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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
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
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[1]del Junco, A. & Rudolph, D. J.. Kakutani equivalence of ergodic ℤn-actions. Ergod. Th. & Dynam. Sys.Google Scholar
[2]Dye, H. A.. On groups of measure-preserving transformations, I., Amer. J. Math. 81 (1959).Google Scholar
[3]Friedman, N. A. & Ornstein, D. S.. Ergodic transformations induce mixing transformations. Adv. in Math. 10 (1973) 147163.Google Scholar
[4]Ornstein, D. S.. Factors of Bernoulli shifts, Israel J. Math. 21 (1975), 145153.Google Scholar
[5]Ornstein, D. S. & Smorodinsky, M.. Ergodic flows of positive entropy can be time changed to become K–flows. Israel J. Math. 26 (1977) 7583.Google Scholar
[6]Rudolph, D. J.. Restricted orbit equivalence, Mem. Amer. Math. Soc. 54 (1985), No. 323.Google Scholar
[7]Thouvenot, J.-P.. Quelques propri´etés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l'un est un schème de Bernoulli. Israel J. Math. 21 (1975), 177203.Google Scholar
[8]Weiss, B., General theory of ℤd-actions. Unpublished notes.Google Scholar