By Idris Assani
The Wiener Wintner ergodic theorem is a strengthening of Birkhoff pointwise ergodic theorem. introduced through N. Wiener and A. Wintner, this theorem has brought the examine of a common phenomenon in ergodic conception within which samplings are "good" for an uncountable variety of platforms. This publication stories the speed of convergence within the uniform model of this theorem and what are termed Wiener Wintner dynamical structures and end up for those platforms pointwise effects: the a.e. double recurrence theorem and the a.e. continuity of the fractional circled ergodic Hilbert rework. a few extensions of the Wiener Wintner ergodic theorem also are given.
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