Herman’s theory revisited

2007/06/30 by Konstantin Khanin, K. Khanin, Alexey Teplinsky +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #msc:37E10

paper · pdf · doi:10.1007/s00222-009-0200-z

published as Invent. Math. 2009, Vol.178, no.2, pp.333-344 · 10 pages

arxiv created 2007/06/30 · openalex publication_date 2009/05/11 · arxiv updated 2010/07/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that a C^2+α-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class D_δ, 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.

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