There is no minimal action of Z^2 on the plane
Dynamical Systems
2010-09-13 v2
Abstract
In this paper it is proved that there is no minimal action (i.e. every orbit is dense) of Z^2 on the plane. The proof uses the non-existence of minimal homeomorphisms on the infinite annulus (Le Calvez-Yoccoz's theorem), and the theory of Brouwer homeomorphisms.
Cite
@article{arxiv.1004.5270,
title = {There is no minimal action of Z^2 on the plane},
author = {Frédéric Le Roux},
journal= {arXiv preprint arXiv:1004.5270},
year = {2010}
}