2019/06/05 by Rostislav Grigorchuk, Grigorchuk, Rostislav, Daniel Lenz +5
Computer Science · Materials Science · Mathematics · #37A20 (Primary) 20E08 #47B36 #68R15 (Secondary) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1906.01898
openalex publication_date 2019/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a class of subshifts governed by finitely many two-sided infinite words. We call these words leading sequences. We show that any locally constant cocycle over such a subshift is uniform. From this we obtain Cantor spectrum of Lebesgue measure zero for associated Jacobi operators if the subshift is aperiodic. Our class covers all simple Toeplitz subshifts as well as all Sturmian subshifts. We apply our results to the spectral theory of Schreier graphs for uncountable families of groups acting on rooted trees.