Orbit equivalence for Cantor minimal  <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="/jams/2008-21-03/S0894-0347-08-00595-X/gif-title0/img1.gif" ALT="$ \mathbb{Z}^{2}$">-systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Orbit equivalence for Cantor minimal $\mathbb{Z}^{2}$ -systems

Authors:	Thierry Giordano Hiroki Matui Ian F Putnam Christian F Skau

Institution:	Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5 Hiroki Matui ; Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Ian F. Putnam ; Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4 Christian F. Skau ; Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway

Abstract:	We show that every minimal, free action of the group $\mathbb{Z}^{2}$ on the Cantor set is orbit equivalent to an AF-relation. As a consequence, this extends the classification of minimal systems on the Cantor set up to orbit equivalence to include AF-relations, $\mathbb{Z}$ -actions and $\mathbb{Z}^{2}$ -actions.

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