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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-1,
author = {Alvaro Coronel and Alejandro Maass and Song Shao},
title = {Sequence entropy and rigid $\sigma$-algebras},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {207-230},
zbl = {1179.37011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-1}
}
Alvaro Coronel; Alejandro Maass; Song Shao. Sequence entropy and rigid σ-algebras. Studia Mathematica, Tome 192 (2009) pp. 207-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-1/