Smooth linearization of commuting circle diffeomorphisms

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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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