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## Colloquium Mathematicum

2009 | 117 | 2 | 207-221

## Induced subsystems associated to a Cantor minimal system

EN

### Abstrakty

EN
Let (X,T) be a Cantor minimal system and let (R,𝓣) 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)].

207-221

wydano
2009

### Twórcy

autor
• Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
autor
• Education and Natural Sciences, Hedemark University College, N-2418 Elverum, Norway