Damanik, DavidFillman, JakeZhang, Zhenghe2024-05-082024-05-082023Damanik, D., Fillman, J., & Zhang, Z. (2023). Johnson–Schwartzman gap labelling for ergodic Jacobi matrices. Journal of Spectral Theory, 13(1), 297–318. https://doi.org/10.4171/jst/449https://hdl.handle.net/1911/115664We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphism on a compact metric space. Given an ergodic probability measure, we study the topological structure of the associated almost sure spectrum. We establish a gap labelling theorem in the spirit of Johnson and Schwartzman. That is, we show that the constant value the integrated density of states takes in a gap of the spectrum must belong to the countable Schwartzman group of the base dynamics. This result is a natural companion to a recent result of Alkorn and Zhang, which established a Johnson-type theorem for the families of Jacobi matrices in question.engExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Journal article10.4171-jst-449https://doi.org/10.4171/jst/449