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Herman’s theory revisited. (English) Zbl 1179.37059
Authors’ abstract: We prove that a C 2+α -smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class D δ ,0δ<α1,α-δ1, is C 1+α-δ -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.

37E10Maps of the circle
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