Examples of C^1-smoothly conjugate diffeomorphisms of the circle with break that are not C^1+γ -smoothly conjugate - Teplins’kyi, O. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We prove the existence of two real-analytic diffeomorphisms of the circle with break of the same size and an irrational rotation number of semibounded type that are not C^1+γ-smoothly conjugate for any γ > 0. In this way, we show that the previous result concerning the C^1-smoothness of conjugacy for these mappings is the exact estimate of smoothness for this conjugacy.