H. Akhadkulov, M. S. Noorani, H. Ibrahim, S. Akhatkulov. Source: Annals of Functional Analysis, Volume 10, Number 4, 562--569.Abstract:
Let $T_{1}$ and $T_{2}$ be two piecewise smooth circle homeomorphisms with countably many break points and identical irrational rotation number. We provide a sufficient condition for $C^{1}$ -smoothness of the conjugation between $T_{1}$ and $T_{2}$ .