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Mosc. Math. J., 2008, Volume 8, Number 3, Pages 477–492 (Mi mmj319)  

This article is cited in 4 scientific papers (total in 4 papers)

A Denjoy Type Theorem for Commuting Circle Diffeomorphisms with Derivatives Having Different Hölder Differentiability Classes

V. A. Kleptsyna, A. Navasb

a Institute of Mathematical Research of Rennes
b Universidad de Santiago de Chile

Abstract: Let $d\ge2$ be an integer number, and let $f_k$, $k\in\{1,…,d\}$, be $C^{1+\tau_k}$ commuting circle diffeomorphisms, with $\tau_k\in]0,1[$ and $\tau_1+\cdots+\tau_d>1$. We prove that if the rotation numbers of the $f_k$'s are independent over the rationals (that is, if the corresponding action of $\mathbf Z^d$ on the circle is free), then they are simultaneously (topologically) conjugate to rotations.

Key words and phrases: denjoy theorem, centralizers, Hölder class of the derivative.

Full text: http://www.ams.org/.../abst8-3-2008.html
References: PDF file   HTML file

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Received: August 14, 2007
Language: English

Citation: V. A. Kleptsyn, A. Navas, “A Denjoy Type Theorem for Commuting Circle Diffeomorphisms with Derivatives Having Different Hölder Differentiability Classes”, Mosc. Math. J., 8:3 (2008), 477–492

Citation in format AMSBIB
\Bibitem{KleNav08}
\by V.~A.~Kleptsyn, A.~Navas
\paper A~Denjoy Type Theorem for Commuting Circle Diffeomorphisms with Derivatives Having Different H\"older Differentiability Classes
\jour Mosc. Math.~J.
\yr 2008
\vol 8
\issue 3
\pages 477--492
\mathnet{http://mi.mathnet.ru/mmj319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2483221}
\zmath{https://zbmath.org/?q=an:1156.22017}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261829800005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Navas A., “Growth of groups and diffeomorphisms of the interval”, Geom Funct Anal, 18:3 (2008), 988–1028  crossref  mathscinet  zmath  isi  scopus
    2. Navas A., “On Centralizers of Interval Diffeomorphisms in Critical (Intermediate) Regularity”, J. Anal. Math., 121 (2013), 1–30  crossref  mathscinet  zmath  isi  scopus
    3. Castro G., Jorquera E., Navas A., “Sharp Regularity For Certain Nilpotent Group Actions on the Interval”, Math. Ann., 359:1-2 (2014), 101–152  crossref  mathscinet  zmath  isi  scopus
    4. Bonatti Ch., Guelman N., “Smooth Conjugacy Classes of Circle Diffeomorphisms With Irrational Rotation Number”, Fundam. Math., 227:2 (2014), 129–162  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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