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 -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