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The differentiability of the conjugation of certain diffeomorphisms of the circle

Published online by Cambridge University Press:  19 September 2008

Y. Katznelson  and
D. Ornstein
Y. Katznelson
Affiliation:
Mathematics Department, Stanford University, Stanford CA 94305, USA
D. Ornstein
Affiliation:
Mathematics Department, Stanford University, Stanford CA 94305, USA
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Abstract

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Our purpose in this paper is to present a more or less complete solution to the problem of the smoothness of the conjugation of aperiodic diffeomorphisms of the circle. We show that the rotation number and the smoothness of the diffeomorphism guarantee a certain smoothness for the homeomorphism which conjugates it with a rigid rotation, and obtain the best smoothness that can be guaranteed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 4 , December 1989 , pp. 643 - 680
Copyright
Copyright © Cambridge University Press 1989

References

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