Inventiones mathematicae

, Volume 184, Issue 3, pp 567–589 | Cite as

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



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 Extending an unpublished example of Tsirelson (A strange two-dimensional symbolic system, 1992), we show that growth complexities of the form exp (n α+o(1)) are possible for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)

37B10 37B40 37B50 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Pacific Institute for the Mathematical ScienceVancouverCanada

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