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In this paper, we study the dynamics of the adjoint of a weighted compositionoperator and we give necessary and sufficient conditions for this adjointoperator to be topologically hyper-transitive on the space of Radon measures ona locally compact Hausdorff space. Moreover, we provide sufficient conditionsfor this operator to be chaotic and we give concrete examples. Next, weconsider the real Banach space of signed Radon measures and we give in thiscontext the sufficient conditions for the convergence of Markov chains inducedby the adjoint of an integral operator. Also, we illustrate this result with aconcrete example. In addition, we obtain some structural results regarding thespace of Radon measures. We characterize a class of cones whose complement isspaceable in the space of Radon measures.

Dynamics of operators on the space of Radon measures