@article{Teplins’kyi_2010, title={Examples of $C^1$-smoothly conjugate diffeomorphisms of the circle with break that are not $C^{1+γ}$ -smoothly conjugate}, volume={62}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2939}, abstractNote={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.}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Teplins’kyiO. Yu.}, year={2010}, month={Aug.}, pages={1092–1105} }