arXiv:1004.5270 Abstract | arXiv Analytics

arXiv:1004.5270 [math.DS]Abstract References Reviews Resources

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

Published 2010-04-29, updated 2010-09-10Version 2

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.

Categories: math.DS

Keywords: minimal action, calvez-yoccozs theorem, infinite annulus, brouwer homeomorphisms

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