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ON THE CLASSIFICATION OF SOME 2-DIMENSIONAL MARKOV SHIFTS WITH GROUP-STRUCTURE
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UNSPECIFIED (1992) ON THE CLASSIFICATION OF SOME 2-DIMENSIONAL MARKOV SHIFTS WITH GROUP-STRUCTURE. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 12 (Part 4). pp. 823-833. ISSN 0143-3857.
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Abstract
For a finite Abelian group G define the two-dimensional Markov shift X(G) = (x is-an-element-of G(Z2): x(i,j) + x(i+1,j) + x(i,j+1) = 0 for all (i,j) is-an-element-of Z2}. Let mu(G) be the Haar measure on the subgroup X(G) subset-of G(Z2). The group Z2 acts on the measure space (X(G), mu(G)) by shifts. We prove that if G1 and G2 are p-groups and E(G1) not-equal E(G2), where E(G) is the least common multiple of the orders of the elements of G, then the shift actions on (X(G1),mu(G1)) and (X(G2),mu(G2)) are not measure-theoretically isomorphic. For any finite Abelian groups G1 and G2 the shift actions on X(G1) and X(G2) are topologically conjugate if and only if G1 and G2 are isomorphic.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ERGODIC THEORY AND DYNAMICAL SYSTEMS | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0143-3857 | ||||
Official Date: | December 1992 | ||||
Dates: |
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Volume: | 12 | ||||
Number: | Part 4 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 823-833 | ||||
Publication Status: | Published |
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