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Factors and extensions of full shifts

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Abstract

Let ∑ A be an irreducible shift of finite type with entropy logn. Then ∑ A is a continuous extension of the fulln-shift. Also, if ∑ A is a continuous factor of the fulln-shift, then it is shift equivalent to the fulln-shift.

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References

  1. Adler, R., W. Goodwyn, andB. Weiss: Equivalence of topological Markov shifts. Israel J. Math.27, 49–63 (1977).

    Google Scholar 

  2. Bowen, R., andO. Lanford: Zeta functions of restrictions of the shift transformation. Proc. Symp. Pure Math. vol. 14, p. 43–50. Providence, R. I.: Amer. Math. Soc. 1970.

    Google Scholar 

  3. Coven, E., andM. Paul: Endomorphisms of irreducible shifts of finite type. Math. Syst. Th.8, 167–175 (1974).

    Google Scholar 

  4. Gantmacher, F.: Theory of Matricies, vol. 2. New York: Chelsea. 1959.

    Google Scholar 

  5. Hedlund, G. A.: Endomorphisms and automorphisms of the shift dynamical system. Math. Syst. Th.3, 320–375 (1959).

    Google Scholar 

  6. Parry, W.: Intrinsic Markov chains. Trans. Amer. Math. Soc.112, 55–66 (1964).

    Google Scholar 

  7. Parry, W., andR. F. Williams: Block Coding and a Zeta Function for Finite Markov Chains. Preprint.

  8. Williams, R. F.: Classification of shifts, of finite type. Ann. Math.98, 120–153 (1973); Errata. Ann. Math.99, 380–381 (1974).

    Google Scholar 

  9. Walters, P.: Ergodic Theory-Introductory Lectures. Lecture Notes Math. 458. Berlin-Heidelberg-New York: Springer. 1975.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, 27514, Chapel Hill, NC, USA

    Brian Marcus

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  1. Brian Marcus
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Additional information

Partially supported by NSF grants MCS 76-05969 and MCS 78-01244.

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Marcus, B. Factors and extensions of full shifts. Monatshefte für Mathematik 88, 239–247 (1979). https://doi.org/10.1007/BF01295238

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  • DOI: https://doi.org/10.1007/BF01295238

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