Automorphisms of Toeplitz $\mathscr{B}$-free systems

TL;DR

This paper proves that the automorphism group of certain Toeplitz B-free subshifts, defined by a specific set of coprime odd numbers, is generated only by powers of the shift, revealing a rigid symmetry structure.

Contribution

It establishes that for a class of Toeplitz B-free systems, the automorphism group is exactly the group of shift powers, demonstrating a rigidity property of these dynamical systems.

Findings

Automorphism group is generated solely by shift powers.

The result applies to B-free subshifts with specific coprime odd number conditions.

Shows rigidity in the symmetry structure of these Toeplitz systems.

Abstract

For each $\mathscr{B}$-free subshift given by $\mathscr{B}=\{2^ib_i\}_{i\in\mathbb{N}}$, where $\{b_i\}_{i\in\mathbb{N}}$ is a set of pairwise coprime odd numbers greater than one, it is shown that its automorphism group consists solely of powers of the shift.