We prove that a ‘small’ extension of a minimal AF equivalence relation on a Cantor set is orbit equivalent to the AF relation. By a ‘small’ extension we mean an equivalence relation generated by the minimal AF equivalence relation and another AF equivalence relation which is defined on a closed thin subset. The result we obtain is a generalization of the main theorem in [GMPS2]. It is needed for the study of orbit equivalence of minimal $\bm{Z}^d$
-systems for $d>2$
[GMPS3], in a similar way as the result in [GMPS2] was needed (and sufficient) for the study of minimal $\bm{Z}^2$
-systems [GMPS1].
Publié le : 2008-10-15
Classification:
Cantor sets,
orbit equivalence,
minimal dynamical systems,
37B05
@article{1225894037,
author = {MATUI, Hiroki},
title = {An absorption theorem for minimal AF equivalence relations on Cantor sets},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 1171-1185},
language = {en},
url = {http://dml.mathdoc.fr/item/1225894037}
}
MATUI, Hiroki. An absorption theorem for minimal AF equivalence relations on Cantor sets. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 1171-1185. http://gdmltest.u-ga.fr/item/1225894037/