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Spaces of ω-limit sets of graph maps

100%

Mai J.-H., Shao S.

Fundamenta Mathematicae

2007

tom 196

nr 1

91-100

Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.

Sequence entropy and rigid σ-algebras

81%

Coronel A., Maass A., Shao S.

Studia Mathematica

2009

tom 194

nr 3

207-230

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

2 Shao S.

1 Coronel A.

1 Maass A.

1 Mai J.-H.

1 2009

1 2007

Wyniki wyszukiwania

Spaces of ω-limit sets of graph maps

Sequence entropy and rigid σ-algebras