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    Begmatov, Abdumajid Dzhalilov, Akhtam and Mayer, Dieter 2014. Renormalizations of circle hoemomorphisms with a single break point. Discrete and Continuous Dynamical Systems, Vol. 34, Issue. 11, p. 4487.


    Dzhalilov, Akhtam Md Noorani, Mohd Salmi and Akhatkulov, Sokhobiddin 2014. On Critical Circle Homeomorphisms with Infinite Number of Break Points. Abstract and Applied Analysis, Vol. 2014, p. 1.


    Буфетов, Александр Игоревич Bufetov, Aleksandr Igorevich Гуревич, Борис Маркович Gurevich, Boris Marcovich Ханин, Константин Михайлович Khanin, Konstantin Mikhailovich Челларози, Франческо and Cellarosi, Francesco 2014. Присуждение Я. Г. Синаю премии Абеля. Успехи математических наук, Vol. 69, Issue. 5(419), p. 167.


    Fayad, Bassam and Khanin, Kostantin 2009. Smooth linearization of commuting circle diffeomorphisms. Annals of Mathematics, Vol. 170, Issue. 2, p. 961.


    Teplinsky, A 2008. On cross-ratio distortion and Schwartz derivative. Nonlinearity, Vol. 21, Issue. 12, p. 2777.


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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: http://dx.doi.org/10.1017/S0143385700005277
  • Published online: 01 September 2008
Abstract
Abstract

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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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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