Dynamics of induced mappings on symmetric products, some answers

Let X be a metric continuum and n is an element of N. Let Fn(X) be the hyperspace of nonempty subsets of X with at most n points. If 1 <= m < n, we con -sider the quotient space Fmn(X) = Fn(X)/Fm(X). Given a mapping f : X X, we consider the induced mappings fn : Fn(X) Fn(X) and fnm: Fmn(X) Fmn(X). In this paper we study relations among the dynamics of the mappings f, fn and fnmand we answer some questions, by F. Barragan, A. Santiago-Santos and J. Tenorio, related to the prop-erties: minimality, irreducibility, strong transitivity and turbulence.