Examples of $C^1$-smoothly conjugate diffeomorphisms of the circle with break that are not $C^{1+γ}$ -smoothly conjugate

  • O. Yu. Teplins’kyi


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.
How to Cite
Teplins’kyi, O. Y. “Examples of $C^1$-Smoothly Conjugate Diffeomorphisms of the Circle With Break That Are Not $C^{1+γ}$ -Smoothly Conjugate”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 8, Aug. 2010, pp. 1092–1105, https://umj.imath.kiev.ua/index.php/umj/article/view/2939.
Research articles