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Diffeomorphisms of manifolds with nonsingular Poincaré flows

Hawkins, Jane (1990) Diffeomorphisms of manifolds with nonsingular Poincaré flows. Journal of Mathematical Analysis and Applications, 145 (2). pp. 419-430. ISSN 0022-247X. doi:10.1016/0022-247X(90)90410-H.

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In this paper we study the question of which countable amenable ergodic equivalence relations can be realized as C∞ group actions on manifolds. It has been proved that every countable equivalence relation which is amenable, nonsingular, and ergodic is orbit equivalent to an ergodic integer action on a measure space [CFW]. Katznelson showed that any ITPFI ergodic equivalence relation is orbit equivalent to some C∞ diffeomorphism of the circle. He also proved that every ergodic C^3 diffeomorphism of the circle generates an amenable ITPFI equivalence relation [Ka].

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Additional Information:© 1990 Published by Elsevier. Received 9 May 1988. Submitted by Dorothy Maharam Stone. Research partially supported by the NSF under Grant DMS-8418431. The author is grateful to R. Wong for helpful discussions on this topic. A. Ramsay and K. Schmidt also helped improve the results of this paper with their suggestions and comments.
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Official Citation:Jane Hawkins, Diffeomorphisms of manifolds with nonsingular Poincaré flows, Journal of Mathematical Analysis and Applications, Volume 145, Issue 2, 1990, Pages 419-430, ISSN 0022-247X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
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Deposited On:30 Mar 2018 21:17
Last Modified:15 Nov 2021 16:59

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