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Radius-zero Extended Symmetries and Irregular Fibres of $\mathbb{Z}^d$-Substitution Subshifts
\'Alvaro Bustos-Gajardo, Daniel Luz, Neil Ma\~nibo
https://arxiv.org/abs/2506.13392

Radius-zero Extended Symmetries and Irregular Fibres of $\mathbb{Z}^d$-Substitution Subshifts
In this work, we consider $\mathbb{Z}^d$-shifts generated by digit substitutions. For such a shift $\mathbb{X}$, we study the elements of the normaliser of $\mathbb{Z}^d$ in the group of self homeomorphisms (called extended symmetries) whose local maps guaranteed by the generalised Curtis--Hedlund--Lyndon theorem have radius-zero. Using the formalism of minimal sets developed by Lemańczyk, Müllner and Yassawi, we provide an algorithm to compute elements of $\mathcal{N}(\mathbb{X})$ that prese…