Induced subsystems associated to a Cantor minimal system

• Autorzy: Heidi Dahl , Mats Molberg
• Języki publikacji: 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)].

Kategorie tematyczne

• 54H20: Topological dynamics
• 37B10: Symbolic dynamics
• 19K14: K 0 as an ordered group, traces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 117
• Numer: 2
• Strony: 207-221

Daty

wydano

2009

Twórcy

autor

Heidi Dahl

• Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

autor

Mats Molberg

• Education and Natural Sciences, Hedemark University College, N-2418 Elverum, Norway

Identyfikatory

DOI

10.4064/cm117-2-4