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Kakutani equivalence of ergodic ℤn actions

Published online by Cambridge University Press:  19 September 2008

Andres Del Junco  and
Daniel J. Rudolph
Andres Del Junco
Affiliation:
Ohio State University, Newark, OH 48055, USA;
Daniel J. Rudolph
Affiliation:
University of Maryland, College Park, MD 20742, USA
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Abstract

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We define two families of relations between ergodic ℤn actions, both indexed equivariantly by non-singular n × n matrices. The first is to be Katok cross-sections of the same flow, indexed in a natural way by the matrices. The second is determined by the existence of an orbit preserving injection with an extra asymptotic linearity condition. We demonstrate that these two families are identical. In one dimension this is the classical theory of Kakutani equivalence.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 89 - 104
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

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