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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Smooth orbit equivalence of ergodic $ {\bf R}\sp{d}$ actions, $ d\geq 2$


Author: Daniel Rudolph
Journal: Trans. Amer. Math. Soc. 253 (1979), 291-302
MSC: Primary 28D05; Secondary 58F11
MathSciNet review: 536948
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Abstract: We show here that any two free ergodic finite measure preserving actions of $ {\textbf{R}^d}$, $ d\, \geqslant \,2$, are orbit equivalent by a measure preserving map which on orbits is $ {C^\infty }$.


References [Enhancements On Off] (What's this?)

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  • [2] J. Feldman, New 𝐾-automorphisms and a problem of Kakutani, Israel J. Math. 24 (1976), no. 1, 16–38. MR 0409763
  • [3] D. Nadler, There exist at least two temperate time-change classes of strictly ergodic zero entropy $ {\textbf{R}^d}$ actions, (in prep.).
  • [4] D. Rudolph, Nonequivalence of measure preserving transformations, Lecture Notes, Institute for Advanced Studies, Hebrew Univ. of Jerusalem, 1975.
  • [5] B. Weiss, Equivalence of measure preserving transformations, Lecture Notes, Institute for Advanced Studies, Hebrew Univ. of Jerusalem, 1975.

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DOI: https://doi.org/10.1090/S0002-9947-1979-0536948-0
Article copyright: © Copyright 1979 American Mathematical Society