Dynamics of induced mappings on symmetric products, some answers

Authors

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 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.

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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

References

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Published

2022-10-03

How to Cite

[1]
A. Illanes and V. Martínez-de-la-Vega, “Dynamics of induced mappings on symmetric products, some answers”, Appl. Gen. Topol., vol. 23, no. 2, pp. 235–242, Oct. 2022.

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