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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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.


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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