Resumen de Dynamics of induced mappings on symmetric products, some answers

Alejandro Illanes, Verónica Martínez de la Vega

• Let X be a metric continuum and n a positive integer. Let Fn (X) be the hyperspace of nonempty subsets of X with at most n points. If 0 < m < n, we consider the quotient space Fnm (X) = Fn (X)/Fm (X). Given a mapping f  from X into X, we consider the induced mappings fn from Fn (X) into Fn (X) and fnm  from Fnm (X) into Fnm (X). In this paper we study the 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 transitive and turbulence.