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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 8, pp. 1092–1105, August, 2010.
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Teplins’kyi, O.Y. Examples of C 1-smoothly conjugate diffeomorphisms of the circle with break that are not C 1+γ-smoothly conjugate. Ukr Math J 62, 1267–1284 (2011). https://doi.org/10.1007/s11253-011-0428-9
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DOI: https://doi.org/10.1007/s11253-011-0428-9