Ergodic Theory and Dynamical Systems

Research Article

The differentiability of the conjugation of certain diffeomorphisms of the circle

Y. Katznelsona1 and D. Ornsteina1

a1 Mathematics Department, Stanford University, Stanford CA 94305, USA


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.

(Received June 22 1987)

(Revised August 27 1988)


† Research partially supported by NSF Grant No. DMS86–05098.