Smooth orbit equivalence of ergodic $\textbf {R}^{d}$ actions, $d\geq 2$
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- by Daniel Rudolph PDF
- Trans. Amer. Math. Soc. 253 (1979), 291-302 Request permission
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
- H. A. Dye, On groups of measure preserving transformations. I, Amer. J. Math. 81 (1959), 119–159. MR 131516, DOI 10.2307/2372852
- J. Feldman, New $K$-automorphisms and a problem of Kakutani, Israel J. Math. 24 (1976), no. 1, 16–38. MR 409763, DOI 10.1007/BF02761426 D. Nadler, There exist at least two temperate time-change classes of strictly ergodic zero entropy ${\textbf {R}^d}$ actions, (in prep.). D. Rudolph, Nonequivalence of measure preserving transformations, Lecture Notes, Institute for Advanced Studies, Hebrew Univ. of Jerusalem, 1975. B. Weiss, Equivalence of measure preserving transformations, Lecture Notes, Institute for Advanced Studies, Hebrew Univ. of Jerusalem, 1975.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 253 (1979), 291-302
- MSC: Primary 28D05; Secondary 58F11
- DOI: https://doi.org/10.1090/S0002-9947-1979-0536948-0
- MathSciNet review: 536948