Recurrence properties and disjointness on the induced spaces

Abstract

A topological dynamical system induces two natural systems,one is on the hyperspace and the other one is on the probability measures space. Theconnection among some dynamical properties on the original space andon the induced spaces are investigated. Particularly, a minimalweakly mixing system which induces a $P$-system on the probability measuresspace is constructed and some disjointness result is obtained.