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Herman’s theory revisited

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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, α−δ≠1, 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, M5S 2E4, Canada

    K. Khanin

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, Kiev, 01601, Ukraine

    A. Teplinsky

Authors
  1. K. Khanin
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  2. A. Teplinsky
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Correspondence to K. Khanin.

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Khanin, K., Teplinsky, A. Herman’s theory revisited. Invent. math. 178, 333–344 (2009). https://doi.org/10.1007/s00222-009-0200-z

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  • DOI: https://doi.org/10.1007/s00222-009-0200-z

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