Universal Weighted Averaging for Ergodic Flows
Dynamical Systems
2025-11-27 v3
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.
Keywords
Cite
@article{arxiv.2511.09229,
title = {Universal Weighted Averaging for Ergodic Flows},
author = {Valery V. Ryzhikov},
journal= {arXiv preprint arXiv:2511.09229},
year = {2025}
}