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The Williams conjecture is false for irreducible subshifts


Authors: K. H. Kim and F. W. Roush
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 105-109
MSC (1991): Primary 58F03, 54H20
DOI: https://doi.org/10.1090/S1079-6762-97-00032-2
Published electronically: October 16, 1997
Accompanying material: Maple program
MathSciNet review: 1472090
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Williams conjecture is false for irreducible subshifts of finite type using relative sign-gyration numbers defined between different subshifts.


References [Enhancements On Off] (What's this?)

  • 1. K. H. Kim and F. W. Roush, Williams's conjecture is false for reducible subshifts, J. Amer. Math. Soc. 5 (1992), 213-215. MR 92j:54055
  • 2. -, Williams's conjecture is false for irreducible subshifts, to appear in Annals of Mathematics.
  • 3. K. H. Kim, F. W. Roush, and J. Wagoner, Automorphisms of the dimension group and gyration numbers, J. Amer. Math. Soc. 5 (1992), 191-212. MR 93h:54026
  • 4. D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, 1995. MR 97a:58050
  • 5. R. F. Williams, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120-153; Errata ibid. 99 (1974), 380-381. MR 48:9769

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Additional Information

K. H. Kim
Affiliation: Mathematics Research Group, Alabama State University, Montgomery, AL 36101-0271, and Korean Academy of Science and Technology
Email: kkim@asu.alasu.edu

F. W. Roush
Affiliation: Mathematics Research Group, Alabama State University, Montgomery, AL 36101-0271
Email: froush@asu.alasu.edu

DOI: https://doi.org/10.1090/S1079-6762-97-00032-2
Keywords: Williams conjecture, irreducible subshift of finite type, strong shift equivalence, gyration numbers
Received by editor(s): June 5, 1997
Published electronically: October 16, 1997
Additional Notes: The authors were partially supported by NSF Grants DMS 9024813 and DMS 9405004.
Communicated by: Svetlana Katok
Article copyright: © Copyright 1997 American Mathematical Society

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