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Core dimension group constraints for factors of sofic shifts

Published online by Cambridge University Press:  19 September 2008

Paul Trow  and
Susan Williams
Paul Trow
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152, USA
Susan Williams
Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, USA
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Abstract

We give constraints on the existence of factor maps between sofic shifts. These constraints yield examples of sofic shifts of entropy log n which do not factor onto the full n-shift. We also show that any prime which divides the degree of an endomorphism of a sofic shift must divide the non-leading coefficients of the characteristic polynomial of the core matrix of the shift.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 213 - 224
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

[AM]Adler, R. L. & Marcus, B.. Topological entropy and equivalence of dynamical systems. Mem. Amer. Math. Soc. 20, no. 219 (1979).Google Scholar
[B1]Boyle, M.. Constraints on the degree of a sofic homomorphism and the induced multiplication of measures on unstable sets. Israel J. Math. 53 (1986), 52–68.CrossRefGoogle Scholar
[B2]Boyle, M.. Shift equivalence and the Jordan form away from zero. Ergod. Th. & Dynam. Sys. 4 (1984), 367–379.CrossRefGoogle Scholar
[BKM]Boyle, M., Kitchens, B. & Marcus, B.. A note on minimal covers of sofic systems. Proc. Amer. Math. Soc. 95 (1985), 403–411.CrossRefGoogle Scholar
[BMT]Boyle, M., Marcus, B. & Trow, P.. Resolving maps and the dimension group for shifts of finite type. Memoirs Amer. Math. Soc. 377 (1987).Google Scholar
[CP]Coven, E. & Paul, M.. Sofic systems. Israel J. Math. 20 (1975), 165–177.CrossRefGoogle Scholar
[H]Hedlund, G. A.. Endomorphisms and automorphisms of the shift dynamical system. Math. Sys. Theory 3 (1969), 320–375.CrossRefGoogle Scholar
[KaM]Karabed, R. & Marcus, B.. Sliding block coding for input restricted channels. I.E.E.E. Trans. Inform. Theory 34 (1988), 2–26.CrossRefGoogle Scholar
[K]Kitchens, B.. An invariant for continuous factors of Markov chains. Proc. Amer. Math. Soc. 83 (1981), 825–828.CrossRefGoogle Scholar
[KMT]Kitchens, B., Marcus, B. & Trow, P.. Eventual factor maps and composition of closing maps. Ergodic Th. & Dynam. Sys. 11 (1991), 85–113.CrossRefGoogle Scholar
[M]Marcus, B.. Factors and extensions of full shifts. Monats. für Math. 88 (1979), 239–247.CrossRefGoogle Scholar
[N]Nasu, M.. An invariant for bounded-to-one factor maps between transitive sofic subshifts. Ergod. Th. & Dynam. Sys. 5 (1985), 85–105.CrossRefGoogle Scholar
[PT]Parry, W. & Tuncel, S.. Classification Problems in Ergodic Theory. London Math. Soc. Lecture Note Series, Vol. 67. Cambridge, Cambridge University Press, 1982.CrossRefGoogle Scholar
[T1]Trow, P.. Degrees of constant-to-one factor maps. Proc. Amer. Math. Soc. 103, no. 1 (1988), 184–188.CrossRefGoogle Scholar
[T2]Trow, P.. Degrees of finite-to-one factor maps. Israel J. Math. 71, no. 2 (1990), 229–238.CrossRefGoogle Scholar
[T3]Trow, P.. Divisibility constraints on degrees of factor maps. Proc. Amer. Math. Soc. to appearGoogle Scholar
[W1]Williams, S.. Lattice invariants for sofic shifts. Ergod. Th. & Dynam. Sys. 11 (1991), 787–801.CrossRefGoogle Scholar
[W2]Williams, S.. A sofic system which is not spectrally of finite type. Ergod. Th. & Dyn. Sys. 8 (1988), 483–490.CrossRefGoogle Scholar