Topological Wiener-Wintner ergodic theorem with polynomial weights

Ai-Hua Fan (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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.

Domaines: Mathématiques [math]

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⟩