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Canonical compactifications for Markov shifts

Published online by Cambridge University Press:  08 February 2012

DORIS FIEBIG
DORIS FIEBIG*
Affiliation:
Universität Kassel, Fachbereich 10, Mathematik und Naturwissenschaften, Institut für Mathematik, D-34109 Kassel, Germany (email: [email protected])
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Abstract

We give a complete characterization of the compact metric dynamical systems that appear as boundaries of the canonical compactification of a locally compact countable state mixing Markov shift. Consider such a compact metric dynamical system. Then there is a pair of non-conjugate Markov shifts with conjugate canonical compactifications, one of which has the given compact system as canonical boundary.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 2 , April 2013 , pp. 441 - 454
Copyright
©2012 Cambridge University Press

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References

[1]Boyle, M., Buzzi, J. and Gomez, R.. Almost isomorphism for countable state Markov shifts. J. Reine Angew. Math. 592 (2006), 23–47.Google Scholar
[2]Boyle, M. and Krieger, W.. Periodic points and automorphisms of the shift. Amer. Math. Soc. 302 (1988), 71–114.Google Scholar
[3]Fiebig, D. and Fiebig, U.. Topological boundaries for countable state Markov shifts. Proc. Lond. Math. Soc. III Ser. 70(3) (1995), 625–643.Google Scholar
[4]Gurevic, B. M.. Topological entropy of enumerable Markov chains. Dokl. Akad. Nauk SSSR 187 (1969), 715–718; English transl. Soviet Math. Dokl. 10 (1969), 911–915.Google Scholar
[5]Kim, K. H., Ormes, N. and Roush, F.. The spectra of non-negative integer matrices via formal power series. J. Amer. Math. Soc. 13 (2000), 773–806.Google Scholar
[6]Kim, K. H. and Roush, F. W.. On the automorphism groups of subshifts. Pure Math. Appl. Ser. B 2 (1991), 3–22.Google Scholar
[7]Kim, K. H. and Roush, F. W.. The William’s conjecture is false for irreducible subshifts. Ann. Math. 149 (1999), 545–558.Google Scholar
[8]Kim, K. H., Roush, F. W. and Wagoner, J. B.. Automorphisms of the dimension group and gyration numbers of automorphisms of a shift. J. Amer. Math. Soc. 5 (1992), 191–211.Google Scholar
[9]Kitchens, B. P.. Symbolic Dynamics. One-sided, Two-sided and Countable State Markov Shifts. Springer, Berlin, Heidelberg, 1998.Google Scholar
[10]Lind, D.. The entropies of topological Markov shifts and a related class of algebraic integers. Ergod. Th. & Dynam. Sys. 4 (1984), 283–300.Google Scholar
[11]Lind, D. and Marcus, B.. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995.Google Scholar
[12]Schraudner, M.. The canonical-boundary representation for automorphism groups of locally compact countable state Markov shifts. Israel J. Math. 159 (2007), 253–275.Google Scholar
[13]Schraudner, M.. On the algebraic properties of the automorphism groups of countable state Markov shifts. Ergod. Th. & Dynam. Sys. 26(2) (2006), 551–583.Google Scholar