A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives

Details A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives

2007-04-08

arxiv.org/abs/0704.1006v1

Mathematics

Dynamical Systems

14 pages, 4 figures

Scientific paper

We prove that if d is an integer number bigger than 1 and f_1,...,f_d are
commuting circle diffeomorphisms respectively of class C^(1+\tau_k), where
\tau_1 + ... + \tau_k > 1, then these maps are simultaneously conjugate to
rotations provided that their rotation numbers are independent over the
rationals.

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