Discrete spectrum for amenable group actions
Dynamical Systems
2019-08-23 v1
Abstract
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete spectrum can be characterized via measure-theoretic complexity using names of a partition and the Hamming distance, and it turns out to be equivalent to both mean equicontinuity and equicontinuity in the mean.
Cite
@article{arxiv.1908.08434,
title = {Discrete spectrum for amenable group actions},
author = {Tao Yu and Guohua Zhang and Ruifeng Zhang},
journal= {arXiv preprint arXiv:1908.08434},
year = {2019}
}