Abstract
We introduce some invariants of Kakutani equivalence and using them we prove that any two distinct cartesian powers of the horocycle flow are inequivalent.
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J. Feldman,Non-Bernoulli K-automorphisms and a problem of Kakutani, Israel J. Math.24 (1976), 16–37.
J. Feldman,r-entropy, equipartition, and Ornstein’s isomorphism theorem in R n, Israel J. Math.36 (1980), 321–345.
J. Feldman and D. Nadler,Reparametrization of N-flows of zero entropy, to appear.
A. B. Katok,Monotone equivalence in the ergodic theory, Izv. Akad. Nauk Math.41 (1977), 104–157 (Russian).
A. B. Katok and E. A. Sataev,Interval exchange transformations and flows on surfaces are standard, Mat. Zamet.20 (1976), 479–488 (Russian).
M. Ratner,The cartesian square of the horocycle flow is not loosely Bernoulli, Israel J. Math.34 (1979), 72–96.
B. Weiss,Equivalence of Measure Preserving Transformations, Lecture Notes, Institute for Advanced Studies, Hebrew University of Jerusalem, 1976.
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Partially supported by NSF Grant MCS74-19388.
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Ratner, M. Some invariants of Kakutani equivalence. Israel J. Math. 38, 231–240 (1981). https://doi.org/10.1007/BF02760808
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DOI: https://doi.org/10.1007/BF02760808