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Automorphisms of one-sided subshifts of finite type

Published online by Cambridge University Press:  19 September 2008

Mike Boyle ,
John Franks  and
Bruce Kitchens
Mike Boyle
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
John Franks
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60201, USA
Bruce Kitchens
Affiliation:
IBM Research, Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA
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Abstract

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We prove that the automorphism group of a one-sided subshift of finite type is generated by elements of finite order. For one-sided full shifts we characterize the finite subgroups of the automorphism group. For one-sided subshifts of finite type we show that there are strong restrictions on the finite subgroups of the automorphism group.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 3 , September 1990 , pp. 421 - 449
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[A]Ashley, J.. Marker automorphisms of the one-sided d-shift. Ergod. Th. & Dynam. Sys. to appear.Google Scholar
[BDK]Blanchard, P., Devaney, R. & Keen, L.. The dynamics of complex polynomials and automorphisms of the shift, preprint.Google Scholar
[B]Boyle, M.. Nasu's simple automorphisms, Dynamical Systems - Maryland 1986–1987. Proceedings of a Special Year, ed. Alexander, J., Springer Lecture Notes 1342. Springer-Verlag: New York, 1988.Google Scholar
[Ha]Hall, M. Jr. The Theory of Groups, Chelsea Pub. Co.: New York, 1976.Google Scholar
[H]Hedlund, G. A.. Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320–375.CrossRefGoogle Scholar
[N]Nasu, M.. Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov chains. Dynamical Systems - Maryland 1986–1987, Proceedings of a Special Year, ed. Alexander, J., Springer Lecture Notes 1342, Springer-Verlag: New York, 1988.Google Scholar
[R]Rotman, J. J.. An Introduction to the Theory of Groups. 3rd ed., Allyn and Bacon, Inc.: Boston, 1984.Google Scholar
[Wa1]Wagoner, J.. Markov partitions and K 2. Pub. Math. IHES No. 65 (1987), 91–129.CrossRefGoogle Scholar
[Wa2]Wagoner, J.. Triangle identities and symmetries of a subshift of finite type. Pacific J. Math., to appear.Google Scholar
[Wa3]Wagoner, J.. Eventual finite order generation for the kernel of the dimension group representation. Trans, of AMS 317 (1) (1990), 331–350.CrossRefGoogle Scholar
[W]Williams, R. F.. Classification of subshifts of finite type. Ann. of Math. 98 (1973), 120–153;CrossRefGoogle Scholar
erratum 99 (1974), 380–381.Google Scholar