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.
Reviewer: Eugene Ershov (St. Petersburg)
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 |
Keywords:
commuting circle diffeomorphisms; smooth linearization; Poincaré rotation number; Diophantine conditionCitations:
Zbl 0689.58031References:
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