrend sets. The complexity is shown to achieve any subexponential growth and is estimated for some classical subshifts (prime and semiprime subshifts). We also show that $\mathscr{B}$-admissible subshifts are transitive only for coprime sets $\mathscr{B}$ which allows one to characterize dynamically the subshifts generated by the Erdös sets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_08273 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dynamics of $\mathscr{B}$-free systems generated by Behrend sets. I Kasjan, Stanisław Lemańczyk, Mariusz Alterman, Sebastian Zuniga Dynamical Systems Number Theory 37B05, 37A44, 11N36 We study the complexity of $\mathscr{B}$-free subshifts which are proximal and of zero entropy. Such subshifts are generated by Behrend sets. The complexity is shown to achieve any subexponential growth and is estimated for some classical subshifts (prime and semiprime subshifts). We also show that $\mathscr{B}$-admissible subshifts are transitive only for coprime sets $\mathscr{B}$ which allows one to characterize dynamically the subshifts generated by the Erdös sets. |
| title | Dynamics of $\mathscr{B}$-free systems generated by Behrend sets. I |
| topic | Dynamical Systems Number Theory 37B05, 37A44, 11N36 |
| url | https://arxiv.org/abs/2205.08273 |