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Core dimension group constraints for factors of sofic shifts

Published online by Cambridge University Press:  19 September 2008

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

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
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), 5268.CrossRefGoogle Scholar
[B2]Boyle, M.. Shift equivalence and the Jordan form away from zero. Ergod. Th. & Dynam. Sys. 4 (1984), 367379.CrossRefGoogle Scholar
[BKM]Boyle, M., Kitchens, B. & Marcus, B.. A note on minimal covers of sofic systems. Proc. Amer. Math. Soc. 95 (1985), 403411.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), 165177.CrossRefGoogle Scholar
[H]Hedlund, G. A.. Endomorphisms and automorphisms of the shift dynamical system. Math. Sys. Theory 3 (1969), 320375.CrossRefGoogle Scholar
[KaM]Karabed, R. & Marcus, B.. Sliding block coding for input restricted channels. I.E.E.E. Trans. Inform. Theory 34 (1988), 226.CrossRefGoogle Scholar
[K]Kitchens, B.. An invariant for continuous factors of Markov chains. Proc. Amer. Math. Soc. 83 (1981), 825828.CrossRefGoogle Scholar
[KMT]Kitchens, B., Marcus, B. & Trow, P.. Eventual factor maps and composition of closing maps. Ergodic Th. & Dynam. Sys. 11 (1991), 85113.Google Scholar
[M]Marcus, B.. Factors and extensions of full shifts. Monats. für Math. 88 (1979), 239247.CrossRefGoogle Scholar
[N]Nasu, M.. An invariant for bounded-to-one factor maps between transitive sofic subshifts. Ergod. Th. & Dynam. Sys. 5 (1985), 85105.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), 184188.CrossRefGoogle Scholar
[T2]Trow, P.. Degrees of finite-to-one factor maps. Israel J. Math. 71, no. 2 (1990), 229238.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), 787801.CrossRefGoogle Scholar
[W2]Williams, S.. A sofic system which is not spectrally of finite type. Ergod. Th. & Dyn. Sys. 8 (1988), 483490.Google Scholar
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