Topological Wiener-Wintner ergodic theorem with polynomial weights

Abstract

For a totally uniquely ergodic dynamical system, we prove a topological Wiener-Wintner ergodic theorem with polynomial weights under the coincidence of the quasi discrete spectrums of the system in both senses of Abramov and of Hahn-Parry. The result applies to ergodic nilsystems. Fully oscillating sequences can then be constructed on nilmanifolds.

31 pages

References in corpus (6)

• Oscillating Sequences, Minimal Mean Attractability and Minimal Mean-Lyapunov-Stability
• Möbius disjointness for non-uniquely ergodic skew products
• Möbius disjointness for topological models of ergodic systems with discrete spectrum
• Uniformity in the Wiener-Wintner theorem for nilsequences
• Measure complexity and Möbius disjointness
• Oscillating sequences of higher orders and topological systems of quasi-discrete spectrum

Cited by in corpus (4)

• On uniformity of $q$-multiplicative sequences
• A note on uniform convergence of Wiener-Wintner ergodic averages
• Maximal pronilfactors and a topological Wiener-Wintner theorem
• A rigorous computer aided estimation for Gelfond exponent of weighted Thue-Morse sequences