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Finite group actions on shifts of finite type

Published online by Cambridge University Press:  19 September 2008

R. L. Adler ,
B. Kitchens  and
B. H. Marcus
R. L. Adler
Affiliation:
IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
B. Kitchens
Affiliation:
IBM Research, 5600 Cottle Road, San Jose, CA 95193, USA
B. H. Marcus
Affiliation:
Mathematics Department, University of North Carolina, Chapel Hill, North Carolina 27514, USA
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Abstract

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A continuous ℤ⊗TG action on a subshift of finite type consists of a subshift of finite type with its shift transformation, together with a group, G, of homeomorphisms of the subshift and a group automorphism T, so that the commutation relation σ ° g = Tg ° ∑A is any positive entropy subshift of finite type, G is any finite group and T is any automorphism of G then there is a non-trivial ℤ⊗TG action on ∑A. We then classify all such actions up to ‘almost topological‘ conjugacy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 1 , March 1985 , pp. 1 - 25
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Adler, R. L. & Marcus, B.. Topological entropy and equivalence of dynamical systems. Mem. Amer. Math. Soc. 219 (1979).Google Scholar
[2]Gray, R. L.. Generalizing period and topological entropy to transitive non-wandering systems. Masters thesis, Univ. of NC, Chapel Hill, 1978.Google Scholar
[3]Hedlund, G. A.. Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320–375.CrossRefGoogle Scholar
[4]Krieger, W.. On the periodic points of topological Markov chains. Math. Z. 169 (1979), 99–104.Google Scholar
[5]Parry, W.. A finitary classification of topological Markov chains and sofic systems. Bull. London Math. Soc. 9 (1977), 86–92.Google Scholar
[6]Rudolph, D. J.. Counting the relatively finite factors of a Bernoulli shift. Israel J. Math. 30, No. 3 (1978), 255–263.Google Scholar
[7]Rudolph, D. J.. An isomorphism theory for Bernoulli Z-skew compact group actions. Advances in Math. 47, No. 3 (1983), 241–257.Google Scholar