Abstract

We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,y,v,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 ACS such that hA µ(T,e | y) = Hµ(e | K.(X | Y)) for all finite partitions e, 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. © Instytut Matematyczny PAN, 2009.