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There is no minimal action of ℤ2 on the plane

Published online by Cambridge University Press:  05 April 2011

FRÉDÉRIC LE ROUX
FRÉDÉRIC LE ROUX*
Affiliation:
Laboratoire de Mathématique (CNRS UMR 8628), Université Paris Sud, 91405 Orsay Cedex, France (email: [email protected])
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Abstract

We prove that there is no minimal action of ℤ2 by homeomorphisms on the plane. This may be seen as a generalization of Le Calvez–Yoccoz’s theorem: there exists no minimal homeomorphism of the infinite annulus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 1 , February 2012 , pp. 167 - 172
Copyright
Copyright © Cambridge University Press 2011

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