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The equivalence theorem for ℤd-actions of positive entropy

Published online by Cambridge University Press:  19 September 2008

J. Roberto Hasfura-Buenaga
J. Roberto Hasfura-Buenaga
Affiliation:
Department of Mathematics, Trinity University, San Antonio, TX 78212, USA
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Abstract

First, the class of id-finitely fixed actions of ℤd on a Lebesgue space is defined. Then, it is demonstrated that this property is stable under id-Kakutani equivalence and that, conversely, any two id-finitely fixed ℤd-actions of the same (finite) positive entropy are id-Kakutani equivalent. By id-Kakutani equivalence we mean that element in A. del Junco and D. Rudolph's family of relations on ℤd-actions corresponding to the identity d × d matrix.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 725 - 741
Copyright
Copyright © Cambridge University Press 1992

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References

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