Sequence entropy and rigid σ-algebras

Alvaro Coronel, Alejandro Maass, and Song Shao. "Sequence entropy and rigid σ-algebras." Studia Mathematica 194.3 (2009): 207-230. <http://eudml.org/doc/285300>.

@article{AlvaroCoronel2009,
abstract = {We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,,ν,T) be a factor of a measure-theoretical dynamical system (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 $h^\{A\}_\{μ\}(T,ξ|) = H_\{μ\}(ξ|(X|Y))$ for all finite partitions ξ, where (X|Y) is the Kronecker algebra over . A similar result holds for rigid algebras over . As an application, we characterize compact, rigid and mixing extensions via relative sequence entropy.},
author = {Alvaro Coronel, Alejandro Maass, Song Shao},
journal = {Studia Mathematica},
keywords = {dynamical system; entropy; spectral invariant},
language = {eng},
number = {3},
pages = {207-230},
title = {Sequence entropy and rigid σ-algebras},
url = {http://eudml.org/doc/285300},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Alvaro Coronel
AU - Alejandro Maass
AU - Song Shao
TI - Sequence entropy and rigid σ-algebras
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 3
SP - 207
EP - 230
AB - We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,,ν,T) be a factor of a measure-theoretical dynamical system (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 $h^{A}_{μ}(T,ξ|) = H_{μ}(ξ|(X|Y))$ for all finite partitions ξ, where (X|Y) is the Kronecker algebra over . A similar result holds for rigid algebras over . As an application, we characterize compact, rigid and mixing extensions via relative sequence entropy.
LA - eng
KW - dynamical system; entropy; spectral invariant
UR - http://eudml.org/doc/285300
ER -