Lesigne, E. 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 Ergodic Theory Dyn. Syst. 10, No. 3, 513-521 (1990). 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 Cited in 10 Documents MSC: 28D10 One-parameter continuous families of measure-preserving transformations 28D05 Measure-preserving transformations Keywords:individual ergodic theorem; Wiener-Wintner theorem; measure-preserving system; disjointness of dynamical systems; isometric extensions PDFBibTeX XMLCite \textit{E. Lesigne}, Ergodic Theory Dyn. Syst. 10, No. 3, 513--521 (1990; Zbl 0688.28008) Full Text: DOI References: [1] DOI: 10.2307/2371534 · Zbl 0025.06504 · doi:10.2307/2371534 [2] Thouvenot, Séminaire Bourbaki none pp none– (1977) [3] Lesigne, Ergod. Th. & Dynam. Sys. 9 pp 115– (1989) [4] Bourgain, Note au C. R. Acad. Sci. 305 pp 397– (1987) [5] DOI: 10.1007/BF01692494 · Zbl 0146.28502 · doi:10.1007/BF01692494 [6] DOI: 10.2307/2372899 · Zbl 0178.38404 · doi:10.2307/2372899 [7] Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory (1981) · Zbl 0459.28023 · doi:10.1515/9781400855162 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.