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 | 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.

**[A]**J. Ashley,*Marker automorphisms of the one sided**-shift*, Ergodic Theory and Dynamical Systems (to appear). MR**1062757 (91k:28019)****[B1]**M. Boyle,*Nasu's simple automorphisms*, Proc. Dynamical Systems (Univ. of Maryland, 1986-1987) (J. Alexander, ed.), Lecture Notes in Math., no. 1342, Springer-Verlag, Berlin, 1988. MR**970546 (89j:54041)****[B2]**-,*Eventual extensions of finite codes*, Proc. Amer. Math. Soc.**104**(1988), 965-972. MR**964880 (92c:28015)****[BK]**M. Boyle and W. Krieger,*Almost Markov and shift equivalent sofic systems*, Proc. of Dynamical Systems (Univ. of Maryland, 1986-1987) (J. Alexander, ed.), Lecture Notes in Math., vol. 1342, Springer-Verlag, Berlin, 1988. MR**970547 (89i:28007)****[BFK]**M. Boyle, D. Lind, and B. Kitchens,*Automorphisms of one-sided subshifts of finite type*, Ergodic Theory and Dynamical Systems**10**(1990), 421-449. MR**1074312 (91h:58037)****[BLR]**M. Boyle, J. Franks, and D. Rudolph,*On the automorphism group of a subshift of finite type*, Trans. Amer. Math. Soc.**306**(1988), 71-114. MR**927684 (89m:54051)****[KR1]**K. H. Kim and F. W. Roush,*Decidability of shift equivalence*, Proc. of Dynamical Systems (Univ. of Maryland, 1986-1987) (J. Alexander, ed.), Lecture Notes in Math., vol. 1342, Springer-Verlag, Berlin, 1988. MR**970567 (90g:54033)****[KR2]**-,*An algorithm for sofic shift equivalence*, Ergodic Theory and Dynamical Systems**10**(1990), 381-393. MR**1062765 (92g:28037)****[KR3]**-,*Structure of inert automorphisms of subshifts*, Trans. Amer. Math. Soc. (submitted).**[W1]**J. Wagoner,*Triangle identities and symmetries of a subshift of finite type*, Pacific J. Math. (to appear). MR**1056673 (91h:28017)****[W2]**-,*Eventual finite order generation for the kernel dimension group representation*, Trans. Amer. Math. Soc.**317**(1990), 331-350. MR**1027363 (91a:54055)****[Wi]**R. F. Williams,*Classification of shifts of finite type*, Ann. of Math.**98**(1973), 120-153; errata, Ann. of Math.**99**(1974), 380-381. MR**0331436 (48:9769)**

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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