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Approximately transitive diffeomorphisms of the circle


Authors: J. Hawkins and E. J. Woods
Journal: Proc. Amer. Math. Soc. 90 (1984), 258-262
MSC: Primary 47A35; Secondary 28A99, 46L55
DOI: https://doi.org/10.1090/S0002-9939-1984-0727245-6
MathSciNet review: 727245
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Abstract: We prove that every $ {C^3}$ diffeomorphism of the circle with an irrational rotation number (and some $ {C^2}$ diffeomorphisms as well) are approximately transitive. This provides a class of examples of approximately transitive transformations which are smooth but non-measure-preserving.


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

  • [1] A. Connes and E. J. Woods, Approximately transitive flows and ITPFI factors (to appear). MR 796751 (86m:46062)
  • [2] J. Hawkins, Non-ITPFI diffeomorphisms, Israel J. Math. 42 (1982), 117-131. MR 687939 (84k:58129)
  • [3] M. R. Herman, Sur la conjugaison différentiable des diffeomorphisms du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. 49 (1979), 5-234. MR 538680 (81h:58039)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0727245-6
Keywords: Classification of von Neumann factors, orbit equivalence of ergodic transformations, diffeomorphisms of the circle
Article copyright: © Copyright 1984 American Mathematical Society

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