En topologie dynamique, une famille classique de systèmes est celle formée par les rotations minimales. La classe des nilsystèmes et de leurs limites projectives en est une extension naturelle. L’étude de ces systèmes est ancienne mais connaît actuellement un renouveau à cause de ses applications, à la fois à la théorie ergodique et en théorie additive des nombres.
Les rotations minimales sont caractérisées par le fait que la relation de proximalité régionale est l’égalité. Nous introduisons une...
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...
In this paper we explore topological factors in between the Kronecker factor and the
maximal equicontinuous factor of a system. For this purpose we introduce the concept of
sequence entropy -tuple for a measure and we show that the set of sequence entropy
tuples for a measure is contained in the set of topological sequence entropy tuples [H-
Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we
introduce a weak notion and a strong notion of complexity pair for a...
Download Results (CSV)