Free orbits for minimal actions on the circle
- 12 October 2017
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 146 (2), 581-587
- https://doi.org/10.1090/proc/13698
Abstract
We prove that if is a countable group without a subgroup isomorphic to <!-- MATH $\mathbb{Z}^2$ --> that acts faithfully and minimally by orientation-preserving homeomorphisms on the circle, then it has a free orbit. We give examples showing that this does not hold for actions by homeomorphisms of the line.
Keywords
This publication has 1 reference indexed in Scilit:
- Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topologyDiscrete & Continuous Dynamical Systems, 2016