2017
Том 69
№ 9

All Issues

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

Teplins’kyi O. Yu.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 8, pp 1267-1284.

Citation Example: Teplins’kyi O. Yu. Examples of $C^1$-smoothly conjugate diffeomorphisms of the circle with break that are not $C^{1+γ}$ -smoothly conjugate // Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1092–1105.

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