Mean sensitivity and mean equicontinuity in semiflows defined on uniform spaces

Abstract

The notions of mean sensitivity and mean equicontinuity have been introduced and studied in semiflows defined on uniform spaces. Both these notions are studied on the arbitrary product of semiflows, on the hyperspatial semiflows and on the factor semiflows. A characterization for mean sensitivity with the help of $G_\delta$-sets is proved. For a certain class of minimal semiflows it is shown that the semiflow is either mean equicontinuous or mean sensitive. Examples and counterexamples are provided throughout the paper wherever necessary.