Topological Wiener-Wintner ergodic theorem with polynomial weights
Dynamical Systems
2018-11-14 v1
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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Cite
@article{arxiv.1708.06093,
title = {Topological Wiener-Wintner ergodic theorem with polynomial weights},
author = {Aihua Fan},
journal= {arXiv preprint arXiv:1708.06093},
year = {2018}
}
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31 pages