Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-02T22:39:15.585Z Has data issue: false hasContentIssue false
  • English
  • Français

Shift equivalence and the Jordan form away from zero

Published online by Cambridge University Press:  19 September 2008

Mike Boyle
Mike Boyle
Affiliation:
IBM, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA and Mathematical Sciences Research Institute, 2223 Fulton Street, Room 603, Berkeley, CA 94720, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Only finitely many shift equivalence classes of non-negative aperiodic integral matrices may share a given diagonal Jordan form away from zero. The diagonal assumption is necessary.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 3 , September 1984 , pp. 367 - 379
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Adler, R. L. & Marcus, B.. Topological entropy and equivalence of dynamical systems. Mem. Amer. Math. Soc. 219 (1979).Google Scholar
[2]Adler, R. L., Coppersmith, D. & Hassner, M.. Algorithms for sliding block codes. IEEE Transactions on Information Theory 29, No. 1 (1983), 5–22.CrossRefGoogle Scholar
[3]Bowen, R.. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Springer Lecture Notes in Mathematics 470 (1975).CrossRefGoogle Scholar
[4]Denker, M., Grillenberger, C. & Sigmund, K.. Ergodic Theory on Compact Spaces. Springer Lecture Notes in Mathematics 527 (1976).CrossRefGoogle Scholar
[5]Effros, E. G.. Dimensions and C*-algebras. CBMS 46 (1981). Amer. Math. Society: Providence, Rhode Island.Google Scholar
[6]Handelman, D.. Reducible topological Markov chains via k o-theory and Ext. In Operator Algebras and K-Theory, Contemporary Mathematics series vol. 10 (1982). Amer. Math. Society: Providence, Rhode Island.Google Scholar
[7]Kim, K. H. & Roush, F. W.. Some results on decidability of shift equivalence. J. Combin. Inform. System Sci. 4, No. 2 (1979), 123–146.Google Scholar
[8]Kitchens, B.. An invariant for continuous factors of Markov shifts. Proc. Amer. Math. Soc. 83 (1981), 825–828.CrossRefGoogle Scholar
[9]Krieger, W.. On dimension functions and topological Markov chains. Invent, math. 56 (1980), 239–250.CrossRefGoogle Scholar
[10]Krieger, W.. On certain notions of equivalence for topological Markov chains. Preprint (1982).CrossRefGoogle Scholar
[11]Newman, M.. Integral matrices. Academic Press: New York, 1972.Google Scholar
[12]Parry, W. and Tuncel, S.. Classification Problems in Ergodic Theory. L.M.S. Lecture Notes 67, Cambridge University Press, 1982.CrossRefGoogle Scholar
[13]Parry, W. and Williams, R. F.. Block-coding and a zeta function for finite Markov chains. Proc. London Math. Soc. 35 (1977), 483–495.CrossRefGoogle Scholar
[14]Stewart, I. N. and Tall, D. O.. Algebraic Number Theory. Chapman and Hall: London, 1979.CrossRefGoogle Scholar
[15]Suprunenko, D. A. & Tyshkevich, R. I.. Commutative Matrices. Academic Press: New York, 1968.Google Scholar
[16]Williams, R. F.. Classification of subshifts of finite type. Ann. of Math. 98 (1973), 120–153; Errata, Ann. of Math. 99 (1974),380–381.CrossRefGoogle Scholar