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Sequence Entropy and Mild Mixing

Entropy characterizations of different spectral and mixing properties of dynamical systems were dealt with by a number of authors (see [5], [6] and [8]). Given an infinite subset Γ = {tn}of N and a dynamical system (X, β,μ, T) one can define sequence entropy along for any finite Petition ξ, and hΓ(T) —supξ hΓ(T,ξ). In [6] Kushnirenko used sequence entropy to give a characterization of systems with discrete spectrum.