Dynamics of induced mappings on symmetric products, some answers

[EN] Let X be a metric continuum and n ∈ N. Let Fn(X) be the hyperspace of nonempty subsets of X with at most n points. If 1 ≤ m < n, we consider the quotient space Fnm(X) = Fn(X)/Fm(X). Given a mapping f : X → X, we consider the induced mappings fn : Fn(X) → Fn(X)and fnm : Fnm(X) → Fnm(X). In this paper we study relations among the dynamics of the mappings f, fn and fnm and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitivity and turbulence.