1Departamento de Ingeniería Matemática Universidad de Chile Av. Blanco Encalada 2120 Santiago, Chile 2Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, P.R. China
Studia Mathematica, Tome 194 (2009) no. 3, pp. 207-230
We study relationships between sequence entropy and
the Kronecker and rigid algebras. Let $(Y,\mathcal Y,\nu, T)$ be a factor
of a measure-theoretical dynamical system $(X,\mathcal X,\mu,T)$ and $S$
be a sequence of positive integers with
positive upper density. We prove there exists a subsequence
$A\subseteq S$ such that $h^A_\mu(T,\xi\,|\,\mathcal Y)= H_\mu(\xi\, |\,\mathcal K(X\,|\,Y))$
for all finite partitions $\xi$, where $\mathcal K(X\,|\,Y)$ is the Kronecker
algebra over $\mathcal Y$. A similar result holds for rigid algebras over
${\cal Y}$. As an application, we characterize compact, rigid and mixing
extensions via relative sequence entropy.
1
Departamento de Ingeniería Matemática Universidad de Chile Av. Blanco Encalada 2120 Santiago, Chile
2
Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, P.R. China
@article{10_4064_sm194_3_1,
author = {Alvaro Coronel and Alejandro Maass and Song Shao},
title = {Sequence entropy and rigid $\sigma$-algebras},
journal = {Studia Mathematica},
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doi = {10.4064/sm194-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm194-3-1/}
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AU - Alejandro Maass
AU - Song Shao
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Alvaro Coronel; Alejandro Maass; Song Shao. Sequence entropy and rigid $\sigma$-algebras. Studia Mathematica, Tome 194 (2009) no. 3, pp. 207-230. doi: 10.4064/sm194-3-1
