There is no minimal action of Z^2 on the plane

Details There is no minimal action of Z^2 on the plane There is no minimal action of Z^2 on the plane

2010-04-29

arxiv.org/abs/1004.5270v2

Mathematics

Dynamical Systems

Scientific paper

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.

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