Solution of two conjectures in symbolic dynamics

Kim, K. H.; Roush, F. W.

doi:10.1090/S0002-9939-1991-1065950-9

Solution of two conjectures in symbolic dynamics
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by K. H. Kim and F. W. Roush

Proc. Amer. Math. Soc. 112 (1991), 1163-1168

DOI: https://doi.org/10.1090/S0002-9939-1991-1065950-9

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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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