Sofic systems

Springer Science and Business Media LLC - Tập 20 - Trang 165-177 - 1975
Ethan M. Coven1,2, Michael E. Paul1,2
1Wesleyan University, Middletown, U.S.A.
2University of Maryland, Baltimore County, Baltimore, U.S.A.

Tóm tắt

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.

Tài liệu tham khảo

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. 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. R. Bowen,Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. J. Math.92 (1970), 907–918. R. Bowen,Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc.153 (1971), 401–414. R. Bowen,Symbolic dynamics for hyperbolic flows, Amer. J. Math.95 (1973), 429–459. 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. E. M. Coven and M. E. Paul,Endomorphisms of irreducible subshifts of finite type, Math. Systems Theory8 (1974), 167–175. F. Gantmacher,The theory of matrices, vol. II, Chelsea, New York, 1959. G. A. Hedlund,Mappings on sequence spaces (Part I), Comm. Research Div. Technical Report No. 1, Princeton, N. J., Feb. 1961. G. A. Hedlund,Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory3 (1969), 320–375. A. Manning,Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc.3 (1971), 215–220. W. Parry,Intrinsic Markov chains, Trans. Amer. Math. Soc.112 (1964), 55–66. S. Smale,Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967), 747–817. B. Weiss,Intrinsically ergodic systems, Bull. Amer. Math. Soc.76 (1970), 1266–1269. B. Weiss,Subshifts of finite type and sofic systems, Monatsh. Math.77 (1973), 462–474.