Dynamics of $\mathscr{B}$-free systems generated by Behrend sets. I
Volume 209 / 2023
Acta Arithmetica 209 (2023), 135-171
MSC: Primary 37B05; Secondary 37B10, 11N05, 11N25, 11N35.
DOI: 10.4064/aa220525-14-2
Published online: 11 May 2023
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 semi-prime subshifts). We also show that $\mathscr {B}$-admissible subshifts are transitive only for coprime sets $\mathscr B$, which allows us to dynamically characterize the subshifts generated by Erdős sets.
