English

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

Dynamical Systems 2008-11-04 v1 Group Theory

Abstract

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 C1C^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.

Keywords

Cite

@article{arxiv.0811.0192,
  title  = {Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function},
  author = {Yoshifumi Matsuda},
  journal= {arXiv preprint arXiv:0811.0192},
  year   = {2008}
}

Comments

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