We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [On the complexity function for sequences which are not uniformly recurrent. Dynamical Systems and Random Processes (Contemporary Mathematics, 736). American Mathematical Society, Providence, RI, 2019, pp. 125--137]. We also bound the number of generic measures such a subshift can support based on its complexity function. Our measure-theoretic bounds generalize those of Boshernitzan [A unique ergodicity of minimal symbolic flows with linear block growth. J. Anal. Math.44(1) (1984), 77–96] and are closely related to those of Cyr and Kra [Counting generic measures for a subshift of linear growth. J. Eur. Math. Soc.21(2) (2019), 355–380].

我们限制了给定线性复杂度传递子移位的不同最小子系统的数量，Ormes 和 Pavlov 的继续工作 [关于不均匀循环的序列的复杂度函数。动力系统和随机过程（当代数学，736）。美国数学会，普罗维登斯，罗德岛州，2019 年，第 125--137 页]。我们还根据其复杂性函数限制了此类子移位可以支持的通用度量的数量。我们的测度理论边界概括了 Boshernitzan [具有线性块增长的最小符号流的独特遍历性。J.肛门。数学。44 (1) (1984), 77-96] 并且与 Cyr 和 Kra [Counting generic measure for a subshift of linear growth]密切相关。J.欧元。数学。社会党。21 (2) (2019), 355–380]。