Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function

Details Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function

2008-11-02

arxiv.org/abs/0811.0192v1

Mathematics

Dynamical Systems

21 pages, to appear in Annales de l'Institut Fourier

Scientific paper

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic group of finite index or a nonabelian free subgroup.

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