Giordano et al. (2010) showed that every minimal free -action of a Cantor space X is orbit equivalent to some ℤ-action. Trying to avoid the K-theory used there and modifying Forrest’s (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map F on X∖one point such that for a residual subset of X the orbits of F are the same as the orbits of a given minimal free -action.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6361-12-2015,
author = {Bartosz Frej and Agata Kwa\'snicka},
title = {A map maintaining the orbits of a given $$\mathbb{Z}$^{d}$-action},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {1-15},
zbl = {06545373},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6361-12-2015}
}
Bartosz Frej; Agata Kwaśnicka. A map maintaining the orbits of a given $ℤ^{d}$-action. Colloquium Mathematicae, Tome 144 (2016) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6361-12-2015/