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Non-standard smooth realizations of Liouville rotations

Published online by Cambridge University Press:  01 December 2007

B. R. FAYAD ,
M. SAPRYKINA  and
A. WINDSOR
B. R. FAYAD
Affiliation:
LAGA, UMR 7539, Université Paris 13, 93430 Villetaneuse, France (email: [email protected])
M. SAPRYKINA
Affiliation:
Department of Mathematics and Statistics, Jeffery Hall, University Avenue, Kingston, ON Canada, K7L 3N6 (email: [email protected])
A. WINDSOR
Affiliation:
Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-0257, USA (email: [email protected])
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Abstract

We augment the conjugation approximation method with explicit estimates on the conjugacy map. This allows us to construct ergodic volume-preserving diffeomorphisms measure-theoretically isomorphic to any a priori given Liouville rotation on a variety of manifolds. In the special case of tori the maps can be made uniquely ergodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1803 - 1818
Copyright
Copyright © Cambridge University Press 2007

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References

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