Monatshefte für Mathematik

, Volume 88, Issue 3, pp 239–247 | Cite as

Factors and extensions of full shifts

  • Brian Marcus
Article

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Adler, R., W. Goodwyn, andB. Weiss: Equivalence of topological Markov shifts. Israel J. Math.27, 49–63 (1977).Google Scholar
  2. [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. [3]
    Coven, E., andM. Paul: Endomorphisms of irreducible shifts of finite type. Math. Syst. Th.8, 167–175 (1974).Google Scholar
  4. [4]
    Gantmacher, F.: Theory of Matricies, vol. 2. New York: Chelsea. 1959.Google Scholar
  5. [5]
    Hedlund, G. A.: Endomorphisms and automorphisms of the shift dynamical system. Math. Syst. Th.3, 320–375 (1959).Google Scholar
  6. [6]
    Parry, W.: Intrinsic Markov chains. Trans. Amer. Math. Soc.112, 55–66 (1964).Google Scholar
  7. [7]
    Parry, W., andR. F. Williams: Block Coding and a Zeta Function for Finite Markov Chains. Preprint.Google Scholar
  8. [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. [9]
    Walters, P.: Ergodic Theory-Introductory Lectures. Lecture Notes Math. 458. Berlin-Heidelberg-New York: Springer. 1975.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Brian Marcus
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

Personalised recommendations