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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173019We 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.21 pages, to appear in Annales de l'Institut FourierDynamical SystemsGroup Theory37E45, 37E10, 57S05, 37B05, 20F67Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number functiontext