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Rotation Topological Factors of Minimal $ℤ^{d}$ -Actions on the Cantor Set

Maria Isabel Cortez, Jean-Marc Gambaudo and Alejandro Maass
Transactions of the American Mathematical Society
Vol. 359, No. 5 (May, 2007), pp. 2305-2315
Stable URL: http://www.jstor.org/stable/20161675
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Rotation Topological Factors of Minimal
            $ℤ^{d}$
            -Actions on the Cantor Set
Preview not available

Abstract

In this paper we study conditions under which a free minimal $ℤ^{d}$ -action on the Cantor set is a topological extension of the action of d rotations, either on the product ${\Bbb T}^{d}$ of d 1-tori or on a single 1-torus ${\Bbb T}^{1}$ . We extend the notion of linearly recurrent systems defined for ℤ-actions on the Cantor set to $ℤ^{d}$ -actions, and we derive in this more general setting a necessary and sufficient condition, which involves a natural combinatorial data associated with the action, allowing the existence of a rotation topological factor of one of these two types.

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