Counting generic measures for a subshift of linear growth
Counting generic measures for a subshift of linear growth
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DOI：
10.4171/jems/838
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发表时间：
2015-05
影响因子：
2.6
通讯作者：
Van Cyr;Bryna Kra
中科院分区：
文献类型：
--
作者：
Van Cyr;Bryna Kra
1984 年，Boshernitzan 证明了线性块增长最小子偏移的遍历测度数量的上限，并询问是否可以在不对偏移进行进一步假设的情况下降低该上限。我们回答这个问题，表明 Boshernitzan 的界限是尖锐的。我们进一步证明，相同的界限适用于先验的更大的非原子通用度量集，并且即使放弃极小性假设，该界限仍然有效。将这些结果应用于区间交换变换，我们给出了最小 IET 的非原子通用度量数量的上限，回答了 Chaika 和 Masur 最近提出的问题。
In 1984 Boshernitzan proved an upper bound on the number of ergodic measures for a minimal subshift of linear block growth and asked if it could be lowered without further assumptions on the shift. We answer this question, showing that Boshernitzan's bound is sharp. We further prove that the same bound holds for the, a priori, larger set of nonatomic generic measures, and that this bound remains valid even if one drops the assumption of minimality. Applying these results to interval exchange transformations, we give an upper bound on the number of nonatomic generic measures of a minimal IET, answering a question recently posed by Chaika and Masur.