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Transactions of the American Mathematical Society

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An extension theorem for closing maps of shifts of finite type


Author: Jonathan Ashley
Journal: Trans. Amer. Math. Soc. 336 (1993), 389-420
MSC: Primary 58F03; Secondary 28D15, 54H20
DOI: https://doi.org/10.1090/S0002-9947-1993-1105064-9
MathSciNet review: 1105064
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Abstract: If there exists some right-closing factor map $ \pi :{\Sigma _A} \to {\Sigma _B}$ between aperiodic shifts of finite type, then any right-closing map $ \varphi :X \to {\Sigma _B}$ from any shift of finite type $ X$ contained in $ {\Sigma _A}$ can be extended to a right-closing factor map from all of $ {\Sigma _A}$ onto $ {\Sigma _B}$. We prove this and give some consequences.


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

  • [AM] R. Adler and B. Marcus, Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc., no. 219, 1979. MR 533691 (83h:28027)
  • [A1 ] J. Ashley, Bounded-to-$ 1$ factors of an aperiodic shift of finite type are $ 1$-to-$ 1$ almost everywhere factors also, Ergodic Theory Dynamical Systems 10 (1990), 615-625. MR 1091417 (92d:58055)
  • [A2] -, Resolving factor maps for shifts of finite type with equal entropy, Ergodic Theory and Dynamical Systems 11 (1991), 219-240. MR 1116638 (92d:58056)
  • [B] M. Boyle, Lower entropy factors of sofic systems, Ergodic Theory and Dynamical Systems 4 (1984), 541-557. MR 753922 (85m:54014)
  • [BMT] M. Boyle, B. Marcus, and P. Trow, Resolving maps and the dimension group for shifts of finite type, Mem. Amer. Math. Soc., no. 377, 1987. MR 912638 (89c:28019)
  • [KM] R. Karabed and B. Marcus, Sliding-block coding for input-restricted channels, IEEE Trans. Inform. Theory 34 (1988), 2-26. MR 936920 (89j:94024)
  • [Kr1] W. Krieger, On dimension functions and topological Markov chains, Invent. Math. 56 (1980), 239-250. MR 561973 (81m:28018)
  • [Kr2] -, On the subsystems of topological Markov chains, Ergodic Theory Dynamical Systems 2 (1982), 195-202. MR 693975 (85b:28020)
  • [M] B. Marcus, Factors and extensions of full shifts, Monatsh. Math. 88 (1979), 239-247. MR 553733 (81g:28023)
  • [S] E. Seneta, Non-negative matrices and Markov chains, 2nd ed., Springer-Verlag, New York, 1981. MR 2209438
  • [We] B. Weiss, Subshifts of finite type and sofic systems, Monatsh. Math. 77 (1973), 462-474. MR 0340556 (49:5308)
  • [Wi] R. 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/S0002-9947-1993-1105064-9
Article copyright: © Copyright 1993 American Mathematical Society

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