Wiener Wintner Ergodic Theorems

The Wiener Wintner ergodic theorem is a strengthening of Birkhoff pointwise ergodic theorem. Announced by N Wiener and A Wintner, this theorem has introduced the study of a general phenomenon in ergodic theory in which samplings are "e;good"e; for an uncountable number of systems. We study the rate of convergence in the uniform version of this theorem and what we call Wiener Wintner dynamical syst...