Dynamics of induced mappings on symmetric products, some answers

Illanes, Alejandro ^[1] ; Martínez-de-la-Vega, Verónica ^[1]
1. [1] Universidad Nacional Autónoma de México
  
  Universidad Nacional Autónoma de México
  
  México
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 235-242
Idioma: inglés
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Resumen
- 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.