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The action of inert finite-order automorphisms on finite subsystems of the shift

Published online by Cambridge University Press:  19 September 2008

Mike Boyle  and
Ulf-Rainer Fiebig
Mike Boyle
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
Ulf-Rainer Fiebig
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900 Heidelberg, Germany
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Abstract

Let (X, S) be a shift of finite type. Let G be the group of automorphisms of (X, S) which are compositions of elements of finite order in the kernel of the dimension representation. We characterize the action of G on finite subsystems of (X, S).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 3 , September 1991 , pp. 413 - 425
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

[B]Boyle, M.. Nasu's simple automorphisms. In: Dynamical Systems-Maryland 1986–1987, Proc. Special Year, Lecture Notes in Mathematics 1342, Springer Verlag (1988), pp 23–32.Google Scholar
[BK]Boyle, M. & Krieger, W.. Periodic points and automorphisms of the shift. Trans. Amer. Math. Soc. 302 (1987), 125–149.CrossRefGoogle Scholar
[BLR]Boyle, M., Lind, D. & Rudolph, D.. The automorphism group of a subshift of finite type. Trans. Amer. Math. Soc. 306 (1988), 71–114.CrossRefGoogle Scholar
[F1]Fiebig, U.. Dissertation. University of Göttingen, Germany, 1987.Google Scholar
[F2]Fiebig, U.. Gyration numbers for involutions of subshifts of finite type, I and II. To appear in Forum Mathematicum.Google Scholar
[F3]Fiebig, U.. Periodic points and finite group actions on the shift. Manuscript in preparation.Google Scholar
[K]Krieger, W.. On the subsystems of topological Markov chains. Ergod. Th. & Dynam. Sys. 2 (1982), 195–202.CrossRefGoogle Scholar
[KR1]Kim, K. H. & Roush, F. W.. On the structure of inert automorphisms of subshifts. Trans. Amer. Math. Soc. submitted.Google Scholar
[KR2]Kim, K. H. & Roush, F. W.. Solution of two conjectures in symbolic dynamics. Preprint. Alabama State University, 1989.Google Scholar
[N]Nasu, M.. Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts. In: Dynamical Systems - Maryland 1986–1987, Proc. Special Year, Springer Lecture Notes in Mathematics 1342, (1988), pp. 608–616.Google Scholar
[W]Wagoner, J.. Eventual finite order generation for the kernel of the dimension group representation. Trans. Amer. Math. Soc. 317(1) (1990), 331–350.CrossRefGoogle Scholar