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Article Dans Une Revue Chaos, Solitons & Fractals Année : 2018

Topological Wiener-Wintner ergodic theorem with polynomial weights

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Résumé

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. (C) 2018 Elsevier Ltd. All rights reserved.

Dates et versions

hal-03622001 , version 1 (28-03-2022)

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Ai-Hua Fan. Topological Wiener-Wintner ergodic theorem with polynomial weights. Chaos, Solitons & Fractals, 2018, 117, pp.105-116. ⟨10.1016/j.chaos.2018.10.015⟩. ⟨hal-03622001⟩
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