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arXiv · 1708.06093

Topological Wiener-Wintner ergodic theorem with polynomial weights

Aihua Fan
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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.

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Aihua Fan. 2017-08-21. Topological Wiener-Wintner ergodic theorem with polynomial weights. https://doi.org/10.1016/j.chaos.2018.10.015

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