In this work, we treat subshifts, defined in terms of an alphabet $\mathcal {A}$ and (usually infinite) forbidden list $\mathcal {F}$ , where the number of n-letter words in $\mathcal {F}$ has ‘slow growth rate’ in n. We show that such subshifts are well behaved in several ways; for instance, they are boundedly supermultiplicative in the sense of Baker and Ghenciu [Dynamical properties of S-gap shifts and other shift spaces. J. Math. Anal. Appl. 430(2) (2015), 633–647] and they have unique measures of maximal entropy with the K-property and which satisfy Gibbs bounds on large (measure-theoretically) sets. The main tool in our proofs is a more general result, which states that bounded supermultiplicativity and a sort of measure-theoretic specification property together imply uniqueness of the measure of maximum entropy and our Gibbs bounds. We also show that some well-known classes of subshifts can be treated by our results, including the symbolic codings of $x \mapsto \alpha + \beta x$ (the so-called $\alpha $ - $\beta $ shifts of Hofbauer [Maximal measures for simple piecewise monotonic transformations. Z. Wahrsch. verw. Geb. 52(3) (1980), 289–300]) and the bounded density subshifts of Stanley [Bounded density shifts. Ergod. Th. & Dynam. Sys. 33(6) (2013), 1891–1928].

在这项工作中，我们处理子移位，根据字母表 $\mathcal {A}$ 和（通常是无限的）禁止列表 $\mathcal {F}$ 定义 ，其中 $\mathcal {F 中的 n个字母单词的数量}$ 在n中具有“缓慢的增长率” 。我们证明了这种子移位在几个方面表现良好；例如，在 Baker 和 Ghenciu 的意义上，它们是有界超乘的[ S -gap 位移和其他位移空间的动态特性。J.数学。肛门。应用程序。430 (2) (2015), 633–647] 并且它们具有具有 K 属性的最大熵的独特度量，并且满足大型（理论上的度量）集的吉布斯界限。我们证明中的主要工具是一个更一般的结果，它指出有界超乘性和一种测度理论规范属性共同暗示了最大熵测度和我们的吉布斯界的唯一性。我们还表明，我们的结果可以处理一些众所周知的子移位类别，包括 $x \mapsto \alpha + \beta x$ 的符号编码（ 所谓 的 $\alpha $ - $\beta $ Hofbauer [简单分段单调变换的最大度量。Z. Wahrsch. verw. Geb. 52 (3) (1980), 289–300]) 和 Stanley 的有界密度子位移 [有界密度位移。埃尔戈德。钍。&动态。系统。 33 (6) (2013), 1891–1928]。