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Zbl 1179.37059
Khanin, K.; Teplinsky, A.
Herman's theory revisited.
(English)
[J] Invent. Math. 178, No. 2, 333-344 (2009). ISSN 0020-9910; ISSN 1432-1297/e

Authors' abstract: We prove that a $C^{2+\alpha }$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D _{\delta }, 0\leq \delta < \alpha \leq 1, \alpha - \delta \neq 1$, is $C^{1+\alpha - \delta }$-smoothly conjugate to a rigid rotation. This is the first sharp result on the smoothness of the conjugacy. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.
[Ljubiša Kocić (Niš)]
MSC 2000:
*37E10 Maps of the circle

Keywords: Diophantine class; cross ratio distortion; circle diffeomorphisms; Denjoy's type inequality

Cited in: Zbl 1224.37022

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