Interest in the prop-erties of subshifts satisfying this condition has grown recently, due to a con-nection with discrete Schrödinger operators, and of particular interest is how restrictive the Boshernitzan condition is. 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.ĪB - Boshernitzan gave a decay condition on the measure of cylinder sets that implies unique ergodicity for minimal subshifts.
#SUBSHIFT SCHOLAR HOW TO#
While it implies zero topological en-tropy, our main theorem shows how to construct minimal subshifts satisfying the condition, and whose factor complexity grows faster than any pre-assigned subexponential rate. N2 - Boshernitzan gave a decay condition on the measure of cylinder sets that implies unique ergodicity for minimal subshifts. The second author was partially supported by NSF grant DMS-1800544. Subshift, complexity, Schrödinger operator, uniquely ergodic. Received by the editors June 2, 2020, and, in revised form, January 28, 2021, and April 15, 2021. T1 - BOSHERNITZAN’S CONDITION, FACTOR COMPLEXITY, AND AN APPLICATION
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