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

MathSciNet review:
1065950

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Abstract | References | Similar Articles | Additional Information

Abstract: We give an example of an inert involution on a subshift of entropy less than 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