论文标题
Boshernitzan的状况，因素复杂性和应用
Boshernitzan's condition, factor complexity, and an application
论文作者
论文摘要
波什尼岑（Boshernitzan）在圆柱套件的量度上发现了一种衰减状态，这意味着最小的子迁移的独特性恐怖性。由于与离散Schrödinger运营商的研究有关，最近对满足此条件的子迁移的特性的兴趣已经增长。特别令人感兴趣的是，波什尼津的状况有多么限制。尽管它意味着零拓扑熵，但我们的主要定理显示了如何构建最小的子迁移，以满足其因子复杂性增长的速度比任何预分配的次指数率更快。作为一种应用，通过Damanik和Lenz的定理，我们表明，没有次指数增长的序列，所有离散的Schrödinger运算符的频谱与与给定序列相比增长快的次移相关的schrödinger运算符的光谱只有有限的差距有限。
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.
