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arXiv · 2511.09229

Universal Weighted Averaging for Ergodic Flows

Valery V. Ryzhikov
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Abstract

This paper studies homothetic and more general weighted averages for flows. Absolutely continuous convolutions of singular weights are considered, thereby strengthening Kozlov-Treshchev's result on nonuniform averages for ergodic flows. The concept of almost mixing, formulated in terms of homothetic weighted average convergences, is proposed. An example of a non-mixing almost mixing flow is given. It is proven that rigid flows are not almost mixing.

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Valery V. Ryzhikov. 2025-11-12. Universal Weighted Averaging for Ergodic Flows. https://arxiv.org/abs/2511.09229

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