Year: 2026
Type: preprint
Abstract: For residually finite groups, we study the automorphism and normalizer groups of odometers and their symbolic extensions: Toeplitz subshifts. In relation to orbit equivalence theory, we show that two continuous orbit equivalent $G$-odometers have commensurable normalizers when $G=\mathbb{Z}^d$, but that this result fails for other nilpotent groups $G$. The automorphism and normalizer groups of any Toeplitz subshift embed into those of its underlying odometer; despite this constraint, they exhibit considerable flexibility. For instance, we exhibit examples of low-complexity $G$-Toeplitz subshifts whose centralizer is isomorphic to $G$ (or, at the other extreme, restricted to its center) yet whose normalizer group is as large as possible.
Source: arXiv (Cornell University)
Authors: Gómez, Jaime, Petite, Samuel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: Inside zero entropy systems
OpenAlex ID: W7220684196