2020/06/02 by Van Cyr, Cyr, Van, Bryna Kra +1
Materials Science · Mathematics · #35J10 #37A35 #37B10 #37B40 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2006.01931
openalex publication_date 2020/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Boshernitzan found a decay condition on the measure of cylinder sets that implies unique ergodicity for minimal subshifts. Interest in the properties of subshifts satisfying this condition has grown recently, due to a connection with the study of discrete Schrödinger operators. Of particular interest is the question of how restrictive Boshernitzan's condition is. While it implies zero topological entropy, our main theorem shows how to construct minimal subshifts satisfying the condition whose factor complexity grows faster than any pre-assigned subexponential rate. As an application, via a theorem of Damanik and Lenz, we show that there is no subexponentially growing sequence for which the spectra of all discrete Schrödinger operators associated with subshifts whose complexity grows faster than the given sequence, have only finitely many gaps.