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Sofic systems

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Abstract

A symbolic flow is called a sofic system if it is a homomorphic image (factor) of a subshift of finite type. We show that every sofic system can be realized as a finite-to-one factor of a subshift of finite type with the same entropy. From this it follows that sofic systems share many properties with subshifts of finite type. We concentrate especially on the properties of TPPD (transitive with periodic points dense) sofic systems.

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References

  1. R. L. Alder and B. Weiss,Similarity of automorphisms of the torus, Mem. Amer. Math. Soc. No. 98, Amer. Math. Soc., Providence, R. I., 1970.

    Google Scholar 

  2. R. Bowen,Topological entropy and axiom A, Global Analysis, Proc. Sympos. Pure Math.XIV, Berkeley, Calif. (1968), 23–41. Amer. Math. Soc., Providence, R. I., 1970.

    Google Scholar 

  3. R. Bowen,Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. J. Math.92 (1970), 907–918.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Bowen,Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc.153 (1971), 401–414.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Bowen,Symbolic dynamics for hyperbolic flows, Amer. J. Math.95 (1973), 429–459.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Bowen and O. E. Lanford III,Zeta functions and restrictions of the shift transformation, Global Analysis, (Proc. Sympos. Pure Math.XIV, Berkeley, Calif., 1968), 43–49. Amer. Math. Soc., Providence, R. I., 1970.

    Google Scholar 

  7. E. M. Coven and M. E. Paul,Endomorphisms of irreducible subshifts of finite type, Math. Systems Theory8 (1974), 167–175.

    Article  MathSciNet  Google Scholar 

  8. F. Gantmacher,The theory of matrices, vol. II, Chelsea, New York, 1959.

    MATH  Google Scholar 

  9. G. A. Hedlund,Mappings on sequence spaces (Part I), Comm. Research Div. Technical Report No. 1, Princeton, N. J., Feb. 1961.

  10. G. A. Hedlund,Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory3 (1969), 320–375.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Manning,Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc.3 (1971), 215–220.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. S. Smale,Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967), 747–817.

    MathSciNet  Google Scholar 

  14. B. Weiss,Intrinsically ergodic systems, Bull. Amer. Math. Soc.76 (1970), 1266–1269.

    Article  MATH  MathSciNet  Google Scholar 

  15. B. Weiss,Subshifts of finite type and sofic systems, Monatsh. Math.77 (1973), 462–474.

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Wesleyan University, 06457, Middletown, Connecticut, U.S.A.

    Ethan M. Coven & Michael E. Paul

  2. University of Maryland, Baltimore County, 21228, Baltimore, Maryland, U.S.A.

    Ethan M. Coven & Michael E. Paul

Authors
  1. Ethan M. Coven
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  2. Michael E. Paul
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Coven, E.M., Paul, M.E. Sofic systems. Israel J. Math. 20, 165–177 (1975). https://doi.org/10.1007/BF02757884

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  • DOI: https://doi.org/10.1007/BF02757884

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