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Zbl 0819.58033
Katznelson, Y.; Ornstein, D.
The differentiability of the conjugation of certain diffeomorphisms of the circle. (English)
[J] Ergodic Theory Dyn. Syst. 9, No.4, 643-680 (1989). ISSN 0143-3857; ISSN 1469-4417/e

Summary: We 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.
MSC 2000:
*37F99 Complex dynamical systems
37B99 Topological dynamics

Keywords: smoothness; conjugation; aperiodic diffeomorphisms; circle; rotation number

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