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It is shown that in a topological dynamical system with positive entropy,there is a measure-theoretically "rather big" set such that a multivariantversion of mean Li-Yorke chaos happens on the closure of the stable or unstableset of any point from the set. It is also proved that the intersections of thesets of asymptotic tuples and mean Li-Yorke tuples with the set of topologicalentropy tuples are dense in the set of topological entropy tuples respectively.

Stable sets and mean Li-Yorke chaos in positive entropy systems