Universal Averages for Ergodic Flows
Abstract
Abstract We study homothetic and more general weight averagings for flows. We strengthen one result of Kozlov–Treschev on nonuniform averagings, viz., we find so-called universal singular measures with respect to which the homothetic averagings for all ergodic flows converge to a constant in the integral norm. We show that each measure with absolutely continuous convolution power is universal. We propose the definition of almost mixing, which is formulated in terms of convergence of time averagings for the flow. We give an example of a nonmixing flow which is almost mixing and also show that rigid flows do not have this property.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Stochastic processes and financial applications
Geometry and complex manifolds
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 5-6
- Pages
- 970–975
- Publication date
- 1 May 2026
- Language
- EN