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Un théorème de disjonction de systèmes dynamiques et une généralisation du théorème ergodique de Wiener-Wintner. (A theorem on disjointness of dynamical systems and a generalization of the Wiener-Wintner ergodic theorem). (French) Zbl 0688.28008

If (\(\Omega\),\({\mathcal T},\mu,T)\) is a measure-preserving system and if \(f\in L^ 1(\mu)\) then, for almost all \(\omega\), for every real polynomial P, the sequence \(\frac{1}{N}\sum^{N-1}_{n=0}\{\exp [iP(n)]\cdot f(T^ b\omega)\}\) converges.
To prove this result we use the concept of disjointness of dynamical systems and the fact that disjointness is preserved by isometric extensions.
Reviewer: E.Lesigne

MSC:

28D10 One-parameter continuous families of measure-preserving transformations
28D05 Measure-preserving transformations
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