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Restricted orbit changes of ergodic ℤd-actions to achieve mixing and completely positive entropy

Published online by Cambridge University Press:  19 September 2008

Adam Fieldsteel  and
N. A. Friedman
Adam Fieldsteel
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA;
N. A. Friedman
Affiliation:
Department of Mathematics and Statistics, State University of New York, Albany, NY 12222, USA
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Abstract

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We show that for every ergodic ℤd-action T, there is a mixing ℤd-action S which is orbit equivalent to T via an orbit equivalence that is a weak a-equivalence for all a ≥ 1 and a strong b-equivalence for all b ∈ (0, 1). If T has positive entropy, then S can be taken to have completely positive entropy. If the dimension d is greater than one, the orbit equivalence may be taken to be bounded and a strong b-equivalence for all b > 0.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 4 , December 1986 , pp. 505 - 528
Copyright
Copyright © Cambridge University Press 1986

References

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