Smooth linearization of commuting circle diffeomorphisms

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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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Fayad, B., & Khanin, K. (2009). Smooth linearization of commuting circle diffeomorphisms. Annals of Mathematics, 170(2), 961–980. https://doi.org/10.4007/annals.2009.170.961

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