In this talk, we study equicontinuity and sensitivity in the mean sense.
We show 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.
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Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5079
[4] http://www.mpim-bonn.mpg.de/webfm_send/271/1
[5] http://www.mpim-bonn.mpg.de/webfm_send/271