Universal Weighted Averaging for Ergodic Flows

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.