Mean proximality and mean Li-Yorke chaos

Abstract

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.

accepted on Proceedings of the American Mathematical Society

References in corpus (1)

• Mean equicontinuity and mean sensitivity

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