Growth-type invariants for Zd subshifts of finite type and arithmetical classes of real numbers
成果类型：
Article
署名作者：
Meyerovitch, Tom
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-010-0296-1
发表日期：
2011
页码：
567-589
关键词：
摘要：
We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson (A strange two-dimensional symbolic system, 1992), we show that growth complexities of the form exp (n (alpha+o(1))) are possible for non-integer alpha's. In terminology of de Carvalho (Port. Math. 54(1):19-40, 1997), such subshifts have entropy dimension alpha. The class of possible alpha's are identified in terms of arithmetical classes of real numbers of Weihrauch and Zheng (Math. Log. Q. 47(1):51-65, 2001).