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Wiener-Wintner return-times ergodic theorem. (English) Zbl 0843.28007
The authors consider ergodic averages of the form $\frac{1}{N}\sum {e}^{in\lambda }{f}^{\text{'}}\left({S}^{n}y\right)·f\left({T}^{n}x\right)$. They investigate how these averages are related to (and characterize) a new factor of the system (and its orthogonal) – the maximal factor of the type “Abelian group extension of a group rotation” which satisfies a certain functional equation.
MSC:
 28D05 Measure-preserving transformations 37A99 Ergodic theory
References:
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