Discrete spectrum for amenable group actions

2019/08/22 by Tao Yu, Yu, Tao, Guohua Zhang +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1908.08434

openalex publication_date 2019/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Bounded complexity, mean equicontinuity and discrete spectrum

Related

• Discrete spectrum of probability measures for locally compact group actions
• Periodic measures are dense in invariant measures for residually finite amenable group actions with specification
• Weak mean equicontinuity for a countable discrete amenable group action
• Mean dimension and a non-embeddable example for amenable group actions
• Amenable actions, invariant means and bounded cohomology