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Rotation topological factors of minimal $\ZM^{d}$-actions on the cantor set

Maria Isabel Cortez·Jean-Marc Gambaudo·Alejandro Maass
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Abstract

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

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Maria Isabel Cortez, Jean-Marc Gambaudo, Alejandro Maass. 2004-09-22. Rotation topological factors of minimal $\ZM^{d}$-actions on the cantor set. https://arxiv.org/abs/math/0405532

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