The differentiability of the conjugation of certain diffeomorphisms of the circle. (English) Zbl 0819.58033

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.


37F99 Dynamical systems over complex numbers
37B99 Topological dynamics