Slow convergence of ergodic averages for actions of amenable groups

TL;DR

This paper demonstrates that weighted ergodic averages for flows and actions of countable amenable groups converge slowly, highlighting limitations in the speed of convergence in such dynamical systems.

Contribution

It provides new insights into the convergence behavior of ergodic averages for amenable group actions, emphasizing their slow convergence rates.

Findings

Weighted ergodic averages converge slowly for amenable group actions.

The results apply to flows and actions of countable amenable groups.

Highlights limitations in ergodic average convergence speed.

Abstract

We show slow convergence of weighted ergodic averages for flows and actions of countable amenable groups.