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On the classification of some two-dimensional Markov shifts with group structure

Published online by Cambridge University Press:  19 September 2008

Mark A. Shereshevsky
Mark A. Shereshevsky
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
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Abstract

For a finite Abelian group G define the two-dimensional Markov shift for all . Let μG be the Haar measure on the subgroup . The group ℤ2 acts on the measure space (XG, MG) by shifts. We prove that if G1, and G2 are p-groups and E(G1,) ≠ E(G2), where E(G) is the least common multiple of the orders of the elements of G, then the shift actions on and are not measure-theoretically isomorphic. For any finite Abelian groups G1 and G2 the shift actions on and are topologically conjugate if and only if G1 and G2 are isomorphic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 823 - 833
Copyright
Copyright © Cambridge University Press 1992

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References

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