Article ID Journal Published Year Pages File Type
4665024 Advances in Mathematics 2017 31 Pages PDF
Abstract

The notion of Δ-weakly mixing set is introduced and studied. It is proved that Δ-weakly mixing sets share many properties with weakly mixing sets, in particular, if a dynamical system has positive topological entropy, then the collection of Δ-weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace. The existence of Δ-weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained. These results generalize several well known results and also answer several open questions.

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Physical Sciences and Engineering Mathematics Mathematics (General)
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