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Solution of two conjectures in symbolic dynamics


Authors: K. H. Kim and F. W. Roush
Journal: Proc. Amer. Math. Soc. 112 (1991), 1163-1168
MSC: Primary 58F03; Secondary 28D20, 54H20
DOI: https://doi.org/10.1090/S0002-9939-1991-1065950-9
MathSciNet review: 1065950
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Abstract: We give an example of an inert involution on a subshift of entropy less than $ \log 2$ which interchanges two fixed points. This proves simple finite order generation (FOG) of Wagoner [W2] is false and answers Questions 1.10 and 1.11 [W2]. We also give an example of two near Markov subshifts which are eventually conjugate but not conjugate, and a near Markov subshift with domain a full shift not equivalent to its time reversal. The former shows sofic shift equivalence does not coincide with strong sofic shift equivalence.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1065950-9
Keywords: Finite order generation, inert automorphism, fixed point, orbit sign, time reversal, sofic strong shift equivalence, near Markov shift
Article copyright: © Copyright 1991 American Mathematical Society

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