Author:
Yu Tao,Zhang Guohua,Zhang Ruifeng
Abstract
<p style='text-indent:20px;'>In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions.</p><p style='text-indent:20px;'>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.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference24 articles.
1. S. Ferenczi.Measure-theoretic complexity of ergodic systems, Israel J. Math., 100 (1997), 189-207.
2. E. Følner.On groups with full {B}anach mean value, Math. Scand., 3 (1955), 243-254.
3. G. Fuhrmann, M. Gröger and D. Lenz, The structure of mean equicontinuous group actions, preprint, arXiv: 1812.10219v1.
4. F. García-Ramos.Weak forms of topological and measure-theoretical equicontinuity: Relationships with discrete spectrum and sequence entropy, Ergodic Theory Dynam. Systems, 37 (2017), 1211-1237.
5. F. García-Ramos, B. Marcus.Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems, Discrete Contin. Dyn. Syst., 39 (2019), 729-746.
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献