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

Frédéric Le Roux (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Systèmes dynamiques [math.DS]

Frédéric Le Roux. There is no minimal action of Z^2 on the plane. 2010. ⟨hal-00477534v2⟩