Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T00:46:36.426Z Has data issue: false hasContentIssue false
  • English
  • Français

Lattice invariants for sofic shifts

Published online by Cambridge University Press:  19 September 2008

Susan Williams
Susan Williams
Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

To a factor map φ from an irreducible shift of finite type ΣA to a sofic shift S, we associate a subgroup of the dimension group (GA, Â) which is an invariant of eventual conjugacy for φ. This invariant yields new necessary conditions for the existence of factor maps between equal entropy sofic shifts.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 787 - 801
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

[AM]Adler, R. & Marcus, B.. Topological entropy and equivalence of dynamical systems. Memoirs Amer. Math. Soc. 20 (219) (1979).CrossRefGoogle Scholar
[B]Boyle, M.. Shift equivalence and the Jordan form away from zero. Ergod. Th. & Dynam. Sys. 4 (1989), 367–379.CrossRefGoogle Scholar
[BMT]Boyle, M., Marcus, B. & Trow, P.. Resolving maps and the dimension group for shifts of finite type. Memoirs Amer. Math. Soc. 70 (337) (1987).CrossRefGoogle Scholar
[BK]Boyle, M. & Krieger, W.. Almost Markov and shift equivalent sofic systems. In: Dynamical Systems: Proc. University of Maryland 1986–87, Springer Lecture Notes in Mathematics 1342, Springer-Verlag, 1988, pp. 33–93.CrossRefGoogle Scholar
[F]Fischer, R.. Sofic systems and graphs. Monatsh. Math. 80 (1975), 179–186.CrossRefGoogle Scholar
[HN]Hamachi, T. & Nasu, M.. Topological conjugacy for 1-block factor maps of subshifts and sofic covers. Dynamical Systems: Proc., University of Maryland 1986–87, Springer Lecture Notes in Mathematics 1342, Springer-Verlag, 1988, pp 251–260.CrossRefGoogle Scholar
[H1]Handelman, D.. Positive matrices and dimension groups affiliated to C*-algebras and topological Markov chains. J. Operator Theory 6 (1981), 55–74.Google Scholar
[H2]Handelman, D.. Eventually positive matrices with rational eigenvectors. Ergod. Th. & Dynam. Sys. 7 (1987), 193–196.CrossRefGoogle Scholar
[Ka]Kaplansky, I.. Infinite Abelian Groups. University of Michigan Press, Ann Arbor, 1954.Google Scholar
[KR]Kim, K. H. & Roush, F.. Some results on decidability of shift equivalence. J. Combinatorics, Info. and Sys. Sci. 4 (1979), 123–146.Google Scholar
[KMT]Kitchens, B., Marcus, B. & Trow, P.. Eventual factor maps and compositions of closing maps. Ergod. Th. & Dynam. Sys. 11 (1991), 85–113.CrossRefGoogle Scholar
[K1]Krieger, W.. On sofic systems I. Israel J. Math. 48 (1984), 305–330.CrossRefGoogle Scholar
[K2]Krieger, W.. On dimension functions and topological Markov chains. Invent. Math. 56 (1980), 239–250.CrossRefGoogle Scholar
[N1]Nasu, M.. An invariant for bounded-to-one factor maps between transitive sofic subshifts. Ergod. Th. & Dynam. Sys. 5 (1985), 89–105.CrossRefGoogle Scholar
[N2]Nasu, M.. Topological conjugacy for sofic systems. Ergod. Th. & Dynam. Sys. 6 (1986), 265–280.CrossRefGoogle Scholar
[W]Williams, S.. A sofic system which is not spectrally of finite type. Ergod. Th. & Dynam. Sys. 8 (1988), 483–490.CrossRefGoogle Scholar
[Wi]Williams, R.. Classification of shifts of finite type. Ann. Math. 98 (1973), 120–153;CrossRefGoogle Scholar
Errata. Ann. Math. 99 (1974), 380–381.Google Scholar