Counting generic measures for a subshift of linear growth

作     者：Cyr, Van Kra, Bryna 

作者机构：Bucknell Univ Lewisburg PA 17837 USA Northwestern Univ Evanston IL 60208 USA 

出 版 物：《JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY》 (J. Eur. Math. Soc.)

年 卷 期：2019年第21卷第2期

页      面：355-380页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：NSF Division Of Mathematical Sciences Direct For Mathematical & Physical Scien Funding Source: National Science Foundation 

主　　题：Subshift automorphism block complexity interval exchange transformation 

摘      要：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.