Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 191–209

Structure of groups of circle diffeomorphisms with the property of fixing nonexpandable points

Article

DOI: 10.1007/s10688-012-0025-1

Cite this article as:
Filimonov, D.A. & Kleptsyn, V.A. Funct Anal Its Appl (2012) 46: 191. doi:10.1007/s10688-012-0025-1

Abstract

We study the structure of groups of circle diffeomorphisms with the property of fixing nonexpandable points. This property generalizes the local expansivity property, and at present there are no known examples of minimal C2 actions of finitely generated groups of circle diffeomorphisms for which this generalized property does not hold.

It turns out that if this property holds for a group action and there is at least one nonexpandable point, then the action admits a rather restrictive characterization. In particular, for such an action, we prove the existence of a Markov partition, and the structure of the action turns out to be similar to that of the Thompson group.

Key words

dynamical systemgroup actioncircle diffeomorphismMarkov partition

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyMoscowRussia
  2. 2.Moscow State University of Railways CommunicationsMoscowRussia
  3. 3.Institut de Recherche Mathématique de RennesCNRSRennesFrance