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

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
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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} 

• http://mi.mathnet.ru/eng/mmj319
• http://mi.mathnet.ru/eng/mmj/v8/i3/p477

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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
2. Navas A., “On Centralizers of Interval Diffeomorphisms in Critical (Intermediate) Regularity”, J. Anal. Math., 121 (2013), 1–30
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
4. Bonatti Ch., Guelman N., “Smooth Conjugacy Classes of Circle Diffeomorphisms With Irrational Rotation Number”, Fundam. Math., 227:2 (2014), 129–162