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Smooth linearization of commuting circle diffeomorphisms. (English) Zbl 1177.37045

It is shown that a finite number of commuting \(C^\infty\) circle diffeomorphisms with simultaneously Diophantine rotation numbers are smoothly (\(C^\infty\)) (and simultaneously) conjugated to rotations. This solves a problem raised by J. Moser [Math. Z. 205, No. 1, 105–121 (1990; Zbl 0689.58031)]. The same result holds in the real analytic category.

MSC:

37E10 Dynamical systems involving maps of the circle
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37E99 Low-dimensional dynamical systems

Citations:

Zbl 0689.58031
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References:

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