Inventiones mathematicae

, Volume 184, Issue 3, pp 567–589

Growth-type invariants for ℤd subshifts of finite type and arithmetical classes of real numbers


DOI: 10.1007/s00222-010-0296-1

Cite this article as:
Meyerovitch, T. Invent. math. (2011) 184: 567. doi:10.1007/s00222-010-0296-1


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 Extending an unpublished example of Tsirelson (A strange two-dimensional symbolic system, 1992), we show that growth complexities of the form exp (nα+o(1)) are possible for non-integer α’s. In terminology of de Carvalho (Port. Math. 54(1):19–40, 1997), such subshifts have entropy dimension α. The class of possible α’s are identified in terms of arithmetical classes of real numbers of Weihrauch and Zheng (Math. Log. Q. 47(1):51–65, 2001).

Mathematics Subject Classification (2000)


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Pacific Institute for the Mathematical ScienceVancouverCanada