Sequence entropy and rigid σ-algebras

• Autorzy: Alvaro Coronel , Alejandro Maass , Song Shao
• Języki publikacji: EN

Abstrakty

EN

We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,𝓨,ν,T) be a factor of a measure-theoretical dynamical system (X,𝓧,μ,T) and S be a sequence of positive integers with positive upper density. We prove there exists a subsequence A ⊆ S such that $h^{A}_{μ}(T,ξ|𝓨) = H_{μ}(ξ|𝓚(X|Y))$ for all finite partitions ξ, where 𝓚(X|Y) is the Kronecker algebra over 𝓨. A similar result holds for rigid algebras over 𝓨. As an application, we characterize compact, rigid and mixing extensions via relative sequence entropy.

Kategorie tematyczne

• 37A25: Ergodicity, mixing, rates of mixing
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 3
• Strony: 207-230

Daty

wydano

2009

Twórcy

autor

Alvaro Coronel

• Departamento de Ingeniería Matemática, Universidad de Chile, Av. Blanco Encalada 2120, Santiago, Chile

autor

Alejandro Maass

• Departamento de Ingeniería Matemática, Universidad de Chile, Av. Blanco Encalada 2120, Santiago, Chile

autor

Song Shao

• Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

Identyfikatory

DOI

10.4064/sm194-3-1