Singular geometric averages for ergodic multiflows

TL;DR

This paper explores ergodic multiflows on probability spaces, applying a universal averaging theorem to manifolds in Euclidean space, advancing the understanding of geometric averages in ergodic theory.

Contribution

It introduces a general theorem on universal averaging for ergodic multiflows and applies it to manifolds in Euclidean space, extending ergodic averaging techniques.

Findings

Established a universal averaging theorem for ergodic multiflows.

Applied the theorem to averaging along manifolds in R^n.

Enhanced the theoretical framework for geometric averages in ergodic systems.

Abstract

We consider ergodic multiflows on a probability space. The general theorem on universal averaging for multiflows is applied to averaging along manifolds in $R^n$.