Mean proximality and mean Li-Yorke chaos
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We prove that if a topological dynamical system is mean sensitive and contains a mean proximal pair consisting of a transitive point and a periodic point, then it is mean Li-Yorke chaotic (DC2 chaotic). On the other hand we show that a system is mean proximal if and only if it is uniquely ergodic and the unique measure is supported on one point. © 2016 American Mathematical Society.
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Mean asymptotic pair; Mean Devaney chaos; Mean Li-Yorke chaos; Mean Li-Yorke set; Mean proximal pair
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