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math.SP2025
On the Kotani-Last Conjecture for the Dirac Operator
Nyah Davis, íris Emilsdóttir, Long Li +1
We prove a dichotomy of almost periodicity for reflectionless one-dimensional Dirac operators whose spectra satisfy certain geometric conditions, extending work of Volberg--Yuditsk…
math.SP2024
Gap Labels and Asymptotic Gap Opening for Full Shifts
David Damanik, Íris Emilsdóttir, Jake Fillman
We discuss gap labelling for operators generated by the full shift over a compact subset of the real line. The set of Johnson--Schwartzman gap labels is the algebra generated by we…
math.SP2023
The Schwartzman Group of an Affine Transformation
David Damanik, Íris Emilsdóttir, Jake Fillman
We compute the Schwartzman group associated with an ergodic affine automorphism of a compact connected abelian group given by the composition of an automorphism of the group and a…