There is no minimal action of ℤ2 on the plane

DOI10.1017/S0143385710000866zbMath1256.37015arXiv1004.5270MaRDI QIDQ2884080

Frédéric Le Roux

Publication date: 24 May 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.5270

zbMATH Keywords

planeaction of \(\mathbb Z^{2}\)Le Calvez-Yoccoz theoremno minimal actionno minimal homeomorphism

Mathematics Subject Classification ID

Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30)

Cites Work

• Brouwer's plane translation theorem and generalizations of the Poincaré-Birkhoff theorem
• An index theorem for the homeomorphisms of the plane near a fixed point
• A new proof of the Brouwer plane translation theorem
• On the set of points with a dense orbit
• A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere

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