Faithful zero-dimensional principal extensions

• Autorzy: Tomasz Downarowicz , Dawid Huczek
• Języki publikacji: EN

Abstrakty

EN

We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).

Kategorie tematyczne

• 37B10: Symbolic dynamics
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 212
• Numer: 1
• Strony: 1-19

Daty

wydano

2012

Twórcy

autor

Tomasz Downarowicz

• Institute of Mathematics and Computer Science, Wrocław Institute of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Dawid Huczek

• Institute of Mathematics and Computer Science, Wrocław Institute of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm212-1-1