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arXiv · 2205.08273

Dynamics of $\mathscr{B}$-free systems generated by Behrend sets. I

Stanisław Kasjan·Mariusz Lemańczyk·Sebastian Zuniga Alterman
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Abstract

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 Erd\"os sets.

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Stanisław Kasjan, Mariusz Lemańczyk, Sebastian Zuniga Alterman. 2022-05-17. Dynamics of $\mathscr{B}$-free systems generated by Behrend sets. I. https://arxiv.org/abs/2205.08273

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