Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T00:33:38.909Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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