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When is a dynamical system mean sensitive?

Published online by Cambridge University Press:  06 November 2017

Instituto de Fisica, Universidad Autonoma de San Luis Potosi, Manuel Nava 6, SLP, Mexico78290 email Catedras CONACyT, Av. Insurgentes Sur 1582, Del. Benito Juárez, Mexico City, Mexico03940
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221116, PR China email Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, PR China
School of Mathematics, Hefei University of Technology, Hefei, Anhui, 230009, PR China email


This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

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© Cambridge University Press, 2017 

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