Boshernitzan’s condition, factor complexity, and an application
Boshernitzan’s condition, factor complexity, and an application
复制标题
Boshernitzan 的条件、因子复杂性和应用
DOI：
10.1090/bproc/90
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kra, Bryna
中科院分区：
文献类型：
--
作者：
Cyr, Van;Kra, Bryna
Boshernitzan给出了柱体集测度的一个衰减条件，该条件暗示了最小子位移的唯一遍历性。最近，由于与离散Schrödinger算子的联系，人们对满足这个条件的子移的性质越来越感兴趣，特别感兴趣的是Boshernitzan条件的限制程度。虽然它意味着零拓扑熵，但我们的主要定理显示了如何构造满足条件的最小子移位，并且其因子复杂度增长速度比任何预先指定的次指数速率快。作为应用，我们利用Damanik和Lenz的一个定理，证明了不存在子位移相关的所有离散Schrödinger算子的谱只有有限多个间隙的亚指数增长序列，其复杂度增长快于给定序列。参考文献
Boshernitzan gave 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 discrete Schrödinger operators, and of particular interest is how restrictive the Boshernitzan condition is. While it implies zero topological entropy, our main theorem shows how to construct minimal subshifts satisfying the condition, and 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. References
影响因子：
1
作者：
BOSHERNITZAN, M
通讯作者：
BOSHERNITZAN, M