Mean equicontinuity and mean sensitivity

2014/08/04 by Jian Li, JIAN LI, SIMING TU +3 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Topology and Set Theory #Advanced Thermodynamics and Statistical Mechanics #Mathematical Dynamics and Fractals

paper · doi:10.1017/etds.2014.41

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 latter property must have zero entropy.

Citations

• Rigidity in topological dynamics

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