Dynamics of induced mappings on symmetric products, some answers

Alejandro Illanes; Verónica Martínez-de-la-Vega

doi:10.4995/agt.2022.17492

Authors

Alejandro Illanes Universidad Nacional Autónoma de México https://orcid.org/0000-0002-7109-4038
Verónica Martínez-de-la-Vega Universidad Nacional Autónoma de México https://orcid.org/0000-0002-1694-6947

DOI:

https://doi.org/10.4995/agt.2022.17492

Keywords:

continuum, dynamical system, induced mapping, irreducibility, symmetric product, turbulence

Abstract

Let X be a metric continuum and n a positive integer. Let F_n (X) be the hyperspace of nonempty subsets of X with at most n points. If 0 < m < n, we consider the quotient space Fⁿ_m (X) = F_n (X)/F_m (X). Given a mapping f from X into X, we consider the induced mappings f_n from F_n (X) into F_n (X) and fⁿ_m from Fⁿ_m (X) into Fⁿ_m (X). In this paper we study the relations among the dynamics of the mappings f, f_n, and fⁿ_m and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitive and turbulence.

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Author Biographies

Alejandro Illanes, Universidad Nacional Autónoma de México

Instituto de Matemáticas

Verónica Martínez-de-la-Vega, Universidad Nacional Autónoma de México

Instituto de Matemáticas

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