Induced subsystems associated to a Cantor minimal system

Heidi Dahl, and Mats Molberg. "Induced subsystems associated to a Cantor minimal system." Colloquium Mathematicae 117.2 (2009): 207-221. <http://eudml.org/doc/284238>.

@article{HeidiDahl2009,
abstract = {Let (X,T) be a Cantor minimal system and let (R,) be the associated étale equivalence relation (the orbit equivalence relation). We show that for an arbitrary Cantor minimal system (Y,S) there exists a closed subset Z of X such that (Y,S) is conjugate to the subsystem (Z,T̃), where T̃ is the induced map on Z from T. We explore when we may choose Z to be a T-regular and/or a T-thin set, and we relate T-regularity of a set to R-étaleness. The latter concept plays an important role in the study of the orbit structure of minimal $ℤ^\{d\}$-actions on the Cantor set by T. Giordans et al. [J. Amer. Math. Soc. 21 (2008)].},
author = {Heidi Dahl, Mats Molberg},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {207-221},
title = {Induced subsystems associated to a Cantor minimal system},
url = {http://eudml.org/doc/284238},
volume = {117},
year = {2009},
}

TY - JOUR
AU - Heidi Dahl
AU - Mats Molberg
TI - Induced subsystems associated to a Cantor minimal system
JO - Colloquium Mathematicae
PY - 2009
VL - 117
IS - 2
SP - 207
EP - 221
AB - Let (X,T) be a Cantor minimal system and let (R,) be the associated étale equivalence relation (the orbit equivalence relation). We show that for an arbitrary Cantor minimal system (Y,S) there exists a closed subset Z of X such that (Y,S) is conjugate to the subsystem (Z,T̃), where T̃ is the induced map on Z from T. We explore when we may choose Z to be a T-regular and/or a T-thin set, and we relate T-regularity of a set to R-étaleness. The latter concept plays an important role in the study of the orbit structure of minimal $ℤ^{d}$-actions on the Cantor set by T. Giordans et al. [J. Amer. Math. Soc. 21 (2008)].
LA - eng
UR - http://eudml.org/doc/284238
ER -