Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs Academic Article uri icon

abstract

  • 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.

author list (cited authors)

  • Grigorchuk, R., Lenz, D., Nagnibeda, T., & Sell, D.

complete list of authors

  • Grigorchuk, Rostislav||Lenz, Daniel||Nagnibeda, Tatiana||Sell, Daniel

publication date

  • June 2019