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On the smoothness of conjugation of circle diffeomorphisms with rigid rotations

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Abstract

We prove that any C3+β-smooth diffeomorphism preserving the orientation of a circle with rotation number from the Diophantine class Dδ, 0 < β < δ < 1, is C2+β−δ-smoothly conjugate to a rigid rotation of the circle by a certain angle.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    O. Yu. Teplins’kyi

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  1. O. Yu. Teplins’kyi
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 268–282, February, 2008.

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Teplins’kyi, O.Y. On the smoothness of conjugation of circle diffeomorphisms with rigid rotations. Ukr Math J 60, 310–326 (2008). https://doi.org/10.1007/s11253-008-0060-5

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  • DOI: https://doi.org/10.1007/s11253-008-0060-5

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