Using dimension group tools and Bratteli-Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.
@article{bwmeta1.element.bwnjournal-article-smv142i1p25bwm,
author = {P. Dartnell and F. Durand and A. Maass},
title = {Orbit equivalence and Kakutani equivalence with Sturmian subshifts},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {25-45},
zbl = {0976.54041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i1p25bwm}
}
Dartnell, P.; Durand, F.; Maass, A. Orbit equivalence and Kakutani equivalence with Sturmian subshifts. Studia Mathematica, Tome 141 (2000) pp. 25-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i1p25bwm/
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