Herman’s Theory Revisited

We prove that a C 2+α-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class Dδ, 0 < δ < α ≤ 1, is C 1+α−δ-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy’s inequality for such diffeomorphisms. 1

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