Israel Journal of Mathematics

, Volume 22, Issue 3–4, pp 332–353 | Cite as

Substitution-like minimal sets

  • Nelson G. Markley


Substitution-like minimal sets are a class of symbolic minimal sets on two symbols which includes the discrete substitution minimal sets on two symbols. They are almost automorphic extensions of then-adic integers and they are constructed by using special subsets of then-adics from which the almost automorphic points are determined by following orbits in then-adics. Through their study a complete classification is obtained for substitution minimal sets of constant length on two symbols. Moreover, the classification scheme is such that for specific substitutions the existence or non-existence of an isomorphism can be determined in a finite number of steps.


Normal Form Characteristic Sequence Periodic Point Prime Extension Arithmetic Progression 
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  1. 1.
    E. Coven,Endomorphisms of substitution minimal sets, Z. Wahrscheinlichkeitstheorie und Verw. Gebíete20 (1971), 129–133.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    E. Coven and M. Keane,The structure of substitution minimal sets, Trans. Amer. Math. Soc.162 (1971), 89–102.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    W. Gottschalk,An irreversible minimal set, inErgodic Theory, Proceedings of an International Symposium (New Orleans, 1961), Academic Press, New York, 1963, pp. 121–134.Google Scholar
  4. 4.
    W. Gottschalk,Substitution minimal sets, Trans. Amer. Math. Soc.109 (1963), 467–491.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    K. Jacobs and M. Keane, 0-1-Sequences of Toeplitz type, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete13 (1969), 123–131.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    H. Keynes,The proximal relation in a class of substitution minimal sets, Math. Systems Theory1 (1967), 165–174.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    B. Klein,Homomorphisms of symbolic dynamical systems, Math. Systems Theory6 (1972), 107–122.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    N. Markley,Characteristic sequences, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete (to appear).Google Scholar
  9. 9.
    J. Martin,Substitution minimal flows, Amer. J. Math.93 (1971), 503–526.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    J. Martin,Minimal flows arising from substitutions of non-constant length, Math. Systems Theory7 (1973), 73–82.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    M. Morse,Recurrent geodesics on a surface of negative curvature, Trans.Amer. Math.Soc.22 (1921), 84–100.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    M. Morse,Symbolic Dynamics, Lectures by Marston Morse, 1937–1938.Notes by Rufus Oldenburger, The Institute for Advanced Study, Princeton, New Jersey, 1966.Google Scholar

Copyright information

© Hebrew University 1976

Authors and Affiliations

  • Nelson G. Markley
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkU.S.A.

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