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

• Autorzy: Bartosz Frej , Agata Kwaśnicka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
• 37B10: Symbolic dynamics
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 1
• Strony: 1-15

Daty

wydano

2016

Twórcy

autor

Bartosz Frej

• Faculty of Pure and Applied Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Agata Kwaśnicka

• Faculty of Pure and Applied Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm6361-12-2015