Mean equicontinuity and mean sensitivity
Dynamical Systems
2016-11-18 v3
Abstract
Answering an open question affirmatively it is shown that every ergodic invariant measure of a mean equicontinuous (i.e. mean-L-stable) system has discrete spectrum. Dichotomy results related to mean equicontinuity and mean sensitivity are obtained when a dynamical system is transitive or minimal. Localizing the notion of mean equicontinuity, notions of almost mean equicontinuity and almost Banach mean equicontinuity are introduced. It turns out that a system with the former property may have positive entropy and meanwhile a system with the later property must have zero entropy.
Cite
@article{arxiv.1312.7663,
title = {Mean equicontinuity and mean sensitivity},
author = {Jian Li and Siming Tu and Xiangdong Ye},
journal= {arXiv preprint arXiv:1312.7663},
year = {2016}
}
Comments
25 pages, changes suggested by the referee incorporated, to appear in Ergodic Theory and Dynamical Systems