Smooth linearization of commuting circle diffeomorphisms

Pages 961-980 from Volume 170 (2009), Issue 2 by Bassam Fayad, Kostantin Khanin

Abstract

We show that a finite number of commuting diffeomorphisms with simultaneously Diophantine rotation numbers are smoothly conjugated to rotations. This solves a problem raised by Moser.

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Mathematical Subject Classification
Primary: , ,
DOI
10.4007/annals.2009.170.961
MR
2552115
Zbl
1177.37045
Milestones
Received: 30 September 2006
Revised: 26 October 2007

Authors

Bassam Fayad

Institut Galilée
Université Paris 13
Avenue Jean-Baptiste Clément
93439 Villetaneuse
France

Kostantin Khanin

Department of Mathematics
University of Toronto
Room 6290, 40 St. George Street
Toronto, ON M5S 2E4
Canada