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Recurrence properties and disjointness on the induced spaces

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  • A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability measures space. The connection among some dynamical properties on the original space and on the induced spaces are investigated. Particularly, a minimal weakly mixing system which induces a $P$-system on the probability measures space is constructed and some disjointness result is obtained.
    Mathematics Subject Classification: Primary: 54B20; Secondary: 54H20.


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