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  • Ergodic Theory and Dynamical Systems, Volume 9, Issue 4
  • December 1989, pp. 643-680

The differentiability of the conjugation of certain diffeomorphisms of the circle

  • Y. Katznelson (a1) and D. Ornstein (a1)
  • DOI:
  • Published online: 01 September 2008

Our purpose in this paper is to present a more or less complete solution to the problem of the smoothness of the conjugation of aperiodic diffeomorphisms of the circle. We show that the rotation number and the smoothness of the diffeomorphism guarantee a certain smoothness for the homeomorphism which conjugates it with a rigid rotation, and obtain the best smoothness that can be guaranteed.

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[C]L. Carleson . A remark on Denjoy's inequality and Herman's theorem. Publ. Math. I.H.E.S. 49 (1979), 235241.

[H]M.R. Herman . Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Publ. Math. I.H.E.S. 49 (1979), 5234.

[HS]J. Hawkins & K. Schmidt . On C2-diffeomorphisms which are of type III1. Invent. Math. 66 (1982), 511518.

[K]Y. Katznelson . The action of diffeomorphisms of the circle on the Lebesgue measure. J. D Anal. Math. 36 (1979), 156166.

[KS]K.M. Khanin & Ya. G. Sinai . A new proof of M. Herman's theorem. Comm. Math. Phys. 112 (1987), 89101.

Math. Notes 10 (1971), 758763.

J. Moser . Perturbation theory for almost periodic solutions for undamped non linear differential equations. Inter. Symp. Nonlinear Differential Equations and Nonlinear Mechanics, pp. 7179. New York, 1963.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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