A map maintaining the orbits of a given ${\mathbb{Z}}^d$-action

Bartosz Frej, and Agata Kwaśnicka. "A map maintaining the orbits of a given $ℤ^{d}$-action." Colloquium Mathematicae 143.1 (2016): 1-15. <http://eudml.org/doc/283875>.

@article{BartoszFrej2016,
abstract = {Giordano et al. (2010) showed that every minimal free $ℤ^\{d\}$-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 $ℤ^\{d\}$-action.},
author = {Bartosz Frej, Agata Kwaśnicka},
journal = {Colloquium Mathematicae},
keywords = {multidimensional dynamical system; zd-action; Bratteli diagram; orbit equivalence; Kakutani-Rokhlin decomposition; block code},
language = {eng},
number = {1},
pages = {1-15},
title = {A map maintaining the orbits of a given $ℤ^\{d\}$-action},
url = {http://eudml.org/doc/283875},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Bartosz Frej
AU - Agata Kwaśnicka
TI - A map maintaining the orbits of a given $ℤ^{d}$-action
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 1
SP - 1
EP - 15
AB - Giordano et al. (2010) showed that every minimal free $ℤ^{d}$-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 $ℤ^{d}$-action.
LA - eng
KW - multidimensional dynamical system; zd-action; Bratteli diagram; orbit equivalence; Kakutani-Rokhlin decomposition; block code
UR - http://eudml.org/doc/283875
ER -