Herman’s theory revisited

By Konstantin Khanin, A. Teplinsky. 2007

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We prove that a C2+α-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class Dδ, 0≤δ<α≤1, α−δ≠1, is C1+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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/61a6892f7d1b6987f73bc63ce4b5b007b99174d7